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Unformatted text preview: Pefect Competition March 29, 2009 1 The Short Run Exercise There are N = 100 firms in the market. The short run cost function is TC ( Q ) = 20 + 4 Q 2 . The non sunk fixed costs are ANSC = 16. Find the market supply in the short run equilibrium. The short run supply in equilibrium is the marginal cost above the shut- down price, and the shutdown price is the minimum of the ANSC curve, where ANSC = AV C + NSFC Q = 4 Q + 16 Q To find the minimum it might be easier to simply take the intersection with the marginal cost, MC = 8 Q . ANSC ( Q min ) = MC ( Q min ) = 4 Q + 16 Q = 8 Q = Q min = 2 The shutdown price is ANSC ( Q min ) = MC ( Q min ) = 16 The individual supply curve satisfies the condition MC = 8 Q = P , therefore Q = P/ 8. The supply is Q s i ( P ) = P 8 ,P 16 P < 16 The aggregate supply is S ( P ) = N * Q s i ( P ) S ( P ) = 100 P 8 ,P 16 P < 16 1 Ex. 9.13 Two types of firms: N A = 100 and N B = 30. The short run supply curves are s A ( P ) = 2 P and s B ( P ) = 10 P . The market demand is D ( P ) = 5000- 500 P . Find the short run P * and quantity produced by each kind of firm. We need to find the aggregate supply: it is clear that both types of firm will be operating in the market at any possible positive equilibrium price. Therefore I dont have to worry about firms shutting down. If both types of firms operate in the market the aggregate supply is S ( P ) = N A s A ( P ) + N B s B ( P ) = 200 P + 300 P = 500 P The equilibrium price is given by D ( P * ) = S ( P * ) 500 P = 5000- 500 P = P * = 5 The quantity produced by the firms are s A (5) = 10 s B (5) = 50 (b) Suppose the supply function for type B firms is s B ( P ) = 10 P- 80 if P > 8. What is the equilibrium price and quantity in the short run? We have to consider two cases: Both types of firm will operate in the market in the short run equilib- rium. The new aggregate supply is If both types of firms operate in the market the aggregate supply is S ( P ) = N A s A ( P ) + N B s B ( P ) = 200 P + 300 P- 2400 = 500 P- 2400 The equilibrium price is given by D ( P * ) = S ( P * ) 500 P- 2400 = 5000- 500 P = P * = 7 . 4 < 8 This price is too low for type B to produce: therefore the conjecture that both firms will be operating in the market is wrong Only type A firms will operate in the market. The aggregate supply is S ( P ) = N A s A ( P ) = 200 P The equilibrium price is given by D ( P * ) = S ( P * ) 200...
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