1 00:00:00,000 --> 00:00:00,972 [SQUEAKING] 2 00:00:00,972 --> 00:00:04,374 [RUSTLING] 3 00:00:04,374 --> 00:00:06,318 [CLICKING] 4 00:00:11,425 --> 00:00:12,550 JONATHAN GRUBER: All right. 5 00:00:12,550 --> 00:00:14,760 Why don't we get started? 6 00:00:14,760 --> 00:00:18,130 Today, we're going to continue our discussion of producer 7 00:00:18,130 --> 00:00:19,120 theory. 8 00:00:19,120 --> 00:00:21,400 Once again, to remember to put this in context, 9 00:00:21,400 --> 00:00:24,280 the first few lectures were working consumer theory 10 00:00:24,280 --> 00:00:26,380 to help us derive a demand curve. 11 00:00:26,380 --> 00:00:27,880 Now we're working on producer theory 12 00:00:27,880 --> 00:00:30,550 to help us come up with a supply curve. 13 00:00:30,550 --> 00:00:32,740 We started last time by talking about how 14 00:00:32,740 --> 00:00:36,730 producers profit maximizes, and the profit maximization 15 00:00:36,730 --> 00:00:39,137 implies cost minimization. 16 00:00:39,137 --> 00:00:40,720 Therefore, to maximize profits, you're 17 00:00:40,720 --> 00:00:43,450 going to want to produce as efficiently as possible. 18 00:00:43,450 --> 00:00:47,140 And basically, to do that, we need 19 00:00:47,140 --> 00:00:50,860 to understand how your costs vary with your output. 20 00:00:50,860 --> 00:00:53,080 If you're going to produce at an efficient level, 21 00:00:53,080 --> 00:00:56,350 you need to understand how what your costs are going to vary 22 00:00:56,350 --> 00:00:58,273 with your level of production. 23 00:00:58,273 --> 00:00:59,940 So essentially, our goal of this lecture 24 00:00:59,940 --> 00:01:02,470 is to develop a cost curve-- 25 00:01:02,470 --> 00:01:07,720 develop a curve which tells you how the cost of your production 26 00:01:07,720 --> 00:01:10,330 varies with how much you produce. 27 00:01:10,330 --> 00:01:12,640 And that's what we're after in this lecture. 28 00:01:12,640 --> 00:01:13,660 OK? 29 00:01:13,660 --> 00:01:15,730 So we're going to start with the short run 30 00:01:15,730 --> 00:01:17,402 and then turn to the long run. 31 00:01:17,402 --> 00:01:19,360 So start with developing a short-run cost curve 32 00:01:19,360 --> 00:01:21,300 and then turn to a long-run. 33 00:01:21,300 --> 00:01:22,090 OK? 34 00:01:22,090 --> 00:01:24,982 And to make this lecture sort of mathematically coherent, 35 00:01:24,982 --> 00:01:26,440 throughout the whole lecture, we'll 36 00:01:26,440 --> 00:01:28,680 work with our favorite functional form-- 37 00:01:28,680 --> 00:01:31,960 a production form of the function q 38 00:01:31,960 --> 00:01:34,660 equals the square root of L times K. Remember, 39 00:01:34,660 --> 00:01:36,190 firms produce goods-- 40 00:01:36,190 --> 00:01:40,910 little q-- using two inputs, labor and capital. 41 00:01:40,910 --> 00:01:43,210 Labor is a variable input. 42 00:01:43,210 --> 00:01:47,030 That means you can change it in the short run and the long run. 43 00:01:47,030 --> 00:01:49,750 Capital is a fixed input, which means that you can only 44 00:01:49,750 --> 00:01:51,670 change it in the long run. 45 00:01:51,670 --> 00:01:52,690 OK? 46 00:01:52,690 --> 00:01:56,170 So in the short run, we're going to have two kinds of costs. 47 00:01:56,170 --> 00:01:58,630 We're going to have fixed costs, which 48 00:01:58,630 --> 00:02:01,720 are going to come from a fixed level of capital, 49 00:02:01,720 --> 00:02:03,910 and we're going to variable costs, which are 50 00:02:03,910 --> 00:02:05,140 going to come from our labor. 51 00:02:05,140 --> 00:02:07,540 So we're going to have two kinds of costs: fixed costs-- 52 00:02:07,540 --> 00:02:08,620 they're fixed, because in the short run, 53 00:02:08,620 --> 00:02:10,570 you can't change the level of capital-- 54 00:02:10,570 --> 00:02:14,950 and variable costs, which are the costs of our labor. 55 00:02:14,950 --> 00:02:17,110 And then we're going to have total costs. 56 00:02:17,110 --> 00:02:20,880 They're simply going to be fixed costs plus variable costs. 57 00:02:20,880 --> 00:02:21,400 OK? 58 00:02:21,400 --> 00:02:23,540 So that's how we think about costs. 59 00:02:23,540 --> 00:02:26,410 The costs of a firm's production in the short run 60 00:02:26,410 --> 00:02:28,600 is the sum of their fixed costs-- 61 00:02:28,600 --> 00:02:30,190 i.e., their capital costs-- 62 00:02:30,190 --> 00:02:31,600 and the variable costs-- 63 00:02:31,600 --> 00:02:33,820 i.e., their labor costs. 64 00:02:33,820 --> 00:02:37,450 Now, we're going to show you how you can turn a production 65 00:02:37,450 --> 00:02:41,780 function into a cost function. 66 00:02:41,780 --> 00:02:48,820 And to do so, you simply need to recognize that cost-- 67 00:02:48,820 --> 00:02:51,450 the costs of firms' production-- 68 00:02:51,450 --> 00:02:53,530 are simply the amount of capital that 69 00:02:53,530 --> 00:02:56,680 uses k bar times the price of that capital, which we'll 70 00:02:56,680 --> 00:03:00,900 call r, plus the amount of labor it uses, 71 00:03:00,900 --> 00:03:04,980 times the price of that labor, which we'll call W, the wage. 72 00:03:04,980 --> 00:03:05,680 OK? 73 00:03:05,680 --> 00:03:07,180 This is the easy part. 74 00:03:07,180 --> 00:03:08,680 Think of the amount of hours of work 75 00:03:08,680 --> 00:03:11,590 you use times the wage per hour, or the amount of workers 76 00:03:11,590 --> 00:03:13,360 times the salary per year. 77 00:03:13,360 --> 00:03:15,270 In any case, this is easier to understand. 78 00:03:15,270 --> 00:03:17,170 Every additional unit of labor comes 79 00:03:17,170 --> 00:03:19,800 with a cost that is the wage of that unit of labor. 80 00:03:19,800 --> 00:03:21,130 Think about an hourly model. 81 00:03:21,130 --> 00:03:24,650 Every hour you work at your convenience store, 82 00:03:24,650 --> 00:03:26,960 they have to pay you the minimum wage for that hour. 83 00:03:26,960 --> 00:03:27,460 OK? 84 00:03:27,460 --> 00:03:29,700 That's the cost of that hour of labor. 85 00:03:29,700 --> 00:03:31,300 Capital is harder. 86 00:03:31,300 --> 00:03:34,370 We call r the rental rate. 87 00:03:34,370 --> 00:03:39,070 And the reason is because we don't think of buying capital. 88 00:03:39,070 --> 00:03:40,840 Don't think of buying a machine. 89 00:03:40,840 --> 00:03:42,850 Think of renting a machine. 90 00:03:42,850 --> 00:03:45,750 The reason we do that is to make the periodicity work. 91 00:03:45,750 --> 00:03:46,330 OK? 92 00:03:46,330 --> 00:03:48,670 You don't buy a worker, thank god. 93 00:03:48,670 --> 00:03:50,110 You rent that worker. 94 00:03:50,110 --> 00:03:53,200 And you rent that worker at a price, w. 95 00:03:53,200 --> 00:03:55,000 So when the firm uses your time, they're 96 00:03:55,000 --> 00:03:58,900 renting your time an hour at a time at a price, w. 97 00:03:58,900 --> 00:04:01,750 When we get machines, think of a firm 98 00:04:01,750 --> 00:04:07,420 as renting machines for a price, r per machine per time period. 99 00:04:07,420 --> 00:04:08,140 OK? 100 00:04:08,140 --> 00:04:10,177 So I understand firms usually don't do this. 101 00:04:10,177 --> 00:04:11,260 They usually buy machines. 102 00:04:11,260 --> 00:04:13,060 And we'll come back to even if you 103 00:04:13,060 --> 00:04:15,940 buy a machine how it effectively is like renting it, 104 00:04:15,940 --> 00:04:18,130 but for ease of thinking about this, 105 00:04:18,130 --> 00:04:20,350 you want to think about flows, not stocks. 106 00:04:20,350 --> 00:04:22,900 Think about the firm's decision as renting a worker 107 00:04:22,900 --> 00:04:26,260 at the price, w, or renting a machine at the price, r. 108 00:04:26,260 --> 00:04:26,907 Yeah. 109 00:04:26,907 --> 00:04:28,532 AUDIENCE: Kind of like also we consider 110 00:04:28,532 --> 00:04:30,332 the gas and electricity a machine can 111 00:04:30,332 --> 00:04:31,330 use in productivity? 112 00:04:31,330 --> 00:04:32,110 JONATHAN GRUBER: All that would be in there, 113 00:04:32,110 --> 00:04:33,277 and we'll come back to that. 114 00:04:33,277 --> 00:04:33,850 That's right. 115 00:04:33,850 --> 00:04:38,510 This is sort of the per period cost of using a machine. 116 00:04:38,510 --> 00:04:42,010 This is the per period cost of using a worker, is the wage. 117 00:04:42,010 --> 00:04:43,510 This is the per period cost of using 118 00:04:43,510 --> 00:04:46,300 a machine, which will include all the costs of running 119 00:04:46,300 --> 00:04:50,660 the machine as well as the costs of renting the machine itself. 120 00:04:50,660 --> 00:04:52,177 OK? 121 00:04:52,177 --> 00:04:54,260 So later, we'll talk about how to own the machine. 122 00:04:54,260 --> 00:04:56,000 And we'll come back to the fact that you can actually 123 00:04:56,000 --> 00:04:56,585 use r as a representation. 124 00:04:56,585 --> 00:04:57,245 It's not bad. 125 00:04:57,245 --> 00:04:59,120 But for now, just think of renting a machine. 126 00:04:59,120 --> 00:05:01,610 Or if it's a building, think of this as the rent 127 00:05:01,610 --> 00:05:03,470 you pay on that building, OK? 128 00:05:03,470 --> 00:05:05,750 Not the cost to build the building. 129 00:05:05,750 --> 00:05:10,800 Now, armed with our production function-- 130 00:05:10,800 --> 00:05:14,812 and let's also say, to make life easy-- 131 00:05:14,812 --> 00:05:16,020 I did this wrong on my notes. 132 00:05:16,020 --> 00:05:19,140 So I hope the other teachers figured it out. 133 00:05:19,140 --> 00:05:24,060 To make life easy, let's say that the rental rate, r, 134 00:05:24,060 --> 00:05:27,260 we're going to say is $10, and the wage rate, w, 135 00:05:27,260 --> 00:05:28,015 is going to be $5. 136 00:05:32,100 --> 00:05:36,350 Now, armed with a production function, 137 00:05:36,350 --> 00:05:38,720 if you simply have the production function 138 00:05:38,720 --> 00:05:42,020 and these two prices, you can derive the short-run cost 139 00:05:42,020 --> 00:05:43,760 function. 140 00:05:43,760 --> 00:05:45,030 How do you do that? 141 00:05:45,030 --> 00:05:46,370 Well, just look at the math. 142 00:05:46,370 --> 00:05:50,060 We know that q equals square root of L times 143 00:05:50,060 --> 00:05:53,330 k bar in the short-run. 144 00:05:53,330 --> 00:05:55,550 L times k bar. 145 00:05:55,550 --> 00:05:56,660 OK? 146 00:05:56,660 --> 00:06:00,650 So inverting that simply means that L equals q 147 00:06:00,650 --> 00:06:02,500 squared over k bar. 148 00:06:06,450 --> 00:06:11,250 L equals q squared over k bar. 149 00:06:11,250 --> 00:06:12,760 OK? 150 00:06:12,760 --> 00:06:24,260 And that means that cost can be written as 10 k bar-- 151 00:06:24,260 --> 00:06:26,420 the price the rental rate is 10, we 152 00:06:26,420 --> 00:06:29,000 have k bar amount of capital-- 153 00:06:29,000 --> 00:06:34,460 plus 5q squared over k bar. 154 00:06:34,460 --> 00:06:36,980 That's our cost function. 