Mas-Colell Chapter 5: Production

For readers who accept and enjoy Mas-Colell's treatment of consumer theory (the first pillar of his teaching method), producer theory (the second pillar) is smooth sailing. The concepts are parallel to consumer theory, but with less concern mess along the way with budgets and turning ordinal preferences into cardinal utility functions.

Production

For Mas-Colell, production is a black box. Some inputs enter the firm and some outputs leave the firm. Put another way, firms buy some goods and sell others. The netput of this process is the production vector 1. Most economists do not care how rubber turns into a tire or seed into corn. All of that occurs within the black box, the firm.

Of course, at anytime, firms need specific inputs to produce specific outputs. Any plans that are possible make up the production set. Just like the consumption bundle in consumer theory, production sets have some specific assumptions. The two key assumptions, which are not always obvious but key, are "No Free Lunch" and "Free Disposal"1.

While these have specific mathematical explanations, they have intuitive interpretations. No free lunch means that it requires inputs to get outputs. Nothing is free. This is obvious, but sometimes forgot. Free disposal means that firms can get rid of inputs at no cost. While this is more controversial, it basically allows us to rule out "too much stuff." We can always get rid of the stuff we do not use.

Firms look to choose the best possible production vector out of all the possibilities. This is just like consumer theory, except the firm's constraint is technology and not its budget.

The easiest example involves multiple inputs and one output, resembling Rothbard's first explanation of production as a combining of at least two goods into another good. Using this framework, economists discuss a marginal rate of technical substitution (MRTS). This is the analog of the consumer's marginal rate of substitution. The MRTS is the rate that the firm can trade between two goods and keep output constant. A farmer could produce the same amount of corner with less acreage and more fertilizer.

The right combination of inputs will dictate the best production vector or schedule given the technology. Again, this mirrors consumer theory, where a consumer tries to pick the best combination of goods to maximize his utility within his budget.

Profit Maximization

The natural next question is "what is the right production schedule?" Words like right or best are hard to work with. Instead, economists try to be slightly more specific.

While utility maximization drives consumers for Mas-Colell, profit maximization drives producers. This seems more natural. Most people do not like the image of humans as computer like calculators of joy and pain. A few more people believe that firms try to make the most money possible, whether the "should" or not.

Mas-Colell does give a little explanation about the origin of profit maximization. Why do firms want to maximize profit, instead of maybe revenue? The answer is actually connected to consumer theory, although readers do not learn this until after everything else about production. There is a link.

There are 2 steps. (1) Individuals want to consume as much as possible, so they always want a bigger budget to buy goods. (2) Individuals own firms and receive part of the profits. Every owner wants the company to maximize profits so that he receives a bigger paycheck, thus increasing his budget in step (1).

Firm as Computer

Just as Mas-Colell assumed that consumers were perfect price takers, he assumes firms are too. The price of inputs and outputs is set by "the market" outside any firm influence. This turns the profit maximization problem into a simple calculation of inputs and outputs given prices.

With prices as given, one requirement of profit maximization is cost minimization. Firms produce a specific level of output  to minimizes costs. If they did not, firms could cut costs for the same amount of sales and have more profits. We assumed profit maximizers, so they must also be cost minimizers.

In order to cut costs, the firm will substitute between possible inputs until the MRTS is equal to the ratio of prices. This is the same calculation that the consumer does. For a specific output, say 10 bushels of corn, the cheapest production is when these rations are equal. If not, firms could cut costs without cutting output.

Once the firm has found the way to minimize costs for every level of ouput, now they decide how much to produce. It is almost trivial at this point. The profit maximizing output is, as is common in economics, when marginal cost equals marginal benefit (MC=MB). In this case, when the marginal cost of inputs equals the marginal price of sales (MC=P). If marginal costs are below marginal price (the market price), then the firm could produce one more unit and sell it above costs, increasing profits. But, we assumed profit maximization, so this is not what the firms do. If marginal costs are above, the reverse in true.

Law of Supply

There is another important parallel between consumer and producer theory. For consumers, utility maximization and the weak axiom of revealed preference lead to the compensated law of demand. For producers, profit maximization and decreasing returns to scale of production lead to the law of supply.

Quantities respond in the same direction as price changes... If the price of an output increases (all other prices remaining the same), then the supply of output increase; and if the price of an input increases, then the demand for the input decreases.-Pg 138

The first sentence follows directly from MC=MB. If the market price of a firm's output increases, they can now produce more before MC=price. The second sentence follows from the MRTS logic. If the price of one good, say land, rises, the ideal bundle for production will then involve less land and more of a substitute, say fertilizer.

Notice that this law does not have the compensated qualifier. Since the firm does not have a "budget" in the sense a consumer does, a firm does not experience wealth effects, but only substitution effects. A drop in prices does not make a firm richer since it does not have a budget.

Aggregation

This difference between compensated and uncompensated is important when it comes to aggregating supply. While Mas-Colell spent a chapter dealing with the issues of aggregating demand, because of problems from the wealth effects, aggregated supply is just a page. The fact that consumers follow compensated law of demand makes this tricky. Here, with a simple law of supply, aggregation amounts to simply adding the firms' supply.

Without the qualifications of chapter 4, Mas-Colell can build a simple aggregate supply function based on aggregate quantities. He can build a maximization for the representative firm, which maximizes profit for the industry. He can also draw welfare implications since all the profits can simply be added to mirror the utilities of consumers. These are the three things he attempted in chapter 4.

Yay for simplifying away the problems.

Analysis

The claim that firms maximize simple profit functions is much more convincing than consumers maximize simple utility functions. While I do not believe that firms actually make every decision to maximize profits, it at least approximates close enough that I can believe predictions based on producer theory. How well this holds in reality is an empirical question and depends on the situation.

For this reason, I enjoy Mas-Colell's discussion on production. This chapter involves a much clearer justification for the assumptions made. It is nice to see Mas-Colell try to explain some assumptions from real human decisions- though it relies on consumer theory which already skipped this step. Nevertheless, he is still trying.

However, as with consumer theory, producer theory sucks economics of all life. There is no discovery; no decisions are made. All of the interesting workings of firms are ignored through the black box. Firms are complete price takers and turn into simple computers. People turn into robots.

Assuming all possible productions are known and prices are known, a computer can run a firm. Of course, some people will believe this claim, but I do not. After working in different firms, this idea is way too simple. Yes, this is econ 101 and models need to be simple, but the model already assumes away the real production part. Producer theory is just buying and selling.

How do firms discover how to produce? How do they learn more efficient mechanisms? Without a Hayekian understanding of prices, these questions, which are fascinating, are dead-ends. Mas-Colell's firms respond to the incentives of prices, but they know everything from the first page. They producers are simply robots. This is different from Hayek and Rothbard and I believe less interesting.


1. Some of the other important assumptions in Mas-Colell are

  1. Production set is nonempty.
  2. Production set is closed.
  3. Firms can produce zero.
  4. Outputs cannot be turned back into the same inputs.
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