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Unformatted text preview: Chapter 10 Profit maximization We now have the basic characteristics of the firm’s technology described in monetary terms through the device of the cost function. We are now in a position to see what happens when we consider profit maximizing behavior, given costs of production. Be aware that profits are also measured as a flow variable  that is profits are measured per unit time. To complete our description of the workings of a firm, we need to describe the revenue side of the equation, and the simplest way of specifying a Revenue Function , R ( x ), is to assume that revenues are the price of a unit of output multiplied by the amount of output, so that R ( x ) = px , where p denotes the price of the product. Given the “one price” assumption, profits can be written as: π ( x ) = px − C ( x ) (10.1) The last task that confronts us is saying something about where the price of the product comes from, and making a decision as to how we wish to build this into the analysis. Recall that from demand theory, the quantity of a product that can be sold depends upon its price. Therefore, we might perhaps really should have written p as a function of x in equation (11.18), i.e., p = p ( x ), where p ( x ) represents the demand curve for the product. There are several different assumptions we might make about how prices and x are related in (11.18), and all are quite interesting in their own right. 221 222 CHAPTER 10. PROFIT MAXIMIZATION The three most common assumptions about how price is determined, and how firms recognize this, are: 1. p is assumed to be given, so the firm does not perceive that p depends upon its output. 2. p is determined by the decisions of the firm, and the firm knows this. 3. p is determined in part by the firm, but the decisions of other firms also contribute. Each assumption produces a picture of different sorts of industry structure. The first assumption produces Perfect Competition , the second produces Monopoly , while the third produces Oligopoly . While one can dress these assumptions up in various ways  and we will do so  just this basic assumption about how the firm’s revenue function works is really enough to generate some rather different pictures as to how industry works, and as to how market prices are determined. It is easiest to begin with monopoly, because in this case there is only one firm in the industry. In fact, what we shall begin with is a discussion of price and output decisions in a weak monopoly or Cournot monopoly . In a weak monopoly, the firm is still restricted in its pricing decisions somewhat in that the firm cannot engage in Price Discrimination charging different consumers different prices. Initially, we shall just discuss how we can obtain solutions to the monopolist’s pricing and output decisions, and in the next chapter, we shall discuss monopoly from the perspective of society. We will start with the simplest case and suppose that the demand function for the firm’s product is given simply by...
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This note was uploaded on 11/13/2009 for the course ECONOMICS 721 taught by Professor Partha during the Fall '09 term at CUNY Hunter.
 Fall '09
 Partha

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