155 00:06:36,980 --> 00:06:41,720 I just plugged in for L and multiplied by the wage rate, w, 156 00:06:41,720 --> 00:06:43,470 which is 5. 157 00:06:43,470 --> 00:06:45,340 OK? 158 00:06:45,340 --> 00:06:48,300 So for example, for a fixed level of capital, this is cost. 159 00:06:48,300 --> 00:06:51,070 So for example, let's imagine our short-run level of capital 160 00:06:51,070 --> 00:06:51,935 is 1. 161 00:06:51,935 --> 00:06:54,310 Let's imagine there's 1 unit of capital in the short run, 162 00:06:54,310 --> 00:06:56,320 just to make the math easy. 163 00:06:56,320 --> 00:07:05,090 Then that simply says that cost equals 10 plus 5q squared. 164 00:07:05,090 --> 00:07:07,570 And that's our cost function. 165 00:07:07,570 --> 00:07:09,620 10 plus 5q squared. 166 00:07:09,620 --> 00:07:13,550 We've just derived the short-run cost function. 167 00:07:13,550 --> 00:07:16,400 10 is the fixed cost component. 168 00:07:16,400 --> 00:07:18,470 That doesn't vary with the amount you produce. 169 00:07:18,470 --> 00:07:20,980 So there's no q part of this. 170 00:07:20,980 --> 00:07:23,740 5q squared is the variable component. 171 00:07:23,740 --> 00:07:26,440 That varies with how much you produce. 172 00:07:26,440 --> 00:07:28,630 So the cost function is a fixed part, 173 00:07:28,630 --> 00:07:31,670 which comes from that one fixed unit of capital, 174 00:07:31,670 --> 00:07:34,120 and the varying part, which comes from the fact 175 00:07:34,120 --> 00:07:39,370 that the amount of q drives the amount of labor we need. 176 00:07:39,370 --> 00:07:40,240 OK? 177 00:07:40,240 --> 00:07:43,270 Questions about that math? 178 00:07:43,270 --> 00:07:44,060 All right. 179 00:07:44,060 --> 00:07:45,965 Now, armed with this cost function, 180 00:07:45,965 --> 00:07:47,670 let's write that down again here. 181 00:07:47,670 --> 00:07:53,453 So C equals 10 plus 5q squared. 182 00:07:53,453 --> 00:07:55,370 That's going to be our short-run cost function 183 00:07:55,370 --> 00:07:56,030 we're going to work with. 184 00:07:56,030 --> 00:07:58,550 And remember, that short-run cost function came directly 185 00:07:58,550 --> 00:08:00,020 from that production function. 186 00:08:00,020 --> 00:08:03,340 To derive this equation, all I needed 187 00:08:03,340 --> 00:08:06,550 was that production function and those two prices, 188 00:08:06,550 --> 00:08:07,930 and I derived it. 189 00:08:07,930 --> 00:08:08,680 OK. 190 00:08:08,680 --> 00:08:11,530 Armed with that, we can define some 191 00:08:11,530 --> 00:08:13,720 of the key concepts that will drive 192 00:08:13,720 --> 00:08:15,580 our entire analysis of firms. 193 00:08:15,580 --> 00:08:17,590 And the single most important concept 194 00:08:17,590 --> 00:08:20,320 is marginal cost, which is what it sounds like-- 195 00:08:20,320 --> 00:08:23,100 the derivative costs with respect to quantity. 196 00:08:23,100 --> 00:08:23,950 OK? 197 00:08:23,950 --> 00:08:28,540 So in this, the marginal cost is delta c delta q. 198 00:08:31,840 --> 00:08:32,860 OK? 199 00:08:32,860 --> 00:08:35,049 That's marginal cost. 200 00:08:35,049 --> 00:08:35,909 OK. 201 00:08:35,909 --> 00:08:41,425 We'll also care about average cost, which is just c over q. 202 00:08:41,425 --> 00:08:42,800 It's very important in this class 203 00:08:42,800 --> 00:08:44,950 to keep our marginals separate from our averages. 204 00:08:44,950 --> 00:08:47,950 The average is simply over the entire range of production. 205 00:08:47,950 --> 00:08:50,410 What is the average cost to produce each unit? 206 00:08:50,410 --> 00:08:53,740 The marginal is what's the cost of producing the next unit? 207 00:08:53,740 --> 00:08:56,020 And since production functions are nonlinear, 208 00:08:56,020 --> 00:08:58,580 those will not be the same, generally. 209 00:08:58,580 --> 00:08:59,080 OK. 210 00:08:59,080 --> 00:09:01,600 Average will not equal marginal in general, 211 00:09:01,600 --> 00:09:04,960 because a nonlinear function delta c delta q is not 212 00:09:04,960 --> 00:09:07,560 the same as c/q. 213 00:09:07,560 --> 00:09:08,930 OK? 214 00:09:08,930 --> 00:09:12,960 So we can actually graph these in figure 6-1. 215 00:09:12,960 --> 00:09:17,430 Figure 6-1 shows the cost curves for this cost function 216 00:09:17,430 --> 00:09:20,370 I just wrote down, which comes from that production function. 217 00:09:20,370 --> 00:09:21,510 OK? 218 00:09:21,510 --> 00:09:25,620 So you can see that the marginal cost, as I said, 219 00:09:25,620 --> 00:09:27,045 is delta c delta q. 220 00:09:27,045 --> 00:09:28,980 Well, that's 10q. 221 00:09:28,980 --> 00:09:33,480 So the marginal cost, the cost of producing the next unit, 222 00:09:33,480 --> 00:09:36,550 rises with the number of units. 223 00:09:36,550 --> 00:09:37,300 Which makes sense. 224 00:09:37,300 --> 00:09:39,123 The cost has a q squared term in it, 225 00:09:39,123 --> 00:09:40,540 So obviously, the marginal cost is 226 00:09:40,540 --> 00:09:42,450 going to have a q term in it. 227 00:09:42,450 --> 00:09:44,620 So basically, the more you produce, 228 00:09:44,620 --> 00:09:46,560 the higher your marginal cost. 229 00:09:46,560 --> 00:09:48,935 The more unit you need to produce, the more the little q, 230 00:09:48,935 --> 00:09:50,800 the higher your marginal cost. 231 00:09:50,800 --> 00:09:54,150 Average cost is this sort of funky shaped thing, 232 00:09:54,150 --> 00:09:55,560 where it's-- 233 00:09:55,560 --> 00:09:58,350 which is 10 over q plus 5q-- 234 00:09:58,350 --> 00:10:01,020 I just divided this by q-- 235 00:10:01,020 --> 00:10:05,120 where it's first declining and then increasing. 236 00:10:05,120 --> 00:10:06,440 Why is that? 237 00:10:06,440 --> 00:10:10,340 Why is average cost first declining and then increasing? 238 00:10:10,340 --> 00:10:11,900 We've seen what-- just intuitively? 239 00:10:11,900 --> 00:10:12,960 Why is that? 240 00:10:12,960 --> 00:10:15,880 Why in general in the short run would we expect that? 241 00:10:15,880 --> 00:10:18,886 Average cost first to fall and then increase. 242 00:10:18,886 --> 00:10:21,640 Anyone have ideas? 243 00:10:21,640 --> 00:10:22,347 Yeah. 244 00:10:22,347 --> 00:10:25,245 AUDIENCE: [INAUDIBLE] start up [INAUDIBLE].. 245 00:10:25,245 --> 00:10:27,370 JONATHAN GRUBER: Well-- no, but it's falling first. 246 00:10:27,370 --> 00:10:29,770 So why is it falling first? 247 00:10:29,770 --> 00:10:30,752 It's about that-- yeah. 248 00:10:30,752 --> 00:10:32,544 AUDIENCE: They have a really high average-- 249 00:10:32,544 --> 00:10:35,510 or first fixed cost is not [INAUDIBLE] the more you make, 250 00:10:35,510 --> 00:10:36,490 the lower that is. 251 00:10:36,490 --> 00:10:37,448 JONATHAN GRUBER: Right. 252 00:10:37,448 --> 00:10:39,406 The first units are paying off your fixed costs 253 00:10:39,406 --> 00:10:40,323 if you think about it. 254 00:10:40,323 --> 00:10:41,990 Well, the first unit you sell, basically 255 00:10:41,990 --> 00:10:44,450 you start with this huge fixed cost. 256 00:10:44,450 --> 00:10:47,105 So actually, by selling two units, yes, 257 00:10:47,105 --> 00:10:48,730 you get the variable cost, second unit, 258 00:10:48,730 --> 00:10:51,370 but you get to pay off the fixed cost, the first unit. 259 00:10:51,370 --> 00:10:52,660 So look at here on this graph. 260 00:10:52,660 --> 00:10:56,620 We show average fixed costs and average variable costs 261 00:10:56,620 --> 00:10:59,410 Average fixed costs are 10/q. 262 00:10:59,410 --> 00:11:02,950 If you only produce one unit, your average fixed cost is $10. 263 00:11:02,950 --> 00:11:04,300 To produce two units it's $5. 264 00:11:04,300 --> 00:11:06,130 With every unit you produce, your average fixed cost 265 00:11:06,130 --> 00:11:06,630 is falling. 266 00:11:06,630 --> 00:11:09,230 You're paying off that fixed cost. 267 00:11:09,230 --> 00:11:12,850 Average variable cost rises. 268 00:11:12,850 --> 00:11:14,650 Every unit you produce, you're getting 269 00:11:14,650 --> 00:11:16,720 more and more variable cost. 270 00:11:16,720 --> 00:11:19,180 You put those together, and you get a function that 271 00:11:19,180 --> 00:11:21,430 first declines and then rises. 272 00:11:21,430 --> 00:11:22,893 You first pay off your fixed costs, 273 00:11:22,893 --> 00:11:24,310 so your average costs are falling, 274 00:11:24,310 --> 00:11:26,080 then your marginal cost-- then you start to rise, 275 00:11:26,080 --> 00:11:28,038 because you've got marginal costs that increase 276 00:11:28,038 --> 00:11:29,470 with quantity produced. 277 00:11:29,470 --> 00:11:33,220 And critically, the marginal cost 278 00:11:33,220 --> 00:11:35,920 intersects the average cost curve 279 00:11:35,920 --> 00:11:38,290 at the minimum of average cost. 280 00:11:38,290 --> 00:11:40,810 And that's just mathematical. 281 00:11:40,810 --> 00:11:44,590 If you have any function, and you take the average, 282 00:11:44,590 --> 00:11:48,850 then the minimum is going to be a derivative that basically-- 283 00:11:48,850 --> 00:11:55,070 before you get to here, 1.5 units, before 1.5 units, 284 00:11:55,070 --> 00:11:58,828 average cost is above marginal cost, 285 00:11:58,828 --> 00:12:00,620 because you're paying off your fixed costs. 286 00:12:00,620 --> 00:12:03,500 Once you get beyond 1.5 units, average cost 287 00:12:03,500 --> 00:12:05,220 is below marginal cost. 288 00:12:05,220 --> 00:12:06,868 So average cost hits marginal cost 289 00:12:06,868 --> 00:12:08,160 at the minimum of average cost. 290 00:12:08,160 --> 00:12:09,020 Yeah. 291 00:12:09,020 --> 00:12:11,360 AUDIENCE: In a relatively large company, 292 00:12:11,360 --> 00:12:14,685 eventually doesn't really worry about their fixed cost, 293 00:12:14,685 --> 00:12:16,560 because if they're having a lot more workers, 294 00:12:16,560 --> 00:12:19,160 their entire cost is going to be considered basically-- 295 00:12:19,160 --> 00:12:21,430 JONATHAN GRUBER: In the short run. 296 00:12:21,430 --> 00:12:22,930 It depends on this function. 297 00:12:22,930 --> 00:12:25,750 You said large, but large can be defined in two ways. 298 00:12:25,750 --> 00:12:26,740 But absolute true. 299 00:12:26,740 --> 00:12:29,770 Certainly, if we take this very function, 300 00:12:29,770 --> 00:12:35,330 for large enough q's average fixed cost asymptotes to 0. 301 00:12:35,330 --> 00:12:37,180 10 over infinity is 0. 