notes_9 - Monopoly April 4, 2009 1 Monopoly: definition...

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Unformatted text preview: Monopoly April 4, 2009 1 Monopoly: definition Monopolies are characterized by: • A single seller • No close substitutes for the good produced by the monopolist • Presence of barriers to entry As you can see, monopoly is the exact opposite of perfect competition. You can imagine things are going to be quite different here. The objective of the monopolist is to maximize profits: max Q Π = P ( Q ) Q | {z } TR- TC ( Q ) To solve this problem we need to take first derivative and set it equal to zero dΠ d Q = P ( Q ) Q + P ( Q ) | {z } MR- MC ( Q ) = 0 Therefore, the profit maximizing quantity is the one that equates marginal revenue to marginal cost: MR ( Q * ) = MC ( Q * ) 1.1 Marginal Revenue Contrary to Perfect Competition, under a monopoly price is not constant anymore - P ( Q ) is a decreasing function - , for obvious reasons. We can derive the marginal revenue by taking derivatives of the total revenue TR ( Q ) = P ( Q ) * Q = ⇒ MR = d TR d Q = P + Q d P d Q |{z} < < P 1 Quantity Price D M R MC c a (a+c)/2 (a-c)/b (a-c)/2b a/b a/2b DWL While in Perfect Competition demand and marginal revenue were the same thing, here marginal revenue lies below the demand. The reason why MR < P is that all units are sold at the same price. Marginal revenue represents the additional revenue from selling an addi- tional unit of output: selling an additional unit of output earns less than the price of the last unit. Why? Anytime I want to increase sales by one unit, I must decrease the price: all the units sold - not only the last one - will earn less revenue than before. 1.2 Special Case: MR with Linear Demand When the demand is linear (that is, in most of your exercises) we can say a lot about the shape of the MR : suppose that the demand is given by the generic equation P = a- bQ , then TR = P * Q = ( a- bQ ) Q = aQ- bQ 2 and MR = d TR d Q = a- 2 bQ When demand is linear, the MR will also be linear. Moreover its slope will be twice the slope of the demand! MR will cut the horizontal axes in the middle of the interval defined by the origin and the demand. 2 1.3 Special Case: Linear Demand and Constant Marginal Cost When demand is linear, P = a- bQ , and marginal cost is constant, MC = c , the solution is pretty easy: MR = a- 2 bQ = MC = c = ⇒ Q m = a- c 2 b P m = a + c 2 Now, if you want to compare this solution to the perfect competition one we can see that the monopoly quantity is exactly half the competitive one: under perfect competition the supply is simply the MC = c . The solution is given by P = MC P = a- bQ = MC = c = ⇒ Q pc = a- c b P pc = c 1.4 Exercise 1) The demand is P = 10- 4 Q , the cost function is TC ( Q ) = 4 + 6 Q ....
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This note was uploaded on 05/09/2009 for the course ECON 200 taught by Professor Junnie during the Spring '08 term at NYU.

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notes_9 - Monopoly April 4, 2009 1 Monopoly: definition...

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