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Unformatted text preview: 2 Market Failure Readings: Chapter 4 in Stiglitz $ Hardins article. In the book, there are short discussions of six basic market failures: & Imperfect competition (monopoly, oligopoly etc.) & Public Goods & Externalities & Incomplete Markets & Imperfect Information & Mysterious Macroeconomic Issues. In lecture, I& ll only talk about monopoly pricing, an example with an externality and an example of an informational failure. We& ll discuss public goods at length soon and you should feel free to ignore anything that has anything to do with macroeconomics. However, you should pay attention to the discussion about incomplete markets in the book. 2.1 Monopoly Pricing Recall that we concluded that competitive equilibria will be Pareto e¢ cient. One crucial assumption for this conclusion is that all agents act as price takers: all agents believe that they have no e/ect on the market prices. This assumption seems relatively OK in some markets, but thinking for example of operating systems for PC computers, it seems borderline ridiculous to postulate that the producers don&t recognize that they have some in¡uence over the price. On the opposite end of the spectrum from a competitive £rm we have the case with a monopoly, meaning that a single £rm is supplying the market. Like a competitive £rm, we 21 assume that the monopolist strives to generate as large pro&ts as possible. That is, it seeks to maximize py & C ( y ) ; where C ( y ) is the (minimal) cost to produce output y: The di/erence with the competitive &rm is that a monopolist understands that it can only sell what the consumers are willing to buy: since it operates alone in the market the &rm understands that it is constrained by picking price¡quantity combinations along the demand curve. Let D ( p ) denote the (direct) demand for the product and note that the monopolist can sell at most D ( p ) units at price p . The optimization problem for the monopolist is max p;y py & C ( y ) subj to y ¡ D ( p ) : Clearly, y = D ( p ) in a solution since otherwise the sales could be increased without lowering the price, so we may rewrite the problem as max p pD ( p ) & C ( D ( p )) ; where we have price as the choice variable. Alternatively we may invert the demand (view it as in the pictures where we have y as the independent variable and p as the dependent variable). Then if p ( y ) is the inverse demand we can write the problem as max p p ( y ) y & C ( y ) ; 2.1.1 Inverse and Direct Demand Mathematically speaking, if y = D ( p ) is the direct demand function, the inverse of D is a function p = D & 1 ( y ) such that D & 1 ( D ( p )  {z } quantity demanded at price p ) = p: 22 X Y x y f R t t } f & 1 Figure 1: The Inverse of a Function The concept is illustrated for a general function f in Figure 1. The point is that if the function f takes x to a value y; then the inverse takes the value y back to the value x we started with. This must be so for each x and each f ( x ) ; so the inverse reverts the operation of the original function...
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This note was uploaded on 11/02/2008 for the course ECON 440 taught by Professor Peternorman during the Spring '08 term at UNC.
 Spring '08
 PeterNorman
 Economics, Externalities, Monopoly, Oligopoly, Perfect Competition, Public Good

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