302 00:12:37,180 --> 00:12:41,790 So for large enough q's, the average fixed cost goes away-- 303 00:12:41,790 --> 00:12:43,490 in the short run. 304 00:12:43,490 --> 00:12:45,870 Remember, we're in the short run with these fixed costs. 305 00:12:45,870 --> 00:12:47,530 OK. 306 00:12:47,530 --> 00:12:48,727 Now, so other questions. 307 00:12:48,727 --> 00:12:49,310 Good question. 308 00:12:49,310 --> 00:12:52,320 Other questions about that? 309 00:12:52,320 --> 00:12:54,440 So that's our basic intuition, the short run-- 310 00:12:54,440 --> 00:12:56,720 is that at first our costs are super high, 311 00:12:56,720 --> 00:13:00,080 because you've got to pay-- you had to build the plant. 312 00:13:00,080 --> 00:13:02,618 But then over time, that plant cost falls, 313 00:13:02,618 --> 00:13:04,160 and then your only costs is basically 314 00:13:04,160 --> 00:13:05,660 the fact you've got to hire more workers if you 315 00:13:05,660 --> 00:13:06,535 want to produce more. 316 00:13:09,740 --> 00:13:14,730 Now, what we want to notice is that in the short run 317 00:13:14,730 --> 00:13:17,780 there is a really close relationship-- 318 00:13:17,780 --> 00:13:21,290 one was the key relationship between marginal cost 319 00:13:21,290 --> 00:13:23,365 and the marginal product of labor, 320 00:13:23,365 --> 00:13:24,490 which we defined last time. 321 00:13:24,490 --> 00:13:28,370 Remember, the marginal product of labor was dq dL. 322 00:13:28,370 --> 00:13:30,895 How much-- remember digging a hole 323 00:13:30,895 --> 00:13:32,270 and diminishing marginal product? 324 00:13:32,270 --> 00:13:34,820 That each additional worker, for a fixed level of capital, 325 00:13:34,820 --> 00:13:36,800 is less and less productive, right? 326 00:13:36,800 --> 00:13:39,220 We talked about that last time. 327 00:13:39,220 --> 00:13:43,150 Well, the marginal cost of production is, as I said, 328 00:13:43,150 --> 00:13:46,170 equal to delta c over delta q. 329 00:13:46,170 --> 00:13:48,210 OK? 330 00:13:48,210 --> 00:13:51,960 Well, we know from last time that delta q over delta 331 00:13:51,960 --> 00:13:54,600 L we defined as the marginal product of labor. 332 00:13:58,220 --> 00:14:04,190 Plugging those and-- so we know marginal cost is delta c delta 333 00:14:04,190 --> 00:14:06,140 q. 334 00:14:06,140 --> 00:14:10,010 And we can write this-- if you take the derivative of the cost 335 00:14:10,010 --> 00:14:12,230 function, so our general cost function up there-- 336 00:14:12,230 --> 00:14:14,540 see the cost function at the top there? 337 00:14:14,540 --> 00:14:18,980 Take the derivative of that with respect to the amount of labor. 338 00:14:18,980 --> 00:14:23,170 Well, the first term drops out, because it's fixed. 339 00:14:23,170 --> 00:14:30,966 So you can rewrite delta c delta q as w times delta L delta q-- 340 00:14:30,966 --> 00:14:33,730 w times delta L delta q. 341 00:14:33,730 --> 00:14:34,680 Right. 342 00:14:34,680 --> 00:14:38,200 I just rewrote delta c-- q delta w-- god. 343 00:14:38,200 --> 00:14:38,700 Brutal. 344 00:14:38,700 --> 00:14:40,650 Sorry, guys. 345 00:14:40,650 --> 00:14:45,640 w times delta L over delta q. 346 00:14:45,640 --> 00:14:46,140 OK. 347 00:14:46,140 --> 00:14:46,990 A little bit better. 348 00:14:46,990 --> 00:14:47,490 OK. 349 00:14:47,490 --> 00:14:49,948 I read that, because I just took the derivative of the cost 350 00:14:49,948 --> 00:14:51,255 function. 351 00:14:51,255 --> 00:14:53,130 First term drops out, we take the derivative. 352 00:14:53,130 --> 00:14:55,080 Second term, I just took the derivative here, 353 00:14:55,080 --> 00:14:58,050 or the discrete derivative, and I just said, delta c delta q 354 00:14:58,050 --> 00:15:00,323 is w times delta L delta q. 355 00:15:00,323 --> 00:15:01,740 Well, we know the marginal product 356 00:15:01,740 --> 00:15:04,890 is delta q over delta L. So we can 357 00:15:04,890 --> 00:15:12,090 rewrite marginal cost as w over the marginal product of labor. 358 00:15:12,090 --> 00:15:15,690 The marginal cost is equal to w over 359 00:15:15,690 --> 00:15:17,610 the marginal product of labor. 360 00:15:17,610 --> 00:15:20,400 And that makes sense. 361 00:15:20,400 --> 00:15:23,160 The marginal cost of the next unit 362 00:15:23,160 --> 00:15:26,310 will be higher the higher the wage 363 00:15:26,310 --> 00:15:29,820 and lower the more productive the worker. 364 00:15:29,820 --> 00:15:35,210 Making another unit with a super productive worker is cheap. 365 00:15:35,210 --> 00:15:37,335 Making another unit with a very unproductive worker 366 00:15:37,335 --> 00:15:39,320 is expensive. 367 00:15:39,320 --> 00:15:42,830 So essentially, the more you pay them for each hour of work, 368 00:15:42,830 --> 00:15:44,870 the higher your marginal cost. 369 00:15:44,870 --> 00:15:47,510 But the less they get done each hour of work, 370 00:15:47,510 --> 00:15:49,850 the higher your marginal cost. 371 00:15:49,850 --> 00:15:52,060 So that's why, roughly speaking, firms 372 00:15:52,060 --> 00:15:55,540 might want to pay a lot to people who are high skilled. 373 00:15:55,540 --> 00:15:58,407 So you might say, gee, why are they paying my friend twice 374 00:15:58,407 --> 00:15:58,990 what I'm paid? 375 00:15:58,990 --> 00:16:01,750 Well, maybe your friend's twice as productive as you. 376 00:16:01,750 --> 00:16:03,310 That would make-- or two and a half times as productive 377 00:16:03,310 --> 00:16:03,810 as you. 378 00:16:03,810 --> 00:16:05,110 And that would make sense. 379 00:16:05,110 --> 00:16:07,183 So we can't just say that it's a mistake 380 00:16:07,183 --> 00:16:08,350 to pay someone higher wages. 381 00:16:08,350 --> 00:16:10,975 We have to consider their wages relative to how productive they 382 00:16:10,975 --> 00:16:12,910 are. 383 00:16:12,910 --> 00:16:18,110 And that's a key relationship we'll come back to. 384 00:16:18,110 --> 00:16:19,370 OK? 385 00:16:19,370 --> 00:16:21,950 Question about that? 386 00:16:21,950 --> 00:16:22,790 All right. 387 00:16:22,790 --> 00:16:24,300 That's the short run. 388 00:16:24,300 --> 00:16:25,860 Now let's go to the long run, which 389 00:16:25,860 --> 00:16:26,820 gets a little more interesting. 390 00:16:26,820 --> 00:16:28,278 Actually, let's write in that side. 391 00:16:28,278 --> 00:16:29,700 I'll switch to this side today. 392 00:16:29,700 --> 00:16:30,408 Switch things up. 393 00:16:34,600 --> 00:16:36,600 This way, this side, I block you less, probably. 394 00:16:36,600 --> 00:16:38,280 So I should do this side. 395 00:16:38,280 --> 00:16:38,850 OK. 396 00:16:38,850 --> 00:16:40,020 Long run cost curves. 397 00:16:43,410 --> 00:16:44,010 OK. 398 00:16:44,010 --> 00:16:45,150 Long run cost. 399 00:16:45,150 --> 00:16:50,720 Now, here what gets interesting, is now K is no longer fixed. 400 00:16:50,720 --> 00:16:54,620 Now we get to choose our input mix. 401 00:16:54,620 --> 00:16:58,700 And now our goal is going to be, how do we choose our input 402 00:16:58,700 --> 00:17:02,410 mix to minimize costs? 403 00:17:02,410 --> 00:17:03,610 That's our goal here. 404 00:17:03,610 --> 00:17:07,599 How we going to choose the mix of workers and machines 405 00:17:07,599 --> 00:17:11,290 to produce a given quantity most efficiently? 406 00:17:11,290 --> 00:17:14,220 Now, that optimal mix may change with the quantity. 407 00:17:14,220 --> 00:17:15,220 So we're going to start. 408 00:17:15,220 --> 00:17:16,220 We're going to do this in two steps. 409 00:17:16,220 --> 00:17:19,060 First, we're going to say, for a given quantity picked out 410 00:17:19,060 --> 00:17:22,720 of a hat, what's the right mix of labor and capital 411 00:17:22,720 --> 00:17:25,480 that minimizes the cost of producing that quantity, given 412 00:17:25,480 --> 00:17:27,280 our production function? 413 00:17:27,280 --> 00:17:29,140 Then we're going to say, as the quantity 414 00:17:29,140 --> 00:17:32,530 varies how does that change the optimal mix of L and K? 415 00:17:32,530 --> 00:17:34,190 And does it? 416 00:17:34,190 --> 00:17:34,860 So two steps. 417 00:17:34,860 --> 00:17:37,040 First say, for a given quantity, what's 418 00:17:37,040 --> 00:17:38,600 the right L and K to minimize costs 419 00:17:38,600 --> 00:17:39,830 of producing that quantity? 420 00:17:39,830 --> 00:17:42,590 Then ask, well, as we vary the quantity how does L-- 421 00:17:42,590 --> 00:17:44,900 how do L and K vary optimally? 422 00:17:44,900 --> 00:17:46,420 OK. 423 00:17:46,420 --> 00:17:51,850 So basically, we want to find the economically efficient 424 00:17:51,850 --> 00:17:55,720 combination of L and K which is a combination that 425 00:17:55,720 --> 00:17:59,470 produces goods at minimum cost. 426 00:17:59,470 --> 00:18:01,343 And to do this, we are going to write down-- 427 00:18:01,343 --> 00:18:03,010 to derive this we're going to write down 428 00:18:03,010 --> 00:18:06,610 what we call isocost curves. 429 00:18:06,610 --> 00:18:08,170 Isocost curves. 430 00:18:08,170 --> 00:18:10,360 Remember last time we did isoquants, 431 00:18:10,360 --> 00:18:12,760 Which felt a lot like the difference curves? 432 00:18:12,760 --> 00:18:16,840 Isocosts are going to feel a lot like budget constraints. 433 00:18:16,840 --> 00:18:20,560 Isocost curves are essentially the firm's budget constraint. 434 00:18:20,560 --> 00:18:23,120 They're essentially mappings of the function 435 00:18:23,120 --> 00:18:26,420 c equals wL plus rK-- 436 00:18:26,420 --> 00:18:30,400 essentially, mappings for different amounts of K and L 437 00:18:30,400 --> 00:18:33,520 of the function c equals rK plus wL. 438 00:18:33,520 --> 00:18:38,930 So if you look at figure 6-2, here we see our isocost lines. 439 00:18:38,930 --> 00:18:39,790 OK. 440 00:18:39,790 --> 00:18:41,870 So let's talk about this for a second. 441 00:18:41,870 --> 00:18:45,960 So for example, take the middle one, the $100 isocost. 442 00:18:45,960 --> 00:18:50,470 This is saying, what combinations of labor 443 00:18:50,470 --> 00:18:54,000 and capital cost you $100? 444 00:18:54,000 --> 00:18:59,220 Well, with a rental rate of $10 and a wage of $5, 445 00:18:59,220 --> 00:19:02,490 that means you can have 10 machines and no workers 446 00:19:02,490 --> 00:19:07,473 or 20 workers and no machines, or some combination in between. 447 00:19:07,473 --> 00:19:08,890 This is just a budget constraints. 