Day 2 was devoted to marginal this, that and the other. I began by asking if a monopolist (with constant unit costs) who suffers an increase in its unit costs should pass along the full unit cost increase to their buyers? To make it more piquant, I asked them to assume a literal monopolist, i.e., sole seller. Some said maybe, because it depends on elasticity of demand. Others said, yes, what choice do buyers have? Alert ones said no, because you must be at an inelastic portion of the demand curve (thank you, markup formula). They will indeed increase the price but the increase is tempered by the high elasticity at the current profit maximizing price. Profit will go down. This example illustrates how both the demand side and cost side interact to influence profits. In day 1 we focused on how the demand side affected price, in day 2 we focus on the cost side.

To motivate the notion of marginal cost, I ask how they would define cost per unit to convey the idea that this is an ambiguous concept. A possible candidate is average cost but ist not helpful maing decisions about whether to increase of decrease output. For this, what we want is marginal cost. Define marginal cost, and onto constant, decreasing and increasing returns to scale and discussion of technologies that would satisfy each of these. Solving quadratics is a good example. The time to solve each is the marginal cost. If you have decreasing returns to scale in solving quadratics, a wit suggested, correctly, that one should give up mathematics.

Next, where do cost functions come from? Opportunity to introduce capital and labor and production function. Cost function is minimum cost way of combining K and L to produce a target quantity. Numerical example with Cobb-Douglas. Without explicitly mentioning isoquants and level curves, solved problem graphically (draw feasible region, move objective function hyperplane) as well as algebraically. Discussed impact of price change of inputs on mix used to produce target volume. Marginal productivity of labor, capital and marginal rate of technical substitution. Eyes glazing over. Why am I wasting time with this stuff? This is reading aloud. Never again.

Onto marginal revenue. By this time they should have realized the word marginal means derivative. Thankfully, they don’t ask why a new word is needed to describe something that already has a label: derivative. Marginal revenue should get their goat. Its a derivative of revenue, but with respect to what? Price or quantity? The term gives no clue. Furthermore, marginal revenue sounds like price. The result? Some students set price equal to marginal cost to maximize profit because thats what the slogan marginal revenue = marginal cost means. To compound matters, we then say the area under the marginal revenue curve is revenue. If marginal revenue is the derivative wrt quantity then integrating it should return the revenue. Does this really deserve comment? Perhaps watching paint dry would be more exciting. Wish I had the courage to dispense with the word `marginal’ altogether. Perhaps next year. Imagine the shock of my colleagues when the phrase `marginal blank’ is greeted with puzzled looks.

They’ve been very patient. Before class ends there should be a payoff. Show that marginal revenue = marginal cost is a necessary condition for profit maximization and is sufficient when we have decreasing returns to scale. This seems like small beer. What happens when we have increasing returns to scale? Why does this break down? Some pictures, of why the slogan is no longer sufficient and a discussion of how this relates to pricing for firms with increasing returns like a producer of an app who must rent server space and gets a quantity discount.

## 4 comments

September 9, 2014 at 9:12 pm

afinetheoremLove these posts. But don’t dispense with “marginal”. History of thought tells us something here. Lots and lots and lots of very intelligent people, who completely knew what a derivative was, nonetheless did not come up with the profit maximization rules. This is especially true when we start talking about monopolistic competition, where it is absolutely not obvious either to undergraduate students or anyone else that one should maximize profits by constructing something called the effective demand curve and setting its derivative/differential equal to price.

Indeed, I bet if you queried your freshman about whether price is determined primarily by the relative scarcity of inputs and about whether maximizing profit margins is sensible, then I am sure you will get the wrong answer on both counts. What this says to me is that a good way to teach pricing is to explain

whyour intellectual forefathers were wrong (flat long run supply curves justify X theories of value, and the markup formula is pretty close to constant for certain assumptions about demand and cost variability). Even better, start everything with games -> monopolistic competition -> special cases of monopoly and perfect, which is an order that has been proposed by quite a few famous economists in the past…September 14, 2014 at 9:40 pm

rvohraHi Kevin

From Walras’ correspondences we discover that it was Henri Poincare who had to explain the distinction between ordinal and cardinal utility to Walras. The origins of `marginalize’ thinking are also a little murky. It is common to credit Jevons, Menger and Walras. However, Walras’ letters show that he relied on the advice on colleagues in Mathematics and Physics at Lausanne to solve constrained optimization problems and arrive at the principle of marginal utility. In fact Stefan Kolm in his review of Walras’ correspondences writes:

“And while mathematicians supply their inputs in scanty but remarkable letters, while all economists whose names are remembered express their enthusiasm, doubts, arguments or claims to priority, Walras tries to gain acceptance for his ideas through hundreds of letters to writers, scientists, publishers, government engineers, philosophers, officials, and friends.”

It would seem then, that derivative came first, marginals later. Had the ancients stuck to derivatives there would have been less confusion!

rakesh

September 11, 2014 at 10:22 am

LucaCost functions are just boring, and there is good reason they are disappearing from graduate teaching (or maybe they have disappeared already and I do not know). On the other hand, it is probably useful to talk about factor demands since the same concepts will come up for consumers.

September 14, 2014 at 9:43 pm

rvohraAgreed, factor demands are a good way to get them warmed up for utility maximization. It has the advantage that the disutility function in this case has a natural interpretation, cost so they can focus on how inputs change as input prices change.