Welcome to week six of the Power of Markets course. We're going to pick up where we left off last week, focusing on cost minimization. We first looked at technologies, productivity matters. And now we've started to develop cost curves. We'll end up at the end of the week also introducing one extreme form of market structure, that of perfect competition. And after we've worked through the logistics of how firms can minimize the cost at any particular output level, we still have to then turn to what output level maximizes profit. What price output combination, perfect competition will be one extreme, market structure, and then we'll look at other of market structures.competitive, monopolistic market structures. They, they wondered the tie, I'm very proud to wear this tie. Especially in light of teaching this Coursera course. We have over 130 different countries represented among the students participating in the course. So, glance through Zmax where we've been plotting where you're all from, and it's a wonderful collections of different locations around the globe. If you haven't yet registered I would encourage you to either take the demographic survey or follow one of the threads that points to the Zmap mapping. This first session we're going to look at short-run cost curves, and look at ways that we can think about them more deeply, geometrically. We're going to look at marginal cost, average cost. We're going to look at the relationship between marginal-average cost curves. We'll see there'll be a very similar connection as what we saw between average product and marginal product. And then, we'll close the session with looking at the geometry of cost curves. Now let me turn to marginal cost and average variable cost. In a short run setting, these cutrves reflect the influence of the variable input. Short run again we assume that some inputs are fixed. In a very simple two factor model, we've been assuming capital is fixed and labor is variable. In this particular simplified setting, what marginal cost is, then, is how much total variable cost changes per change in output, per change in q. And if there's only one variable input of labor, total variable cost changes by the amount that we increase labor, the change in alt produce the additional output, the additional change in q. And we've gotta multiply that change in labor by the wage rate, by the price of that input, which is assumed to be fixed. And represented by the letter w. And then if we, if we, do some mathematics with that equation, what we end up with is marginal cost as the wage rate divided by the marginal product of labor. we divide both the top and the bottom by the change in labor. We end up with a denominator that's the change in q over the change in l. Which is the same as the marginal product of labor. Average variable cost similarly is total variable cost divided by quantity, and total variable cost is just the wage rate times labor since, again labor's the variable input. We divide numerator and denominator of this bottom equation by l, the amount of labor, and what we end up with is the wage rate divided by the average product of labor. because the the average product of labor is just q divided by l. So what we can see with these two equations, is that in the short run, mapped marginal cost an average variable cost, both are driven by the law of diminishing returns. If marginal product of labor is diminishing, that means that the marginal cost curve will be rising. We'll be dividing that Input price w by a smaller and smaller number, so marginal cost, the ratio of the two would be rising. And for the law of diminishing returns holds, average product of labor, the average will also get driven up. will, sorry, will also get pulled down by the following marginal pract of labor. And so we'll be dividing the wage rate by a smaller and smaller average product of labor amount. And so we're dividing that same wage rate by smaller and smaller average product. That will mean that average variable cost will also be increasing as we try to scale up output. So [INAUDIBLE] returns that we learned about last week has an important has the driving role in determining the shapes of marginal costs and average variable cost. Now lets look at figure 8.3 geometrically at how we can depict in the top panel, we're looking at one of the total cost curves. we could do the same with the total cost, but in this case we're going to focus on total variable cost. Note something interesting about this total variable cost. all total variable costs start at a height of zero. So if you produce zero, there are no variable costs you incur. Total costs in the short run starts at a higher level if there are fixed costs involved in the production process. And this total variable cost first diminishes in slope and then starts rising in slope. The bottom panel depicts the marginal costs and average variable costs, the curves associated with the total variable cost depicted in the top panel. Let's see how this works. To figure out average variable cost and total variable cost, what we need to do is connect the origin in the top panel at any point on the total variable cost curve. So let's say we're looking at point A. If we connect the origin to point A. The slope of that cord is 60 divided by the output of three. So average variable cost, the rise over one of that cord is $20. And that's the same, or sorry my eyesight's a little week on this. It's $65 divided by three. So that, that average turns out to be $21.67, or the height of the average variable cost curve in the bottom panel. Now note what happens to slope of this cord as we move further out the total variable cost curve. The slope diminishes of the cord as we move to point b, and it reaches its minimum at point c where the chord just nicks the outside of the total variable cost curve. Where the cord is at a minimum, that's where average variable cost has a minimum height in the below panel. At an output level of five, we're dividing $100 in variable costs by five. $20 is the average variable cost curve, average variable cost at that point. That's represented by the height of the average variable cost curve in the bottom most panel. And beyond that point, if we connect the origin to higher points on the total variable cost curve. The slope of those cords continue to rise. So when we get to point d, average variable cost, the slope of the quart is higher than it is at point c. And that's where represented on the below panel at an output of six. Average variable cost has a higher, is A higher amount than it is at an output level of five. Marginal cost is represented by the slope, or the total variable cost at any particular point. It's not the cord from the origin, but it's the slope at a particular point on the total variable cost curve. So note what happens to the slope. It, it first diminishes, there's some advatages to teamwork to specialization and then because of the law of diminishing returns the slope of the total variable cost curve starts to speed up. One final point. Marginal cost at point c in the top panel is the same as the slope of the cord from the origin. So where average variable cost is at its minimum, marginal cost equals average variable cost. At point c in the below panel. And this is just the same average marginal relationship we saw before. And if we look at the below panel, when marginal cost comes in below the average variable cost, average variable cost is still falling. Up to an output of five. Beyond an output of five when marginal cost is higher than average variable cost, average variable cost is being pulled up by the greater marginal incremental cost. And where marginal comes in right at the level of average variable cost, average variable cost has bottomed out. So same exact relationship we saw with marginal product and average product shows up here between marginal cost and average variable cost. We'll pick up from there in the next session.