448 00:19:08,890 --> 00:19:10,682 It's just saying, given the amount of money 449 00:19:10,682 --> 00:19:14,168 you want to spend, given your cost, 450 00:19:14,168 --> 00:19:15,960 how many machines and workers can you have? 451 00:19:15,960 --> 00:19:18,127 The difference is, we don't start-- 452 00:19:18,127 --> 00:19:19,710 I didn't start this example by saying, 453 00:19:19,710 --> 00:19:21,330 your parents give you x dollars. 454 00:19:21,330 --> 00:19:23,628 That's why firm theory is harder than consumer theory. 455 00:19:23,628 --> 00:19:25,920 I pin down the consumer theory problem much more easily 456 00:19:25,920 --> 00:19:27,720 by saying, your parents give you x dollars, which 457 00:19:27,720 --> 00:19:29,012 told you which line to derive-- 458 00:19:29,012 --> 00:19:29,512 graph. 459 00:19:29,512 --> 00:19:30,510 I don't have that here. 460 00:19:30,510 --> 00:19:31,718 I haven't told you that here. 461 00:19:31,718 --> 00:19:33,990 So you have to graph a series of isocost curves, 462 00:19:33,990 --> 00:19:36,778 because you don't know what the optimal cost is going to be. 463 00:19:36,778 --> 00:19:38,070 That's to be pinned down later. 464 00:19:38,070 --> 00:19:40,260 That's what makes supply theory harder. 465 00:19:40,260 --> 00:19:41,670 You have to draw the series. 466 00:19:41,670 --> 00:19:44,250 So you draw these series of isocost curves-- 467 00:19:44,250 --> 00:19:47,310 different combinations that represent different 468 00:19:47,310 --> 00:19:49,350 amounts, different totals of cost. 469 00:19:49,350 --> 00:19:54,010 And of course, the slope of that isocost curve 470 00:19:54,010 --> 00:20:01,382 is delta K delta L, or minus w over r. 471 00:20:01,382 --> 00:20:02,090 That's the slope. 472 00:20:02,090 --> 00:20:09,070 Or in this case, minus 0.5. 473 00:20:09,070 --> 00:20:10,652 Now, those of you thinking ahead-- 474 00:20:10,652 --> 00:20:12,610 I know you guys are very insightful as a class, 475 00:20:12,610 --> 00:20:14,440 I'm sure many of you are thinking ahead-- 476 00:20:14,440 --> 00:20:17,200 might think, gee, that slope might 477 00:20:17,200 --> 00:20:19,480 change as the number of workers and machines change. 478 00:20:19,480 --> 00:20:22,092 Could you imagine the relative price of capital labor changes 479 00:20:22,092 --> 00:20:24,550 in different costs-- and it might, and we'll put that aside 480 00:20:24,550 --> 00:20:25,720 for now. 481 00:20:25,720 --> 00:20:29,290 For now, assuming for every relevant quantity these prices 482 00:20:29,290 --> 00:20:31,500 $5 and $10 are fixed-- 483 00:20:31,500 --> 00:20:33,250 let's ignore where those prices come from. 484 00:20:33,250 --> 00:20:34,208 They're just given now. 485 00:20:34,208 --> 00:20:36,153 We'll come back to that later. 486 00:20:36,153 --> 00:20:38,570 Like I said, this course is sort of like peeling an onion. 487 00:20:38,570 --> 00:20:40,570 We raise things, then we come back go to the next layer. 488 00:20:40,570 --> 00:20:41,660 Where'd that come from? 489 00:20:41,660 --> 00:20:44,633 Right now-- we'll tell you where w and r come from. 490 00:20:44,633 --> 00:20:46,550 Right now we're just going to take them fixed. 491 00:20:46,550 --> 00:20:48,380 And we'll assume they're always $5 and $10, 492 00:20:48,380 --> 00:20:50,900 regardless of the amount produced. 493 00:20:50,900 --> 00:20:52,020 OK. 494 00:20:52,020 --> 00:20:54,312 Now, here's the question. 495 00:20:54,312 --> 00:20:55,770 You're a firm that wants to release 496 00:20:55,770 --> 00:20:58,700 a certain amount of units. 497 00:20:58,700 --> 00:21:02,350 You have a production function and a cost function. 498 00:21:02,350 --> 00:21:07,210 How do you graphically figure out the right combination 499 00:21:07,210 --> 00:21:09,190 of capital labor to use to produce 500 00:21:09,190 --> 00:21:11,100 a certain amount of units? 501 00:21:11,100 --> 00:21:13,475 Yeah. 502 00:21:13,475 --> 00:21:17,690 AUDIENCE: Could it be the tension between the isoquant 503 00:21:17,690 --> 00:21:18,960 and the isocost curves? 504 00:21:18,960 --> 00:21:20,970 JONATHAN GRUBER: That's exactly right. 505 00:21:20,970 --> 00:21:23,880 Just as I asked you, what is the right combination of pizza 506 00:21:23,880 --> 00:21:27,090 and cookies, and you told me that it 507 00:21:27,090 --> 00:21:29,580 was the tangency of the indifference 508 00:21:29,580 --> 00:21:33,810 curve and the budget constraint, it's the exact same logic here. 509 00:21:33,810 --> 00:21:36,000 The optimal mix of capital and labor 510 00:21:36,000 --> 00:21:40,770 comes from the tangency of the isoquant with the isocost, 511 00:21:40,770 --> 00:21:43,470 as we see in figure 6-3. 512 00:21:43,470 --> 00:21:45,420 And ignore the, like-- 513 00:21:45,420 --> 00:21:47,545 somehow that curve is sort of connected at the top. 514 00:21:47,545 --> 00:21:49,003 It's sort of a glitch a PowerPoint. 515 00:21:49,003 --> 00:21:49,740 Just ignore that. 516 00:21:49,740 --> 00:21:52,620 It's not actually like a square or a trapezoid. 517 00:21:52,620 --> 00:21:53,877 It's just a curve. 518 00:21:53,877 --> 00:21:54,960 What would you call that-- 519 00:21:54,960 --> 00:21:56,127 the curve and the two sides. 520 00:21:56,127 --> 00:21:57,920 Is that a-- that's not a trapezoid. 521 00:21:57,920 --> 00:22:00,650 That's not-- it's not a polygon. 522 00:22:00,650 --> 00:22:01,730 It's just a line. 523 00:22:01,730 --> 00:22:03,080 All right. 524 00:22:03,080 --> 00:22:05,360 So basically-- is there a name for that? 525 00:22:05,360 --> 00:22:06,350 A curve and two lines? 526 00:22:06,350 --> 00:22:07,745 I don't think so. 527 00:22:07,745 --> 00:22:08,870 It's just a polygon, right? 528 00:22:08,870 --> 00:22:09,380 OK. 529 00:22:09,380 --> 00:22:11,930 So it's not a polygon, it's just a curve. 530 00:22:11,930 --> 00:22:16,160 So the curve is the isoquant for the square root of 12.5. 531 00:22:16,160 --> 00:22:17,700 What do I mean by that? 532 00:22:17,700 --> 00:22:21,730 I mean that is the combination of capital and labor 533 00:22:21,730 --> 00:22:26,230 that delivers square root of 12.5 units of production. 534 00:22:26,230 --> 00:22:30,070 So what that curve is all possible combinations 535 00:22:30,070 --> 00:22:33,310 of capital and labor that deliver 536 00:22:33,310 --> 00:22:37,158 square root of 12.5 units. 537 00:22:37,158 --> 00:22:39,700 Just like the indifference curve is all possible combinations 538 00:22:39,700 --> 00:22:41,980 of pizza and cookies that leaves you equally happy, 539 00:22:41,980 --> 00:22:43,355 this is all possible combinations 540 00:22:43,355 --> 00:22:45,523 of capital and labor that leads you 541 00:22:45,523 --> 00:22:46,690 to a given production level. 542 00:22:49,510 --> 00:22:51,500 And as we said, the further out the isoquant, 543 00:22:51,500 --> 00:22:52,810 the more you can produce. 544 00:22:52,810 --> 00:22:55,830 So you want to produce as much as you can given the prices you 545 00:22:55,830 --> 00:22:57,250 face in the market. 546 00:22:57,250 --> 00:22:59,160 Well, those prices you face in the market 547 00:22:59,160 --> 00:23:01,780 are delivered by the isocost curve. 548 00:23:01,780 --> 00:23:04,080 So the tangency is the best-- 549 00:23:04,080 --> 00:23:06,450 is the cost minimizing point. 550 00:23:06,450 --> 00:23:10,080 That's when you're producing the most you can given the costs 551 00:23:10,080 --> 00:23:12,575 you face in the market-- 552 00:23:12,575 --> 00:23:14,950 the most you can, given the costs you face in the market. 553 00:23:17,670 --> 00:23:20,090 And that tangency condition-- once again, 554 00:23:20,090 --> 00:23:22,550 considering our parallels to consumer theory, 555 00:23:22,550 --> 00:23:27,000 the tangency condition is going to deliver that the marginal 556 00:23:27,000 --> 00:23:29,130 product-- 557 00:23:29,130 --> 00:23:32,520 is going to deliver that the marginal product of labor 558 00:23:32,520 --> 00:23:35,460 over the marginal product of capital, which we remember 559 00:23:35,460 --> 00:23:37,830 called last time the marginal rate 560 00:23:37,830 --> 00:23:45,883 of technical substitution, is going to be equal to w/r-- 561 00:23:45,883 --> 00:23:47,550 actually, the negative of these is going 562 00:23:47,550 --> 00:23:48,290 to be equal to each other. 563 00:23:48,290 --> 00:23:49,915 But we'll just cross out the negatives. 564 00:23:49,915 --> 00:23:52,540 So the negative of MPL over MPK, which 565 00:23:52,540 --> 00:23:55,240 we called the marginal rate of technical substitution, 566 00:23:55,240 --> 00:23:58,780 is equal to the negative of w/r. 567 00:23:58,780 --> 00:24:01,602 The slope, the optimal point, is where 568 00:24:01,602 --> 00:24:03,310 the marginal rate of technical subsection 569 00:24:03,310 --> 00:24:09,650 equals the slope, which is the wage to rental rate ratio. 570 00:24:09,650 --> 00:24:12,150 Alternatively-- I don't know if anyone besides me likes this 571 00:24:12,150 --> 00:24:22,620 intuition-- we can rewrite this as MPL/w equals MPK/r, 572 00:24:22,620 --> 00:24:25,170 my bang-for-the-buck formulation that I like-- 573 00:24:25,170 --> 00:24:30,310 that the next dollar of wages, if you ask, 574 00:24:30,310 --> 00:24:33,070 should I spend next dollar on wages or machines, 575 00:24:33,070 --> 00:24:35,770 you should do it until the next dollar of wages 576 00:24:35,770 --> 00:24:40,260 delivers you the same return as the next dollar of machines. 577 00:24:40,260 --> 00:24:43,370 This is what you get for the next dollar of wages, MPL/w. 578 00:24:43,370 --> 00:24:46,100 This it what you get for the next dollar of machines, MPK/r. 579 00:24:46,100 --> 00:24:48,590 You want to continue to trade off machines and workers 580 00:24:48,590 --> 00:24:51,900 until that condition is true. 581 00:24:51,900 --> 00:24:55,600 So let's actually now solve for this for our example. 582 00:24:55,600 --> 00:24:56,850 Let's actually solve for that. 583 00:25:01,410 --> 00:25:04,500 If we solve for this, we know that the marginal product 584 00:25:04,500 --> 00:25:14,700 of labor, which is dq dL, is 0.5 times K over square root of K 585 00:25:14,700 --> 00:25:18,910 times L. And the marginal product of capital, 586 00:25:18,910 --> 00:25:26,820 which is dq dK, equals 0.5 times L over the square root-- 587 00:25:26,820 --> 00:25:31,015 0.5 times L over the square root of K times L. Just taking 588 00:25:31,015 --> 00:25:32,390 the derivative of the-- all I did 589 00:25:32,390 --> 00:25:36,070 was take the derivative of the production function. 590 00:25:36,070 --> 00:25:38,928 So therefore, putting these together, 591 00:25:38,928 --> 00:25:40,720 we're going to-- we know that marginal rate 592 00:25:40,720 --> 00:25:43,840 of technical substitution in this example 593 00:25:43,840 --> 00:25:50,620 is equal to minus K over L. That's not a general formula. 