0:04

We're going to pick up where we left off last week, focusing on cost minimization.

Â We first looked at technologies, productivity matters.

Â And now we've started to develop cost curves.

Â We'll end up at the end of the week also

Â introducing one extreme form of market structure, that of perfect competition.

Â And after we've worked through the logistics

Â of how firms can minimize the cost at

Â any particular output level, we still have to

Â then turn to what output level maximizes profit.

Â What price output combination, perfect competition

Â will be one extreme, market structure,

Â and then we'll look at other

Â of market structures.competitive, monopolistic market structures.

Â 0:54

They, they wondered the tie, I'm very proud to wear this tie.

Â Especially in light of teaching this Coursera course.

Â We have over 130 different countries represented

Â among the students participating in the course.

Â So, glance through Zmax where we've been plotting where you're all

Â from, and it's a wonderful collections of different locations around the globe.

Â If you haven't yet registered

Â I would encourage you to either take the demographic survey or

Â follow one of the threads that points to the Zmap mapping.

Â This first session we're going to look at short-run cost curves, and look at

Â ways that we can think about them more deeply, geometrically.

Â We're going to look at marginal cost, average cost.

Â We're going to look at the relationship between

Â marginal-average cost curves.

Â We'll see there'll be a very similar connection as

Â what we saw between average product and marginal product.

Â And then, we'll close the session with looking at the geometry of cost curves.

Â Now let me turn to marginal cost and average

Â variable cost. In a short run setting, these cutrves

Â reflect the influence of the variable input.

Â Short run again we assume that some inputs are fixed.

Â In a very simple two factor model, we've

Â been assuming capital is fixed and labor is variable.

Â 2:25

In this particular simplified setting, what marginal cost is,

Â then, is how much total variable cost changes per change in output,

Â per change in q.

Â And if there's only one variable input of

Â labor, total variable cost changes by the amount

Â that we increase labor, the change in alt

Â produce the additional output, the additional change in q.

Â And we've gotta multiply that change in labor by the wage rate, by the price of

Â that input, which is assumed to be fixed. And represented by the letter w.

Â And then if we, if we, do some mathematics with that equation, what we end

Â up with is marginal cost as the wage rate divided by the marginal product of labor.

Â we divide both the top and the bottom by the change in labor.

Â We end up with a denominator that's the change in q over the change in l.

Â Which is the same as the marginal product of labor.

Â 3:56

So what we can see with these two equations, is that in the short run,

Â mapped marginal cost an average variable cost, both

Â are driven by the law of diminishing returns.

Â If marginal product of labor is diminishing, that

Â means that the marginal cost curve will be rising.

Â We'll be dividing that Input

Â price w by a smaller and smaller number, so

Â marginal cost, the ratio of the two would be rising.

Â 4:26

And for the law of diminishing returns holds, average

Â product of labor, the average will also get driven up.

Â will, sorry, will also get pulled down by the following marginal pract of labor.

Â And so we'll be dividing the wage rate by

Â a smaller and smaller average product of labor amount.

Â And so we're dividing that same wage rate by smaller and smaller average product.

Â That will mean that average variable cost will also

Â be increasing as we try to scale up output.

Â So

Â [INAUDIBLE]

Â returns that we learned about last week has an important has the

Â driving role in determining the shapes of marginal costs and average variable cost.

Â 5:11

Now lets look at figure 8.3 geometrically at how we can depict

Â in the top panel, we're looking at one of the total cost curves.

Â we could do the same with the total cost, but in this case we're going to focus on

Â total variable cost.

Â 5:27

Note something interesting about this total variable cost.

Â all total variable costs start at a height of zero.

Â So if you produce zero, there are no variable costs you incur.

Â Total costs in the short run starts at a higher

Â level if there are fixed costs involved in the production process.

Â 7:30

At an output level of five, we're dividing $100

Â in variable costs by five.

Â $20 is the average variable cost curve, average variable cost at that point.

Â That's represented by the height of the average

Â variable cost curve in the bottom most panel.

Â 7:51

And beyond that point, if we connect the origin

Â to higher points on the total variable cost curve.

Â The slope of those cords continue to rise.

Â So when we get to point

Â d, average variable cost, the slope of the quart is higher than it is at point c.

Â 8:21

Marginal cost is represented by the slope, or the total variable

Â cost at any particular point.

Â It's not the cord from the origin, but it's the

Â slope at a particular point on the total variable cost curve.

Â 8:36

So note what happens to the slope.

Â It, it first diminishes, there's some advatages to

Â teamwork to specialization and then because of the

Â law of diminishing returns the slope of the

Â total variable cost curve starts to speed up.

Â 8:52

One final point. Marginal cost at point c in the top panel

Â is the same as the slope of the cord from the origin.

Â So where average variable cost is at

Â its minimum, marginal cost equals average variable cost.

Â At point c in the below panel.

Â 9:31

Beyond an output of five when marginal cost is higher than average variable cost,

Â average variable cost is being pulled up by the greater marginal incremental cost.

Â And where marginal comes in right at the level

Â of average variable cost, average variable cost has bottomed out.

Â So same exact relationship we saw with marginal product and average

Â product shows up here between marginal cost and average variable cost.

Â We'll pick up from there in the next session.

Â