Welcome back. Let's turn in the second session of the week to what happens in the long run. How do we minimize the cost of producing any given output level in the long run perspective where we're not stuck with any particular level of input usage. We can vary the different inputs that go into producing a final output. We'll introduce the concept of an isocost line, which basically like a budget constraint, represents all the different ways you can spend a fixed amount of money on inputs. And then we'll turn to developing what is known as the golden rule of cost minimization. How do we minimize the cost of producing any given output level? Let's turn to figure 8.4. And for those of you that are following along in the book or the PDF versions, what we're covering this week is sections 8.4 to 8.9 of chapter eight and then also sections 9.1 to 9.5 of chapter nine, just as an aside. Figure 8.4 in the left most panel shows a series of isocost lines. All the ways we can take a certain amount of total expenditure, total cost represented by TC and spend it across two inputs. It's very simplified scenario. The input's been capital and labor. And what we represent as being the cost of labor per unit is w or the wage rate. And r for the price of capital, the run all rate of capital. So lets say we start it of with TC 1, that was the total dollar amount we could spend on capital and labor, at one extreme we could blow it all on capital. So at one endpoint we divide TC1 by the price of the capital input. At the other extreme we divide TC1 by the wage rate, the price of labor, or any combination in between. So very similar to what we saw earlier when we were studying consumer theory budget constraints. And then there are a series of isocost lines higher then TC1 if we have more money to spend on these two inputs. What the rightmost panel shows, is now we're combining isocost with isoquants. And asking the question if we had a certain amount of expenditure that we can make on inputs, what's the highest level of output we could achieve? And it will turn out that this is the same exact problem as minimizing the cost of producing any given level of final output. So let's look in particular at the middle isocost line, the one involved with total input expenditure of TC2. Given this input expenditure, what's the most output we can achieve? And what we'll see there is we can just reach isoquant 6, with expenditure TC2. That is the point, at point b, that nicking point, that tangentcy point, where we've maximized output per given total expenditure. Now note that same TC2, we could attain a higher level, we could attain, sorry, a lower level of output at point d. We could reach isoquant 3, but point d doesn't involve the maximum output we can attain with a given total expenditure of TC2. Now think about it in inverse fashion. And we want to ask the question, what's the minimum way, with the minimum cost way to achieve a certain output level, so we thought of it in terms of total output. We want to achieve isoquant 6. What's the least costly way to get to isoquant 6? It will give us the same answer. That will happen in point b, where we're spending TC2 on the two inputs of labor and capital. It's true that point e's also a solution, we could spend TC3 more total expenditure on inputs to achieve that same isoquant, but we be spending more money at TC3 than using TC2. So point binvolves the least costly way to produce an output level of six. Points a, b and c identify the least costly way to produce successively higher levels of total output. Point a's where we can produce an output of three at lowest cost. Point b, an output level of six. Point c, an output level of nine. And each of them involve, as you can see, a tangency point. The isoquant is, has the same slope as the isocost line that just allows us to reach that isoquant. And if we connect all those, all those intersections where we reach the highest possible isoquant with the given isocost line, we get what is known as an expansion pack. How if we increase input expenditure, what increased amount of outputs we can achieve. Now, we know that at these expansion point, expansion path points, the slopes of the isoquants and isocosts are equal. We're just nicking the highest possible isoquant with a given isocost. What does that end up meaning? And let's turn to the next page. The slope of the isoquant as we saw last week is the marginal rate of technical substitution. It tells you the rate at which you have to give up capital in exchange for labor and keep output the same. The slope of the isocost line is the price of the input on the horizontal axis, over the price of the input on the vertical axis. So in this simple case its the way trade over the rental rate of capital. Now let's look at the left side of the top equation. If we have to give up two units of capital for one unit of labor to maintain output at the same level. That means that each unit of labor is twice as productive as each unit of capital. The marginal rate of technical substitution as we saw last week is also the same as the marginal productivity ratios, but flipped around. Labor, marginal productivity of labor over marginal productivity of capital. And then, let's in the final line rearrange things further. What that means is at the least costly way to produce a given output level, the marginal product of labor divided by its wage rate is the same as the marginal product to capital divided by its input price, the rental rate of capital. What do these two final ratios mean? Say where we're using labor that its marginal product is ten units of output. And the way trade of labor is $5 per unit. What MPL over w means is to get ten additional units of output we're spending $5. So per dollar we spend on labor we're getting two units of output. At the tangentcy points we want these productivity to price input price ratios to be equal. And that's what we're going to call the golden rule of cost minimization. And think about what that means, that these ratios have to be equal. It means per dollar we spend on the different inputs we're using, the rate of return on that dollar has to be equal. So if I'm Larry Ellison and running Oracle, and I have to on one side, spend either money on software engineers or on the other side on MBA graduates, I want to make sure the per dollar I spend in software engineers equals the return in productivity per dollar I spend on MBAs. It's as if I'm investing in two banks. I want to keep reallocating until the rates of return I earn on those two banks, money invested in those two banks, is the same. Now, a few examples of cost minimization at work. American Airlines during the early days of deregulation in the United States provides a wonderful example. they were run by CEO at the time Robert Crandall where they literally left no stone unturned to make sure they were minimizing production cost. during that time period, none of the American Airlines planes were painted, they not only saved on paint and the only thing that was painted were stripes and certain insignias on the tail and the name American on the fuselage. They figured they could save $12,000 on average per plane by not having that added weight of the paint flying through the air. They figured out a way too, to shed 1500 pounds per flight. Smaller pillows, different galleys stripping out certain metal from the interior components inside the, the fuselage. They figured they could save an additional $22,000 per plane by, by stripping out 1,500 pounds per plane. Crandall once figured out too, if he took the olives out of the first class salads, he was leafing through the trash one time and noticed that people weren't eating the olives. So they figured out they could save $72,000 a year. The marginal rate of return per the olive input wasn't worth the expenditure the company was making on it. So none of the salads in first class started having olives after a certain point. Crandall even fired a watchdog one time. As the story goes before he was CEO he was the CFO of the company and was reviewing different divisions and how they were doing and noticed in one of their Caribbean units that they were hiring a watchman full time. And Crandall questioned, do we really need that money on a watchmen? Couldn't we hire somebody part time? And so the unit had agreed, we'll hire the watchmen, reduce his hours, go part time. And next year the budget review happened again. Crandall was looking at this line item in this Caribbean unit, and said well, do we really need a watchman? Could we hire a, a dog instead? It's a lot cheaper. So, they ended up getting rid of the watchman and hired the dog. Next year, reviewing the budgets again, Crandall said, well, do we really need the dog? Can't we just hire a tape recorder and record a dog snarling and that did the trick. So, companies have a strong incentive to minimize the cost of production, because the more you can minimize cost, it translates into higher profit. And we'll still need to determine what output level once we've gone through how do we minimize cost of production