594 00:25:50,620 --> 00:25:51,898 That's just this example. 595 00:25:51,898 --> 00:25:53,690 The marginal rate of technical substitution 596 00:25:53,690 --> 00:25:58,610 is equal to the negative of the ratio of capital to labor. 597 00:25:58,610 --> 00:26:03,170 We also know that the wage rate-- 598 00:26:03,170 --> 00:26:05,720 we also know we want to set this equal to the negative 599 00:26:05,720 --> 00:26:07,750 of the wage rate-- 600 00:26:07,750 --> 00:26:11,000 I'm sorry, the wage rental rate ratio. 601 00:26:11,000 --> 00:26:13,170 And we know that's negative 1/2. 602 00:26:13,170 --> 00:26:18,030 We know that's a 1/2, because that's 5 and that's 10. 603 00:26:18,030 --> 00:26:21,540 So we want to set the marginal rate of technical substitution 604 00:26:21,540 --> 00:26:23,880 to the wage rental rate ratio, which 605 00:26:23,880 --> 00:26:27,120 means we set minus K over L equal to minus 1/2. 606 00:26:27,120 --> 00:26:34,890 Or at the optimum, that means that your labor, your capital, 607 00:26:34,890 --> 00:26:37,080 at the optimum-- that means the amount of capital-- 608 00:26:37,080 --> 00:26:40,830 should be half as much as the amount of labor. 609 00:26:40,830 --> 00:26:45,390 In this example, we just solved for the efficient combination 610 00:26:45,390 --> 00:26:47,980 of inputs, the efficient combination 611 00:26:47,980 --> 00:26:52,210 is you should use capital to labor in a ratio of 1/2. 612 00:26:52,210 --> 00:26:55,890 You should use half as much capital as use labor. 613 00:26:55,890 --> 00:26:58,140 So let me pause there. 614 00:26:58,140 --> 00:27:01,120 And let's talk about where this is coming from. 615 00:27:01,120 --> 00:27:02,002 Yeah. 616 00:27:02,002 --> 00:27:04,460 AUDIENCE: So does that mean that at any given price of cost 617 00:27:04,460 --> 00:27:08,540 [INAUDIBLE] line, that is the optimal point where 618 00:27:08,540 --> 00:27:09,790 it will be tangent [INAUDIBLE] 619 00:27:09,790 --> 00:27:10,900 JONATHAN GRUBER: Exactly. 620 00:27:10,900 --> 00:27:13,630 Exactly. 621 00:27:13,630 --> 00:27:15,180 That's the graphic intuition. 622 00:27:15,180 --> 00:27:17,010 Let's come to the economics intuition. 623 00:27:17,010 --> 00:27:20,190 The economics intuition is the following. 624 00:27:20,190 --> 00:27:22,540 The production function delivers this relationship-- 625 00:27:22,540 --> 00:27:24,540 that the marginal rate of technical substitution 626 00:27:24,540 --> 00:27:26,860 was minus K over L. In other words, 627 00:27:26,860 --> 00:27:30,178 when you're producing goods, given this production function 628 00:27:30,178 --> 00:27:31,970 you're indifferent between the next machine 629 00:27:31,970 --> 00:27:32,803 and the next worker. 630 00:27:32,803 --> 00:27:34,928 That's just the way this production function worked 631 00:27:34,928 --> 00:27:35,450 out-- 632 00:27:35,450 --> 00:27:37,850 that one more machine delivers you the same amount 633 00:27:37,850 --> 00:27:40,550 as one more worker. 634 00:27:40,550 --> 00:27:44,660 Now, I've just told you that one machine 635 00:27:44,660 --> 00:27:47,580 costs half of one more worker. 636 00:27:47,580 --> 00:27:51,110 So which you want more of? 637 00:27:51,110 --> 00:27:52,100 No? 638 00:27:52,100 --> 00:27:55,370 One machine delivers the same return as one worker. 639 00:27:55,370 --> 00:27:56,960 You want more workers. 640 00:27:56,960 --> 00:28:01,660 Workers cost half machines, they're equally productive, 641 00:28:01,660 --> 00:28:04,330 so you want more workers. 642 00:28:04,330 --> 00:28:06,400 So the optimal amount of machines 643 00:28:06,400 --> 00:28:10,140 is going to be half as many as the number of workers. 644 00:28:10,140 --> 00:28:13,380 You want more workers, because you're indifferent-- 645 00:28:13,380 --> 00:28:14,910 look at that production function. 646 00:28:14,910 --> 00:28:17,190 You're indifferent. 647 00:28:17,190 --> 00:28:19,290 You don't give a shit about L versus K. 648 00:28:19,290 --> 00:28:22,190 They're the same to you. 649 00:28:22,190 --> 00:28:24,180 You're a hard capitalist, man. 650 00:28:24,180 --> 00:28:25,770 Machine or worker, you don't care. 651 00:28:25,770 --> 00:28:28,950 But the market's telling you you can get a worker for half 652 00:28:28,950 --> 00:28:30,710 the price of a machine. 653 00:28:30,710 --> 00:28:33,660 So you, as a good cost minimizing capitalist, 654 00:28:33,660 --> 00:28:35,415 take twice as many workers as machines. 655 00:28:38,560 --> 00:28:41,835 And that's the outcome that you get here. 656 00:28:41,835 --> 00:28:42,710 Questions about that? 657 00:28:45,360 --> 00:28:46,080 OK. 658 00:28:46,080 --> 00:28:51,990 So that's basically what we do to derive this. 659 00:28:51,990 --> 00:28:57,360 Now, what I want to do is take this and then derive 660 00:28:57,360 --> 00:29:01,470 our ultimate goal, which is, what is the long run cost 661 00:29:01,470 --> 00:29:02,430 function? 662 00:29:02,430 --> 00:29:04,860 That's sort of what we-- why we started this lecture. 663 00:29:04,860 --> 00:29:06,318 What is the long run cost function? 664 00:29:06,318 --> 00:29:07,215 Let's do the math. 665 00:29:07,215 --> 00:29:08,790 We'll do the math in five steps. 666 00:29:08,790 --> 00:29:19,880 Step one, q equals square root of K times L. Step two, 667 00:29:19,880 --> 00:29:25,040 we know from up there that K/L equals w/r. 668 00:29:25,040 --> 00:29:30,295 We derived that, leading us to the conclusion that K-- 669 00:29:30,295 --> 00:29:31,920 lead us to the conclusion that K equals 670 00:29:31,920 --> 00:29:37,180 1/2 L. We just derived that. 671 00:29:37,180 --> 00:29:46,450 Therefore, we can rewrite q as the square root of 1/2 times L 672 00:29:46,450 --> 00:29:52,150 squared, just substituting it, because K equals 1/2 L. 673 00:29:52,150 --> 00:29:56,860 Therefore, we can solve for L is going 674 00:29:56,860 --> 00:30:00,760 to be square root of 2 over q. 675 00:30:03,340 --> 00:30:10,330 And K is going to be square root of 2 over 2 over q. 676 00:30:18,473 --> 00:30:22,090 L is square root of 2 over q, K is square root of 2 over 2 677 00:30:22,090 --> 00:30:24,480 over q. 678 00:30:24,480 --> 00:30:25,960 I'm sorry-- no, not over q. 679 00:30:25,960 --> 00:30:26,460 I'm sorry. 680 00:30:26,460 --> 00:30:27,810 That's my bed. 681 00:30:27,810 --> 00:30:28,920 Error. 682 00:30:28,920 --> 00:30:29,550 Error. 683 00:30:29,550 --> 00:30:31,290 Go back. 684 00:30:31,290 --> 00:30:32,600 Should always look at my notes. 685 00:30:32,600 --> 00:30:34,590 It's square root of 2 times q. 686 00:30:34,590 --> 00:30:35,610 My bad. 687 00:30:35,610 --> 00:30:37,290 L is square root of 2 times q. 688 00:30:41,540 --> 00:30:46,460 And K is square root of 2 over 2 times q. 689 00:30:49,260 --> 00:30:51,060 OK. 690 00:30:51,060 --> 00:30:55,110 Therefore, armed with this L and K, 691 00:30:55,110 --> 00:30:57,990 we can rewrite our cost function. 692 00:30:57,990 --> 00:31:03,990 So step five is that the cost function-- given this stuff, 693 00:31:03,990 --> 00:31:11,824 the cost function equals r times square root of 2 times q-- 694 00:31:11,824 --> 00:31:14,880 I'm sorry, r times square root of 2 over 2 times q-- 695 00:31:14,880 --> 00:31:18,180 plus w times square root of 2 times q. 696 00:31:18,180 --> 00:31:21,740 I just plugged in the optimal L and K into my cost function. 697 00:31:25,210 --> 00:31:29,260 Now I can plug in the 10 and the 5 698 00:31:29,260 --> 00:31:38,170 to get C equals 10 times square root of 2 times q. 699 00:31:38,170 --> 00:31:40,040 And I'm done. 700 00:31:40,040 --> 00:31:41,992 I just derived the cost function. 701 00:31:41,992 --> 00:31:43,200 That's what we came here for. 702 00:31:43,200 --> 00:31:46,143 This is what you got up this morning and wanted to see. 703 00:31:46,143 --> 00:31:47,560 You got up this morning, you said, 704 00:31:47,560 --> 00:31:51,210 I want to know how does the cost of a firm 705 00:31:51,210 --> 00:31:53,220 vary with the quantity it produces? 706 00:31:53,220 --> 00:31:55,400 And I've just told you. 707 00:31:55,400 --> 00:31:58,010 This tells you how the costs that you pay 708 00:31:58,010 --> 00:31:59,660 vary the quantity you produce. 709 00:31:59,660 --> 00:32:03,740 And I did that by deriving the optimal mix of L and K 710 00:32:03,740 --> 00:32:08,180 you want to use, and then simply imposing 711 00:32:08,180 --> 00:32:11,802 the prices of those two, and I get a cost function. 712 00:32:11,802 --> 00:32:12,612 Yeah. 713 00:32:12,612 --> 00:32:14,570 AUDIENCE: Wouldn't you be adding the two terms? 714 00:32:14,570 --> 00:32:14,840 JONATHAN GRUBER: I'm sorry? 715 00:32:14,840 --> 00:32:16,670 AUDIENCE: Wouldn't you be adding the two terms? 716 00:32:16,670 --> 00:32:17,930 JONATHAN GRUBER: Which two terms? 717 00:32:17,930 --> 00:32:18,380 Oh, I see. 718 00:32:18,380 --> 00:32:18,880 Yeah, plus. 719 00:32:18,880 --> 00:32:19,490 I'm sorry. 720 00:32:19,490 --> 00:32:20,100 You're right. 721 00:32:20,100 --> 00:32:20,600 My bad. 722 00:32:20,600 --> 00:32:22,490 That's a plus. 723 00:32:22,490 --> 00:32:25,010 Thanks. 724 00:32:25,010 --> 00:32:27,230 This is the most math I'll do in a lecture all year, 725 00:32:27,230 --> 00:32:28,503 you'll be pleased to know. 726 00:32:28,503 --> 00:32:30,170 It's why it's my least favorite lecture. 727 00:32:30,170 --> 00:32:30,670 Yeah? 728 00:32:30,670 --> 00:32:34,700 AUDIENCE: So is five generally true? 729 00:32:34,700 --> 00:32:37,210 JONATHAN GRUBER: You mean this particular functional form? 730 00:32:37,210 --> 00:32:37,580 AUDIENCE: Yeah. 731 00:32:37,580 --> 00:32:38,180 JONATHAN GRUBER: No. 732 00:32:38,180 --> 00:32:39,800 This is all dependent on that production 733 00:32:39,800 --> 00:32:40,717 function I wrote down. 734 00:32:40,717 --> 00:32:42,830 What's generally true is this-- 735 00:32:42,830 --> 00:32:44,300 or actually, K wouldn't be-- 736 00:32:44,300 --> 00:32:46,767 what's generally true is just C equals-- 737 00:32:46,767 --> 00:32:48,350 in the long run, what's generally true 738 00:32:48,350 --> 00:32:52,310 is C equals wL plus rK. 739 00:32:52,310 --> 00:32:54,020 That's what's generally true. 740 00:32:54,020 --> 00:32:54,830 I just made-- 741 00:32:54,830 --> 00:32:59,310 But what I've showed you is, given three things-- 742 00:32:59,310 --> 00:33:02,240 a production-- all I gave you was a production function, 743 00:33:02,240 --> 00:33:05,210 a wage rate, and a rental rate. 744 00:33:05,210 --> 00:33:07,400 Given those three things, you can then 745 00:33:07,400 --> 00:33:10,880 derive the cost function. 