Econ100C-Fall2009-Final-sols

# Econ100C-Fall2009-Final-sols - Economics 100C...

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Economics 100C: Microeconomics C Solutions to Final Exam: Fall 2009 1. (12 pts) A monopolist has the short run cost function of ( ) 2 4 CQ F Q =+ where F > 0 is a fixed cost. Inverse market demand is equal to ( ) 60 2 D PQ Q =− . a. Assuming no shut down find the monopolists profit maximizing price and quantity. ()( ) ( ) () 2 max 60 2 4 First order condition: 60 4 8 0 5 60 2 5 50 Q M M QQ Q F Q Q Q P π + = = = b. For what values of F (if any) will the monopolist shut down? Explain. The monopolist will shut down if P < AVC : 2 45 50 20 which is never satisfied. 5 <= The monopolist will not shut down for any values of F . c. Describe how the equilibrium will change if the government charges a per unit tax of t for each unit of the good that’s sold. You do not need to do any calculations but describe the direction of the changes in the equilibrium quantity, consumer surplus, producer surplus and deadweight loss. The tax will raise the price paid by the consumer and lower the price received by the monopolist. Q M will fall. CS will fall. PS will fall and DWL will increase.

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2. (16 pts) A monopolist serves two separate markets and has the long run cost function of () ( ) 12 1 2 ,4 Cqq q q =+ . The firm can distinguish between customers in the two markets. Inverse demand in the first market is equal to 2 11 1 52 D Pq q =− . Inverse demand in the second market is equal to ( ) 2 22 2 151 D q = . The monopolist can charge different prices in each market. a. Assuming no shut down find the monopolist’s profit maximizing prices and quantities in these two markets. ( ) ( ) 1 1 2 2 1 2 , 2 1 2 2 2 1 2 2 max , 52 151 4 First order conditions: 52 3 4 0 4 151 3 4 0 7 52 4 36 151 7 102 qq M M M M q q p p π + + = = =−− = = =−= = Suppose the government requires that the monopolist charges the same price in each market. b. Formulate (but do not solve) the monopolist’s new profit maximization problem. ( ) ( ) 2 2 1 2 1 2 , max , 52 151 4 s.t. 52 151 q q + + (This could also be done by horizontally summing the demand curves and maximizing profit over the entire market.) c. Is it possible the monopolist’s profit will be higher in (b) than in (a)?
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Econ100C-Fall2009-Final-sols - Economics 100C...

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