# PS2 - Econ100C #2 Fall2009 1 A monopolist has the cost...

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Econ 100C Solutions to Problem Set #2 Fall 2009 1. A monopolist has the cost function of C ( Q ) = A + Q 2 where A > 0. Inverse market demand is equal to P ( Q ) = 60 – 4 Q . a. Write out the monopolist’s profit function. π ( Q ) = P ( Q ) Q C ( Q ) = (60 – 4 Q ) Q – ( A + Q 2 ) = 60 Q – 5 Q 2 A b. Assuming no shut down find the monopolist’s profit maximizing price and quantity. () 2 max 60 5 First order condition: 60 10 0 6 60 4 6 36 Q M M QQ Q A Q Q Q P π =−− =− = = = c. If the above cost function is for the short run for what values of A will the monopolist shut down. Explain. AVC ( Q ) = Q AVC (6) = 6 < 36 = P M The firm will never shut down because price is above average variable cost regardless of the value of A . d. If the above cost function is for the long run for what values of A will the monopolist shutdown? The monopolist will shutdown when price is less than average cost. 66 6 Shutdown when 6 . 36 6 180 6 A AC Q Q Q A AC PA C A A =+ < <+ ⇒ >

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For the rest of the problem assume A = 0. e. Give the monopolist’s profit maximizing price and quantity. These didn’t depend on A . We’ll have the same answer as before. 6, 36 MM QP == f. Calculate the demand elasticity at the point you found in (e). Verify that this elasticity is in the elastic region. The demand function is Q ( P ) = 15 – P /4. 11 3 6 1.5 1 44 6 P PQ Q ε = = < g. Calculate the Lerner index using elasticity. 12 3 L =− = h. Calculate the Lerner index using price and marginal cost. ( ) 36 2 6 2 36 3 PM C L P = i. Briefly explain how the Lerner index will change if demand becomes more elastic. If demand becomes more elastic the Lerner index will become smaller (closer to 0). The monopolist will have less market power because consumers will be more responsive to changes in price.
j. Calculate consumer surplus, producer surplus and deadweight loss at the monopoly price and quantity.

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## This note was uploaded on 06/08/2010 for the course ECON 171 taught by Professor Newhouse during the Spring '07 term at UCSD.

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PS2 - Econ100C #2 Fall2009 1 A monopolist has the cost...

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