746 00:33:10,880 --> 00:33:14,042 Given those three things, you can derive the cost function. 747 00:33:14,042 --> 00:33:16,500 In fact, given two things you can derive the cost function. 748 00:33:16,500 --> 00:33:19,632 You could actually derive the cost function given one thing-- 749 00:33:19,632 --> 00:33:21,090 given just the production function, 750 00:33:21,090 --> 00:33:25,750 derive the cost function as a function of these input prices. 751 00:33:25,750 --> 00:33:26,340 OK. 752 00:33:26,340 --> 00:33:30,000 So that's a lot of results from one function, 753 00:33:30,000 --> 00:33:33,340 from one production function. 754 00:33:33,340 --> 00:33:35,380 Now, other question about this? 755 00:33:35,380 --> 00:33:36,470 Other math I got wrong? 756 00:33:36,470 --> 00:33:38,530 Sorry about that. 757 00:33:38,530 --> 00:33:39,180 Yeah. 758 00:33:39,180 --> 00:33:40,920 AUDIENCE: Sorry, could you just repeat the three inputs 759 00:33:40,920 --> 00:33:41,520 that you were using? 760 00:33:41,520 --> 00:33:42,760 JONATHAN GRUBER: [INAUDIBLE] all I used. 761 00:33:42,760 --> 00:33:43,810 Somebody tell me. 762 00:33:43,810 --> 00:33:46,270 What do you need to get the magical cost function? 763 00:33:46,270 --> 00:33:48,080 What three things do you need? 764 00:33:48,080 --> 00:33:49,490 Yeah. 765 00:33:49,490 --> 00:33:52,362 AUDIENCE: w and r and then q. 766 00:33:52,362 --> 00:33:54,170 JONATHAN GRUBER: No, w, r, and-- 767 00:33:54,170 --> 00:33:54,923 what about q? 768 00:33:54,923 --> 00:33:56,840 You need q, but what about-- what do you need? 769 00:33:56,840 --> 00:34:00,297 w, r, and the production function. 770 00:34:00,297 --> 00:34:01,880 So armed with the production function, 771 00:34:01,880 --> 00:34:06,990 that mathematical equation, this mathematical equation, w and r, 772 00:34:06,990 --> 00:34:07,580 I'm done. 773 00:34:07,580 --> 00:34:09,080 Everything I've done in this lecture 774 00:34:09,080 --> 00:34:10,750 comes from those three things. 775 00:34:10,750 --> 00:34:13,219 The math is hard and annoying. 776 00:34:13,219 --> 00:34:15,380 We will have you practice it. 777 00:34:15,380 --> 00:34:17,380 You will not like it. 778 00:34:17,380 --> 00:34:18,820 OK. 779 00:34:18,820 --> 00:34:21,320 It's just kind of what you've got to do. 780 00:34:21,320 --> 00:34:21,820 All right? 781 00:34:21,820 --> 00:34:23,695 I don't like it, you're not going to like it. 782 00:34:23,695 --> 00:34:25,237 It's just what we've got to do to get 783 00:34:25,237 --> 00:34:26,510 to the more interesting stuff. 784 00:34:26,510 --> 00:34:27,010 OK? 785 00:34:27,010 --> 00:34:27,800 Yeah. 786 00:34:27,800 --> 00:34:29,620 AUDIENCE: Is the bar on the K? 787 00:34:29,620 --> 00:34:32,260 JONATHAN GRUBER: It's fixed in the short run. 788 00:34:32,260 --> 00:34:32,998 The bar on the-- 789 00:34:32,998 --> 00:34:34,540 shouldn't see a bar on a K over here. 790 00:34:34,540 --> 00:34:37,159 That's all over here when I was doing the short run. 791 00:34:37,159 --> 00:34:38,080 Yeah? 792 00:34:38,080 --> 00:34:41,212 AUDIENCE: Can you use r and w in order to get to the fifth step? 793 00:34:41,212 --> 00:34:42,920 JONATHAN GRUBER: Yeah, we needed r and w. 794 00:34:42,920 --> 00:34:45,040 AUDIENCE: Well, in the sense that, to simplify, 795 00:34:45,040 --> 00:34:46,856 K equals 1/2 L? 796 00:34:46,856 --> 00:34:47,882 JONATHAN GRUBER: To K-- 797 00:34:47,882 --> 00:34:48,590 oh, you're right. 798 00:34:48,590 --> 00:34:49,159 That's a good point. 799 00:34:49,159 --> 00:34:50,420 I needed r and w back here. 800 00:34:50,420 --> 00:34:50,962 You're right. 801 00:34:50,962 --> 00:34:52,520 That's a good point. 802 00:34:52,520 --> 00:34:53,310 Good point. 803 00:34:53,310 --> 00:34:54,970 But I still could have done this whole thing as a function of r 804 00:34:54,970 --> 00:34:56,239 and w if I wanted to-- 805 00:34:56,239 --> 00:34:59,300 if I wanted to really screw up my math. 806 00:34:59,300 --> 00:35:00,180 All right? 807 00:35:00,180 --> 00:35:00,900 OK. 808 00:35:00,900 --> 00:35:02,820 So now, armed with this, let's talk 809 00:35:02,820 --> 00:35:05,598 about what happens when input prices change. 810 00:35:05,598 --> 00:35:07,140 We talked about with consumer theory, 811 00:35:07,140 --> 00:35:09,510 what happens when the price of pizza and cookies change. 812 00:35:09,510 --> 00:35:12,900 What happens when the price of labor and capital changes? 813 00:35:12,900 --> 00:35:14,200 What does that do? 814 00:35:14,200 --> 00:35:17,470 So let's talk about changes in input prices. 815 00:35:17,470 --> 00:35:18,230 OK. 816 00:35:18,230 --> 00:35:19,310 Let's go to figure 6-4. 817 00:35:22,320 --> 00:35:25,490 And let's look at, with the same production function, 818 00:35:25,490 --> 00:35:27,990 square root of L times K-- we're not changing our production 819 00:35:27,990 --> 00:35:33,180 function-- we're going to change the wage rental ratio. 820 00:35:33,180 --> 00:35:45,090 So line-- we have our initial line, our initial wage rental 821 00:35:45,090 --> 00:35:54,210 ratio, which is that basically you have a wage rate, 822 00:35:54,210 --> 00:35:57,473 but the budget constraint, essentially, that's flatter 823 00:35:57,473 --> 00:35:58,890 is our original budget constraint. 824 00:35:58,890 --> 00:36:01,320 The flatter budget constraint is our original budget constraint. 825 00:36:01,320 --> 00:36:03,570 That's the budget constraint with the price of capital 826 00:36:03,570 --> 00:36:04,860 of $10 and a wage of $5. 827 00:36:04,860 --> 00:36:07,830 And that intersects our isoquant at point x. 828 00:36:07,830 --> 00:36:14,020 So we chose five units of labor. 829 00:36:14,020 --> 00:36:16,960 Now we have a new-- 830 00:36:16,960 --> 00:36:19,463 we chose five units of labor and two and a half machines. 831 00:36:19,463 --> 00:36:20,380 That was our original. 832 00:36:20,380 --> 00:36:21,797 This is sort of a messed up graph. 833 00:36:21,797 --> 00:36:25,560 But our original intersection was at point x. 834 00:36:25,560 --> 00:36:28,270 The cost minimizing combination, the square root 835 00:36:28,270 --> 00:36:33,010 of 12.5 production, was to have five workers and two and a half 836 00:36:33,010 --> 00:36:34,450 machines. 837 00:36:34,450 --> 00:36:37,870 Now let's say the price of workers rises to $10. 838 00:36:37,870 --> 00:36:40,690 The wage rate rises to $10 an hour. 839 00:36:40,690 --> 00:36:44,550 So now, workers and machines cost the same. 840 00:36:44,550 --> 00:36:49,430 What is now the optimal mix of workers and machines? 841 00:36:49,430 --> 00:36:53,610 Well, graphically we know we still 842 00:36:53,610 --> 00:36:56,430 want to produce the square root of 12.5. 843 00:36:56,430 --> 00:36:58,660 So we want to stay tangent to the same isoquant. 844 00:37:02,480 --> 00:37:04,040 So based on-- what we're saying is, 845 00:37:04,040 --> 00:37:08,000 this is as if we said to consumers, keep your utility 846 00:37:08,000 --> 00:37:10,280 changed, change the price. 847 00:37:10,280 --> 00:37:11,442 What do we call that? 848 00:37:11,442 --> 00:37:12,650 Remember what we called that? 849 00:37:12,650 --> 00:37:16,550 Keeping utility constant, changing the price? 850 00:37:16,550 --> 00:37:19,280 Anyone remember what we call that? 851 00:37:19,280 --> 00:37:19,900 Who said that? 852 00:37:19,900 --> 00:37:20,400 All right. 853 00:37:20,400 --> 00:37:21,140 Raise your hand next. 854 00:37:21,140 --> 00:37:21,740 Be proud. 855 00:37:21,740 --> 00:37:23,442 Substitution effect. 856 00:37:23,442 --> 00:37:24,650 That's the substation effect. 857 00:37:24,650 --> 00:37:25,650 It's the same idea here. 858 00:37:25,650 --> 00:37:29,570 We want to know, for a given level of production, 859 00:37:29,570 --> 00:37:32,190 what happens as the price of the inputs change? 860 00:37:32,190 --> 00:37:35,060 And so we shift along the isoquant for point x 861 00:37:35,060 --> 00:37:36,920 to point y. 862 00:37:36,920 --> 00:37:39,860 And you'll see we choose a mix where 863 00:37:39,860 --> 00:37:44,660 we use fewer workers and more machines. 864 00:37:44,660 --> 00:37:51,270 And just as the substitution effect is always nonpositive, 865 00:37:51,270 --> 00:37:54,570 this shift as the wage rate rises, the price 866 00:37:54,570 --> 00:37:56,380 of the good, the x-axis rises. 867 00:37:56,380 --> 00:38:00,540 You will unambiguously use no more, and almost certainly 868 00:38:00,540 --> 00:38:03,700 less, workers. 869 00:38:03,700 --> 00:38:04,700 OK. 870 00:38:04,700 --> 00:38:06,690 And you can see that graphically-- 871 00:38:06,690 --> 00:38:08,420 think about graphically, you're looking 872 00:38:08,420 --> 00:38:11,750 for the tangency between this curve and the line. 873 00:38:11,750 --> 00:38:14,780 The slope of the line just got steeper. 874 00:38:14,780 --> 00:38:17,150 Therefore, you must move to the left on the curve. 875 00:38:17,150 --> 00:38:19,540 It's the same proof as we used the substitution effect, 876 00:38:19,540 --> 00:38:23,020 where substitution effect was always nonpositive. 877 00:38:23,020 --> 00:38:23,550 OK. 878 00:38:23,550 --> 00:38:25,960 It's the same intuition here we use for y. 879 00:38:25,960 --> 00:38:27,730 A rise in the wage rate will lead 880 00:38:27,730 --> 00:38:30,960 you to hire fewer workers and more machines. 881 00:38:30,960 --> 00:38:32,130 Guess what? 882 00:38:32,130 --> 00:38:35,177 You just entered the debate on the minimum wage. 883 00:38:35,177 --> 00:38:37,260 And if you follow the debate in minimum wage, what 884 00:38:37,260 --> 00:38:38,043 do people say? 885 00:38:38,043 --> 00:38:40,210 Well, if you raise the wage you have to pay workers, 886 00:38:40,210 --> 00:38:41,543 they'll be replaced by machines. 887 00:38:41,543 --> 00:38:43,520 That's this. 888 00:38:43,520 --> 00:38:46,250 This is the math-- this is the mathematical and graphical 889 00:38:46,250 --> 00:38:48,590 intuition behind the debate on minimum wage, which we'll 890 00:38:48,590 --> 00:38:50,310 get into later in the semester. 891 00:38:50,310 --> 00:38:51,920 But the basic idea of that debate 892 00:38:51,920 --> 00:38:54,695 is, gee, if you force firms to pay more to workers, 893 00:38:54,695 --> 00:38:56,570 they're going to substitute towards machines. 894 00:38:56,570 --> 00:38:58,790 That's exactly right, in theory. 895 00:38:58,790 --> 00:39:00,810 And practice, there's a lot of complications. 