Profit Maximization and the Profit Function

Motivation

Profit Maximization

Problems

Comparative Statics

The profit function

Supply and demand functions

Profit Maximization and the Profit Function

Juan Manuel Puerta September 30, 2009

Motivation

Profit Maximization

Problems

Comparative Statics

The profit function

Supply and demand functions

Profits: Difference between the revenues a firm receives and the cost it incurs

Cost should include all the relevant cost (opportunity cost) Time scales: since inputs are flows, their prices are also flows (wages per hour, rental cost of machinery)

We assume firms want to maximize profits.

Let a be a vector of "actions" a firm may take and R(a) and C(a)

the "Revenue" and "Cost" functions respectively.

Firms seek to maxa1,a2,...,an R(a1, a2, ..., an) - C(a1, a2, ..., an)

The

optimal

set

of

actions

a

are

such

that

R(a ) ai

=

C(a ) ai

Motivation

Profit Maximization

Problems

Comparative Statics

The profit function

Supply and demand functions

From the Marginal Revenue=Marginal Cost there are three fundamental interpretations

The actions could be: output production, labor hiring and in each the principle is MR=MC Also, it is evident that in the long-run all firms should have similar profits given that they face the same cost and revenue functions

In order to explore these possibilities, we have to break up the revenue (price and quantity of output) and costs (price and quantity of inputs).

Motivation

Profit Maximization

Problems

Comparative Statics

The profit function

Supply and demand functions

But the prices are going to come as a result of the market interaction subject to 2 types of constraints:

Technological constraints: (whatever we saw in chapter 1) Market constraints: Given by the actions of other agents (monopoly,monopsony etc)

For the time being, we assume the simplest possible behavior, i.e. firms are price-takers. Price-taking firms are also referred to as competitive firms

Motivation

Profit Maximization

Problems

Comparative Statics

The profit function

Supply and demand functions

The profit maximization problem

Profit Function (p) = max py, such that y is in Y Short-run Profit Function (p,z) = max py, such that y is in Y(z) Single-Output Profit Function (p, w)=max pf (x) - wx Single-Output Cost Function c(w, y) = min wx such that x is in V(y). Single-Output restricted Cost Function c(w, y, z) = min wx such that (y,-x) is in Y(z).

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