Use the demand and supply equations and the value for the quantity restriction t

Question

Use the demand and supply equations and the value for the quantity restriction that were e-mailed to your UNCP e-mail address. First, assume that there are no restrictions on the market and that the market will achieve its free-market equilibrium. Find . . . a. the market clearing price and quantity. b. the consumers' surplus. c. the producers' surplus d. the total benefit created by the market for consumers and producers. Next, suppose that for some reason, the quantity that may be sold is restricted to the number that was e-mailed to you. Find . . . e. the demand price and the supply price, PD and PS. f. the consumers' surplus. g. the producers' surplus. h. the total benefit created by the market for consumers and producers. i. the deadweight loss that is caused by the quantity restriction. emand and supply equations are QD = 8950 - 50P QS = 200P - 14800 The quantity restriction for parts e - i is 2800.

Explanation / Answer

QD = 8950 - 50P QS = 200P - 14800 a) QD = QS 8950 - 50P = 200P - 14800 23750 = 250P P = $95 Q = 8950 - 50*95 = 4200 Ans: price = P= $95 quantity = Q = 4200 b) Pmax = ? QD = 0 8950 - 50 P = 0 P = $179 Consumer surplus = 0.5*Q*(Pmax - P) = 0.5*4200*(179-95) = $ 176400 .......here P = $95 and Q = 4200 are market price and quantity c) Pmin = ? QS = 0 200P - 14800 =0 P = $74 Producer's Surplus = 0.5*Q*(P-Pmin) = 0.5*4200*(95 - 74) = $ 44100 .......here P = $95 and Q = 4200 are market price and quantity d) Total benefit = Producer's surplus + consumer's surplus = $ 220500 Now when Q = 2800 d) Demand price ; 2800 = 8950 - 50 P P = $123 supply price ; 2800 = 200P - 14800 P = $88 f) So consumer's surplus = 0.5*2800*(179-123) = $78400 .....here P = $123 and Q = 2800 are market price and quantity & Pmax = $123 g) Producer's surplus = 0.5*2800*(88-74) = $ 19600 .....here P = $88 and Q = 2800 are market price and quantity & Pmin = $74 h) Total benefit = Producer's surplus + consumer's surplus = $ 78400 + $ 19600 = $ 98000 i ) deadweight loss = initial total benefit - total benefit after restriction = $ 220500 - $ 98000 = $ 122500

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