896 00:39:00,810 --> 00:39:03,435 But this gives you the theory of why people make that argument. 897 00:39:03,435 --> 00:39:04,160 Yeah. 898 00:39:04,160 --> 00:39:08,790 AUDIENCE: So in this example, only the wage for workers 899 00:39:08,790 --> 00:39:10,460 [INAUDIBLE] not the machines. 900 00:39:10,460 --> 00:39:11,942 JONATHAN GRUBER: Not the machine. 901 00:39:11,942 --> 00:39:16,220 AUDIENCE: So why does the isocost not 902 00:39:16,220 --> 00:39:18,685 have the same y-intercept? 903 00:39:18,685 --> 00:39:20,060 JONATHAN GRUBER: Ah, great point. 904 00:39:20,060 --> 00:39:22,880 Because here I'm drawing a new-- 905 00:39:22,880 --> 00:39:26,750 I am drawing the isocost that I would use while still producing 906 00:39:26,750 --> 00:39:29,870 square root of 12.5. 907 00:39:29,870 --> 00:39:32,150 So that's it's just the substitution effect. 908 00:39:32,150 --> 00:39:35,917 I'm not drawing the full set of isocosts at the new price. 909 00:39:35,917 --> 00:39:38,000 I'm just saying, to produce the same amount what's 910 00:39:38,000 --> 00:39:40,125 my new-- if I want to produce the same amount, what 911 00:39:40,125 --> 00:39:42,960 combination do I now have to use? 912 00:39:42,960 --> 00:39:43,930 OK? 913 00:39:43,930 --> 00:39:44,551 Yeah. 914 00:39:44,551 --> 00:39:46,910 AUDIENCE: The total cost of production [INAUDIBLE].. 915 00:39:46,910 --> 00:39:49,340 JONATHAN GRUBER: The total cost of production-- let's see. 916 00:39:49,340 --> 00:39:51,540 Yeah, it has to be-- no. 917 00:39:51,540 --> 00:39:52,040 Let's see. 918 00:39:52,040 --> 00:39:53,832 No, total cost doesn't have to be the same. 919 00:39:53,832 --> 00:39:56,690 The total cost used to be five workers at $5 an hour, 920 00:39:56,690 --> 00:39:58,030 that's $25. 921 00:39:58,030 --> 00:39:59,660 So it used to be $50. 922 00:39:59,660 --> 00:40:01,190 Now what is it? 923 00:40:01,190 --> 00:40:03,320 Now it's $70. 924 00:40:03,320 --> 00:40:04,505 The total cost has gone up. 925 00:40:04,505 --> 00:40:06,880 AUDIENCE: So it's not like the budget constraint or the-- 926 00:40:06,880 --> 00:40:07,610 JONATHAN GRUBER: Exactly. 927 00:40:07,610 --> 00:40:08,480 It's not like the budget constraint 928 00:40:08,480 --> 00:40:09,310 where your income is fixed. 929 00:40:09,310 --> 00:40:11,120 That's what's hard about producer theory. 930 00:40:11,120 --> 00:40:13,430 Because basically, the budget constraint 931 00:40:13,430 --> 00:40:15,950 was sort of asking, keeping your budget fixed. 932 00:40:15,950 --> 00:40:18,890 This is like asking, keeping your total production fixed. 933 00:40:18,890 --> 00:40:21,560 And so now you have to pay more to get 934 00:40:21,560 --> 00:40:23,420 that level of production. 935 00:40:23,420 --> 00:40:24,260 OK? 936 00:40:24,260 --> 00:40:25,400 Good questions. 937 00:40:25,400 --> 00:40:26,150 OK. 938 00:40:26,150 --> 00:40:29,770 Now, ultimately what does this lead to? 939 00:40:29,770 --> 00:40:31,890 So that gives us our change in input prices. 940 00:40:31,890 --> 00:40:33,830 Other questions about that? 941 00:40:33,830 --> 00:40:36,240 Now, remember I said at the beginning of the lecture, 942 00:40:36,240 --> 00:40:38,810 we are first going to solve for what 943 00:40:38,810 --> 00:40:40,720 is the cost minimizing combination 944 00:40:40,720 --> 00:40:42,500 of inputs for a given quantity? 945 00:40:42,500 --> 00:40:43,880 We derived that up there. 946 00:40:43,880 --> 00:40:45,110 It's half as much-- 947 00:40:45,110 --> 00:40:46,880 going back to our old prices, it's 948 00:40:46,880 --> 00:40:49,010 half as much capital as labor. 949 00:40:49,010 --> 00:40:51,680 Now we want to ask, how does your cost 950 00:40:51,680 --> 00:40:54,080 change as the quantity changes? 951 00:40:54,080 --> 00:40:58,820 And we call that the long run expansion path. 952 00:41:02,740 --> 00:41:04,570 The long run expansion path, which 953 00:41:04,570 --> 00:41:08,780 is, how do your costs expand as you produce more? 954 00:41:08,780 --> 00:41:11,580 And we see that in figure 6-5. 955 00:41:11,580 --> 00:41:14,680 In figure 6-5, we show the particular case 956 00:41:14,680 --> 00:41:16,720 of a linear long run expansion path. 957 00:41:16,720 --> 00:41:18,520 That's what you get in this example. 958 00:41:18,520 --> 00:41:21,110 It's a particular case. 959 00:41:21,110 --> 00:41:26,660 What this case says is, at any given level of production, 960 00:41:26,660 --> 00:41:30,740 the optimal mix of labor and capital is the same. 961 00:41:30,740 --> 00:41:34,490 In other words, you always want to have-- 962 00:41:34,490 --> 00:41:38,340 essentially, given the price of labor 963 00:41:38,340 --> 00:41:40,880 is half the price of capital, you always 964 00:41:40,880 --> 00:41:44,020 want to have twice as many workers as machines. 965 00:41:44,020 --> 00:41:46,420 So if you want to produce square root of 12.5, 966 00:41:46,420 --> 00:41:48,540 you want five workers and two and a half machines. 967 00:41:48,540 --> 00:41:50,550 If you want to produce square root of 50, 968 00:41:50,550 --> 00:41:52,110 you want 10 workers and 5 machines. 969 00:41:52,110 --> 00:41:54,630 If you want to produce square root of 112.5, 970 00:41:54,630 --> 00:41:57,420 you want 15 workers and 7 and 1/2 machines. 971 00:41:57,420 --> 00:42:00,180 So the long run-- given this production function, 972 00:42:00,180 --> 00:42:02,040 the long run expansion path is linear. 973 00:42:02,040 --> 00:42:05,340 You always want the same ratio of workers to machines. 974 00:42:05,340 --> 00:42:06,869 Yeah. 975 00:42:06,869 --> 00:42:08,681 AUDIENCE: [INAUDIBLE] consumer and firms, 976 00:42:08,681 --> 00:42:10,290 is the reason why we don't necessarily 977 00:42:10,290 --> 00:42:13,288 have a strict budget, per se, and then isn't 978 00:42:13,288 --> 00:42:15,455 the idea that if we really want increase production, 979 00:42:15,455 --> 00:42:17,080 we can take a loan out? 980 00:42:17,080 --> 00:42:18,140 JONATHAN GRUBER: This is what I tried to say. 981 00:42:18,140 --> 00:42:19,450 It's sort of-- I always say it over here, but it's hard, 982 00:42:19,450 --> 00:42:20,742 and we have to come back to it. 983 00:42:20,742 --> 00:42:22,840 The reason producer theory is harder 984 00:42:22,840 --> 00:42:25,960 is because we're not given a fixed constant we 985 00:42:25,960 --> 00:42:27,340 are with consumers. 986 00:42:27,340 --> 00:42:28,920 Consumers, we're saying, look-- 987 00:42:28,920 --> 00:42:31,420 you've got a resource, you've got to constrain maximization. 988 00:42:31,420 --> 00:42:34,060 We haven't constrained the maximization yet. 989 00:42:34,060 --> 00:42:36,350 There's another constraint we need. 990 00:42:36,350 --> 00:42:39,933 They have an extra degree of freedom relative to consumers. 991 00:42:39,933 --> 00:42:42,100 Now, in fact, consumers have degree of freedom, too. 992 00:42:42,100 --> 00:42:44,267 When you grow up, your parents don't give you money. 993 00:42:44,267 --> 00:42:45,434 You decide how much to make. 994 00:42:45,434 --> 00:42:47,267 So in reality, consumers-- you can do this-- 995 00:42:47,267 --> 00:42:49,027 will have the same degrees of freedom. 996 00:42:49,027 --> 00:42:50,860 But we started with the easy consumer theory 997 00:42:50,860 --> 00:42:53,603 case, where you constrict-- we took away a degree of freedom. 998 00:42:53,603 --> 00:42:55,270 Now we're writing it back, which is, you 999 00:42:55,270 --> 00:42:56,740 can choose how much to produce. 1000 00:42:56,740 --> 00:42:59,720 Like, you being able choose your income as a consumer. 1001 00:42:59,720 --> 00:43:01,303 That leads to long run expansion path. 1002 00:43:01,303 --> 00:43:02,803 Let me go on, because I want to make 1003 00:43:02,803 --> 00:43:04,090 sure I get through this stuff. 1004 00:43:04,090 --> 00:43:04,780 OK? 1005 00:43:04,780 --> 00:43:08,990 Now, the long run expansion path does not have to be linear. 1006 00:43:08,990 --> 00:43:14,090 So think about-- look at figure 6-5b and 6-5c. 1007 00:43:14,090 --> 00:43:19,870 So 6-5b is a long run expansion path for a production function 1008 00:43:19,870 --> 00:43:23,680 such that capital becomes less productive the more you 1009 00:43:23,680 --> 00:43:24,200 produce. 1010 00:43:24,200 --> 00:43:26,200 I don't have the example of production function. 1011 00:43:26,200 --> 00:43:28,300 But when you write down production functions which 1012 00:43:28,300 --> 00:43:31,180 have the feature that the more you produce the less 1013 00:43:31,180 --> 00:43:33,728 productive capital becomes, the less 1014 00:43:33,728 --> 00:43:35,645 each additional unit capital helps [INAUDIBLE] 1015 00:43:35,645 --> 00:43:38,110 additional unit of workers. 1016 00:43:38,110 --> 00:43:40,360 So you know, we could think of this roughly as 1017 00:43:40,360 --> 00:43:43,600 sort of like a fast food restaurant. 1018 00:43:43,600 --> 00:43:45,300 That kind of-- you know, each addition-- 1019 00:43:45,300 --> 00:43:47,290 that basically, there's so much stuff 1020 00:43:47,290 --> 00:43:49,420 to do where workers can efficiently share tasks 1021 00:43:49,420 --> 00:43:50,232 and things. 1022 00:43:50,232 --> 00:43:52,690 Each additional worker-- that the marginal product of labor 1023 00:43:52,690 --> 00:43:54,670 essentially diminishes less quickly 1024 00:43:54,670 --> 00:43:58,260 than the marginal product of capital. 1025 00:43:58,260 --> 00:44:00,450 On the other hand, in figure 6-5c 1026 00:44:00,450 --> 00:44:04,440 we can have a long run expansion path where labor becomes less 1027 00:44:04,440 --> 00:44:06,640 productive relative to capital. 1028 00:44:06,640 --> 00:44:09,300 Think of it as like heavy machinery, 1029 00:44:09,300 --> 00:44:12,100 where basically all workers can do is run the machine. 1030 00:44:12,100 --> 00:44:13,410 So that second worker-- 1031 00:44:13,410 --> 00:44:16,215 workers don't really do much but sit there and flip a switch. 1032 00:44:16,215 --> 00:44:17,840 You need the worker to flip the switch. 1033 00:44:17,840 --> 00:44:18,632 That's all they do. 1034 00:44:18,632 --> 00:44:21,210 So the second worker, you're already flipping the switch. 1035 00:44:21,210 --> 00:44:23,543 So really, adding more machines is a more productive way 1036 00:44:23,543 --> 00:44:25,880 to expand the output. 1037 00:44:25,880 --> 00:44:27,570 None of these is right or wrong. 1038 00:44:27,570 --> 00:44:32,100 We're just saying that the shape of this expansion path 1039 00:44:32,100 --> 00:44:35,700 can basically vary with how much-- 1040 00:44:35,700 --> 00:44:38,830 with different production functions. 