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Unformatted text preview: York University - ECON2350 - V. Bardis Answers to Practice Set 3 1. See notes or text. 2. . Assumptions Demand Supply-Large number of consumers-Large Number of (identical) Firms (therefore, each is a price taker) (each firm is a price taker)-Utility Maximizers-Produce a Homogeneous good ⇒ Aggregate Demand Q d = D ( p )-Profit Maximizers ( Price = MC ) ⇒ Short-Run Aggregate Supply Q s = S ( p )-Free Entry and Exit in the Long-Run Equilibrium Conditions Short-Run Long-Run Q d = Q s Firm Profit is Zero If Profit is greater (less) than zero firms enter (exit) ⇒ Long-run Agg. Supply ( p * =minimum Average Cost of the ‘representative’ firm) 3. First find the long-run total cost by solving min K SRC ( K,q ) = 1 /K + Kq 2 This gives- 1 K 2 + q 2 = 0 ⇒ K c = 1 /q and therefore the long run cost function is C ( q ) = SRC ( K c ,q ) = 2 q Since in the long run MC = AC = 2, the long run equlibrium price is p * = 2. Therefore, the total output produced can be found from the demand function: Q * = 2 , 200- 23(2) = 2 , 154. 4. (a) In the short run each firm’s supply is its MC curve for any price above minimum AV C . Here MC = 10 + 2 q and AV C = 10 + q . AV C is minimum at q = 0 and so minAV C = AV C (0) = 10. Therefore, each firm i has inverse supply p = MC ( q ) or p = 10 + 2 q for q ≥ 0 and its supply function is q i = p/ 2- 5 , if p ≥ 10 and q = 0 if p < 10 The industry supply is Q s = 10 X 1 q i ⇒ Q s = 10 q ⇒ Q s = 10( p/ 2- 5) ⇒ Q s = 5 p- 50 1 In the short run the equilibrium price is found by setting Q s = Q d which gives 5 p- 50 = 400- 4 p ⇒ p * sr = 50 and the equilibrium quantity is found by pluggind p * in either the demand or the suplly function so Q * sr = 5(50)- 50 = 200. Since there are 10 firms each of them produces q * = 200 / 10 = 20 units....
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This note was uploaded on 02/29/2012 for the course ECON 2350 taught by Professor Bardis during the Fall '12 term at York University.
- Fall '12