problem set 5

# problem set 5 - 2 Consumer surplus falls to 0 it falls by A...

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Econ 100B Problem Set 5 – Answers Fall 08-09 Problem 1 a) Set P = MC above min( AVC ) C = 15 + 4 q + q 2 MC = 4 + 2 q AVC = 4 + q S one firm : P = MC = 4 + 2 q q one firm = P ! 4 2 if P > 4 b) Multiply by 5 firms: q one firm = P ! 4 2 Q supply : 5 " P ! 4 2 = 5 2 P ! 10 c) Set supplied quantity equal to demand: Q demand = 20 ! 1 2 P = 5 2 P ! 10 30 = 3 P P = 10 Q = 20 ! 1 2 (10) = 15

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Problem 2 LRAC = 16 q + q LRMC = 2 q LRAC = LRMC 16 q + q = 2 q q = 16 q q 2 = 16 ! q = 4 min( LRAC ) occurs at q = 4: min(LRAC) = 16 4 + 4 = 8 Setting P = min( LRAC ) for long run supply: P = 8. Solving for intersection of demand and supply: Q demand = 24 ! P P = 8 Q = 24 ! 8 = 16 Finally, each firm produces at min( LRAC ), or q = 4. Number of firms = 16/4 = 4.
Problem 3 At the initial equilibrium price of P 0 and quantity of Q 0 consumer surplus is A and producer surplus is B + D. 1. Producer surplus falls to D – C; this is a decline of (B + C).
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Unformatted text preview: 2. Consumer surplus falls to 0; it falls by A. 3. When the government gives the goods away for free, price is 0 and consumer surplus will rise to A + B + C + D + E. Producer surplus will still be D – C. Government expenditure will be D + E. Total surplus (including the governments expenditure) will be A + B + D. That’s the same surplus as in the competitive case so there will be no deadweight loss. (Note that if you don’t consider the government’s loss, total surplus would be A + B + 2D + E.) A B C D Q P 1 P D S P Q E...
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