Lecture_20_Monopoly

Lecture_20_Monopoly - Lecture 20: Monopoly. c & 2008...

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Unformatted text preview: Lecture 20: Monopoly. c & 2008 Je/rey A. Miron Outline 1. Introduction 2. Maximizing Pro&ts 3. Examples: Linear Demand Curves and Monopoly 4. The Ine ciency of Monopoly 5. The Deadweight Loss of Monopoly 6. Price Discrimination 7. Natural Monopoly 8. What Causes Monopoly? 1 Introduction So far, we have examined price and quantity determination in a competitive industry, meaning one with many price-taking &rms. We next consider the opposite extreme, monopoly, meaning a market with exactly one &rm in the industry. This &rm is unlikely to take price as given. A monpolist cannot choose price and quantity independently, since any outcome must lie on the demand curve. But the monopolist will know that its output decision a/ects the price at which it can sell its output. Note that we can think of the monopolist as choosing price and letting the demand curve determine quantity; alternatively, we can think of the monopolist as choosing quantity and letting the market determine price. The two approaches are equivalent. It will be more natural to describe a monopolists decision in one way or the other depending on the situation. 1 2 Maximizing Pro&ts Let p ( y ) be the market inverse demand curve. Let c ( y ) be the cost function. The revenue function is r ( y ) = p ( y ) y . Then the monopolist&s problem is max f y g p ( y ) y & c ( y ) Intuitively, the solution must be to choose the level of output such that MR = MC . Why? Because if this condition did not hold, the monopolist could increase prot by changing the level of output. For example, if the monopolist had chosen y such that MR > MC; the extra rev- enue from increasing production a small amount would be greater than the increase in costs from increasing output, so the initial choice of y could not have been prot maximizing. This approach to choosing an output level is analogous to what a pure competitor does, except that for a pure competitor, price does not depend on output, so MR = p . We can also solve the monopolist&s problem formally. The FOC is p ( y ) + yp ( y ) = c ( y ) which is exactly the statement that MR = MC . Remember that MR has two components: the extra unit of output produced brings in extra revenue in the amount p ( y ) per unit of output; but it also drives down the price at which the monopolist can sell all existing units because the monopolist faces a downward sloping demand curve. Another way to present this result is what is through a concept known as markup pricing. Rearranging the rst-order condition gives the following: p ( y ) & 1 + yp ( y ) p ( y ) = c ( y ) Then, impose the result that since p ( y ) is the inverse demand curve, its derivative is the reciprocal of the derivative of the demand curve itself. That is, p ( y ) = 1 y ( p ) 2 where y ( p ) = p & 1 ( y ) is the market demand curve. We can therefore write the FOC as p ( y ) B @ 1 + 1 y ( p ) p y 1 C A = c ( y ) or p ( y ) & 1 + 1 & ( y ) = c ( y ) where & ( y ) is the elasticity of the market demand curve. We write it as a function ofis the elasticity of the market demand curve....
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This note was uploaded on 09/16/2009 for the course ECONOMICS 1010A taught by Professor Jeffreya.miron during the Fall '09 term at Harvard.

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Lecture_20_Monopoly - Lecture 20: Monopoly. c & 2008...

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