1041 00:44:38,830 --> 00:44:41,730 But they're all the same idea. 1042 00:44:41,730 --> 00:44:47,700 Now, so basically, that tells you-- 1043 00:44:47,700 --> 00:44:49,980 but here's the bottom line that we wanted to come to. 1044 00:44:49,980 --> 00:44:54,300 That long run expansion path is a long run cost curve. 1045 00:44:57,170 --> 00:45:00,650 So ultimately, if you want to ask, 1046 00:45:00,650 --> 00:45:04,250 how do my costs vary with how much I produce, 1047 00:45:04,250 --> 00:45:06,370 this curve tells you. 1048 00:45:06,370 --> 00:45:08,870 Because what it does, it says, for every level of production 1049 00:45:08,870 --> 00:45:12,190 I'll tell you the optimal combination of L and K. 1050 00:45:12,190 --> 00:45:15,280 Given the price of L and K, that will tell you the costs. 1051 00:45:15,280 --> 00:45:18,170 And so you trace out the costs with every level of production. 1052 00:45:18,170 --> 00:45:19,570 This is your cost curve. 1053 00:45:19,570 --> 00:45:21,790 This long run expansion path tells you 1054 00:45:21,790 --> 00:45:24,268 what the costs are for every level of production. 1055 00:45:24,268 --> 00:45:25,810 And it tells you that, because you've 1056 00:45:25,810 --> 00:45:29,170 made-- you're doing the efficient level of production. 1057 00:45:29,170 --> 00:45:31,710 That's what the long run expansion path is telling you. 1058 00:45:31,710 --> 00:45:32,210 OK. 1059 00:45:32,210 --> 00:45:33,530 This is hard. 1060 00:45:33,530 --> 00:45:35,205 I'm about to make it harder. 1061 00:45:35,205 --> 00:45:36,580 Which is, we're now going to talk 1062 00:45:36,580 --> 00:45:40,715 about the relationship between short run costs and long run 1063 00:45:40,715 --> 00:45:41,215 costs. 1064 00:45:43,830 --> 00:45:49,110 And the key insight is that long run costs are everywhere 1065 00:45:49,110 --> 00:45:50,745 lower than short run costs. 1066 00:45:50,745 --> 00:45:53,370 Without looking at the figure-- because the figure doesn't help 1067 00:45:53,370 --> 00:45:54,150 with this-- 1068 00:45:54,150 --> 00:45:55,740 why does that make sense? 1069 00:45:55,740 --> 00:45:58,830 Why our long run costs-- 1070 00:45:58,830 --> 00:46:02,430 why, if you can optimize over the long run, 1071 00:46:02,430 --> 00:46:03,960 will you always have costs that are 1072 00:46:03,960 --> 00:46:09,670 no higher, and in general lower, than optimizing the short run? 1073 00:46:09,670 --> 00:46:10,310 Yeah. 1074 00:46:10,310 --> 00:46:13,330 AUDIENCE: [INAUDIBLE] already had the right capital. 1075 00:46:13,330 --> 00:46:14,705 JONATHAN GRUBER: Because you have 1076 00:46:14,705 --> 00:46:15,965 an extra degree of freedom. 1077 00:46:15,965 --> 00:46:17,590 I think that's LeChatelier's Principle. 1078 00:46:17,590 --> 00:46:19,480 Is that right, for the chemists among us? 1079 00:46:19,480 --> 00:46:21,280 That basically, like-- essentially, 1080 00:46:21,280 --> 00:46:22,993 an extra degree of freedom means, 1081 00:46:22,993 --> 00:46:24,910 the more you can optimize over, the better you 1082 00:46:24,910 --> 00:46:25,822 can do in optimizing. 1083 00:46:25,822 --> 00:46:27,280 In the short run you're constrained 1084 00:46:27,280 --> 00:46:28,923 by the size of the building. 1085 00:46:28,923 --> 00:46:30,340 In the long run, you could choose. 1086 00:46:30,340 --> 00:46:32,470 So let's-- to see that, let's go to figure 6-6. 1087 00:46:34,975 --> 00:46:36,100 This is a confusing figure. 1088 00:46:36,100 --> 00:46:38,770 So bear with me as I walk you through it. 1089 00:46:38,770 --> 00:46:39,430 OK? 1090 00:46:39,430 --> 00:46:43,420 Consider a firm with three possible sizes of plants. 1091 00:46:43,420 --> 00:46:45,070 They're going to build a plant. 1092 00:46:45,070 --> 00:46:46,803 So the capital here is the building. 1093 00:46:46,803 --> 00:46:48,220 And there's three possible sizes-- 1094 00:46:48,220 --> 00:46:49,420 small, medium, and large. 1095 00:46:52,310 --> 00:46:57,390 The small plant has the curve SRAC1. 1096 00:46:57,390 --> 00:46:58,840 What does that curve mean? 1097 00:46:58,840 --> 00:47:00,840 That means that the small plant-- 1098 00:47:00,840 --> 00:47:02,430 I'm sorry, the small plant is SRAC2, 1099 00:47:02,430 --> 00:47:07,160 the medium plant is SRAC2, and the large plant has SRAC3. 1100 00:47:07,160 --> 00:47:10,500 Compare SRAC1 to SRAC3. 1101 00:47:10,500 --> 00:47:15,710 What this is saying is, for small quantities of production, 1102 00:47:15,710 --> 00:47:18,780 SRAC1 lies below SRAC3. 1103 00:47:21,910 --> 00:47:25,300 For small quantities production, if you extend SRAC3 out, 1104 00:47:25,300 --> 00:47:30,960 you see at levels of production like q1 or even q2, 1105 00:47:30,960 --> 00:47:34,220 SRAC3 is way above SRAC1. 1106 00:47:34,220 --> 00:47:37,590 When you go to a level of production like q3, 1107 00:47:37,590 --> 00:47:39,820 SRAC1, if you extend that dashed line out, 1108 00:47:39,820 --> 00:47:43,310 is going to be much, much higher than SRAC3. 1109 00:47:43,310 --> 00:47:47,100 So the right-- and SRAC2 is in between. 1110 00:47:47,100 --> 00:47:50,380 So essentially, for different levels of production 1111 00:47:50,380 --> 00:47:54,050 these give the different optimal short run cost curves. 1112 00:47:54,050 --> 00:47:57,550 In the long run, you get to choose. 1113 00:47:57,550 --> 00:47:59,220 So the long run average cost curve 1114 00:47:59,220 --> 00:48:03,690 is the lower envelope of the short run average cost curves. 1115 00:48:03,690 --> 00:48:06,270 Because in the long run you say, well, here's 1116 00:48:06,270 --> 00:48:07,680 my production level. 1117 00:48:07,680 --> 00:48:08,920 I know in the long run-- 1118 00:48:08,920 --> 00:48:11,250 so if I know I'm going to build a lot of things, 1119 00:48:11,250 --> 00:48:13,170 I choose SRAC3. 1120 00:48:13,170 --> 00:48:14,790 I choose the biggest plant. 1121 00:48:14,790 --> 00:48:17,010 If I know my production is going to be low, 1122 00:48:17,010 --> 00:48:18,750 I choose the smallest plant. 1123 00:48:18,750 --> 00:48:20,280 But I can optimize in the long run 1124 00:48:20,280 --> 00:48:24,120 by choosing the right sized plant for my production level. 1125 00:48:24,120 --> 00:48:24,683 This is hard. 1126 00:48:24,683 --> 00:48:26,100 And I'm almost out of time, so let 1127 00:48:26,100 --> 00:48:29,040 me end with an example that perfectly illustrates this. 1128 00:48:29,040 --> 00:48:30,240 Tesla. 1129 00:48:30,240 --> 00:48:30,810 Elon Musk. 1130 00:48:30,810 --> 00:48:33,510 Everybody's favorite guy these days. 1131 00:48:33,510 --> 00:48:37,230 Tesla, when they came out, had to decide 1132 00:48:37,230 --> 00:48:38,655 how big a plant to build-- 1133 00:48:38,655 --> 00:48:39,780 how many batteries to make. 1134 00:48:39,780 --> 00:48:43,140 Batteries are the key [INAUDIBLE] Teslas. 1135 00:48:43,140 --> 00:48:46,980 And they expected to make-- to have demand for 20,000 cars 1136 00:48:46,980 --> 00:48:49,050 by the year 2017. 1137 00:48:49,050 --> 00:48:52,740 So they built a plant like SRAC1. 1138 00:48:52,740 --> 00:48:54,960 They built a plant that was the efficient plant 1139 00:48:54,960 --> 00:48:57,360 to produce 20,000 cars. 1140 00:48:57,360 --> 00:49:01,557 The problem is, demand was for 200,000 cars. 1141 00:49:01,557 --> 00:49:03,640 And as a result, there's a three-year waiting list 1142 00:49:03,640 --> 00:49:05,032 to get Teslas. 1143 00:49:05,032 --> 00:49:07,240 It turned out that was not the right size to produce. 1144 00:49:07,240 --> 00:49:09,400 They lost money-- relative to the optimum. 1145 00:49:09,400 --> 00:49:10,150 They made money. 1146 00:49:10,150 --> 00:49:11,380 Musk is incredibly rich. 1147 00:49:11,380 --> 00:49:14,005 But they didn't do what was most efficient given the underlying 1148 00:49:14,005 --> 00:49:14,810 demand. 1149 00:49:14,810 --> 00:49:18,100 But now, Musk can re-optimize. 1150 00:49:18,100 --> 00:49:19,900 Now he's saying, wait a second. 1151 00:49:19,900 --> 00:49:21,580 People want way more cars. 1152 00:49:21,580 --> 00:49:23,200 Well, producing them at the tiny plant 1153 00:49:23,200 --> 00:49:24,400 was exorbitantly expensive. 1154 00:49:24,400 --> 00:49:25,990 I had to run it over and overtime-- 1155 00:49:25,990 --> 00:49:27,000 pay workers overtime. 1156 00:49:27,000 --> 00:49:28,670 To produce 200k cars in that tiny plant 1157 00:49:28,670 --> 00:49:30,250 just was exorbitantly expensive. 1158 00:49:30,250 --> 00:49:32,290 That's if you take that dashed line and extend it way the hell 1159 00:49:32,290 --> 00:49:32,950 up. 1160 00:49:32,950 --> 00:49:36,950 The SRAC1 extended way the hell up, incredibly expensive. 1161 00:49:36,950 --> 00:49:38,500 So what is Musk doing now? 1162 00:49:38,500 --> 00:49:41,710 Building the largest battery plant in the world. 1163 00:49:41,710 --> 00:49:43,870 In Nevada, he is building a battery plant 1164 00:49:43,870 --> 00:49:47,200 that can produce batteries for 500,000 cars. 1165 00:49:47,200 --> 00:49:51,560 So he shifted from SRAC1 to SRAC3. 1166 00:49:51,560 --> 00:49:53,660 He's now saying in the long run, I 1167 00:49:53,660 --> 00:49:55,660 can more-- if I'm going to produce 200,000 cars, 1168 00:49:55,660 --> 00:49:59,020 I can do that more efficiently with a giant battery plant. 1169 00:49:59,020 --> 00:50:00,563 And that's what he's doing. 1170 00:50:00,563 --> 00:50:01,480 So he's re-optimizing. 1171 00:50:01,480 --> 00:50:04,798 Now, what if Musk is wrong? 1172 00:50:04,798 --> 00:50:07,090 What if it turns out Teslas suck and people are like, I 1173 00:50:07,090 --> 00:50:07,830 don't want them anymore? 1174 00:50:07,830 --> 00:50:10,205 Someone else-- or, you know, Chevy finally figures it out 1175 00:50:10,205 --> 00:50:11,888 and makes a good electric car. 1176 00:50:11,888 --> 00:50:13,930 Then what's going to happen is he's going to have 1177 00:50:13,930 --> 00:50:16,720 made a mistake in the long run. 1178 00:50:16,720 --> 00:50:19,750 Then the third period, he'll go back to a smaller plant again. 1179 00:50:19,750 --> 00:50:22,450 But he always can do what's efficient in the long run, 1180 00:50:22,450 --> 00:50:24,130 given the underlying demand. 1181 00:50:24,130 --> 00:50:27,400 So Tesla is an example of this sort of long run, short run 1182 00:50:27,400 --> 00:50:27,937 dichotomy. 1183 00:50:27,937 --> 00:50:29,770 Anyway, it's a lot of stuff for one lecture. 1184 00:50:29,770 --> 00:50:32,350 We'll come back next time, talk more about costs. 1185 00:50:32,350 --> 00:50:35,730 And then we'll start getting into competition.