MIDTERM_TESTBANK_NEW

# MIDTERM_TESTBANK_NEW - BPUB 250 Midterm Answers Spring 2006...

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BPUB 250 Midterm Answers Spring 2006 Question 1 (a) The input demand functions are derived from the production function where marginal bene&t equals marginal cost of the inputs. The &rm±s cost minimization problem is to choose k and l to: min L = wl + rk + & & Q & 10 p kl ± : The &rst-order conditions are given by: 5 & p l p k = r = > & = r p k 5 p l (1) 5 & p k p r = w = > & = w p l 5 p k (2) Q & 10 p kl = 0 (3) Equations (1) and (2) imply: r p k 5 p l = w p l 5 p k = > l = k r w Substituting into equation (3) yields the input demand functions: Q = 10 r k 2 r w = 10 k r r w = > k = Q 10 r w r l = Q 10 r r w (b) We now get: l = 250 10 r 1 4 = 12 : 5 k = 250 10 p 4 = 50 1
(c) In the short run k is &xed. Since the restaurant continues to sell 250 burgers per day, it has to hire the same l as before. Given the new labor cost, the restaurant±s new total cost is: c 1 = w 0 & l + k & r = 50 & 12 : 5 + 10 & 50 = 1125 The old cost is: c 0 = w & l + k & r = 40 & 12 : 5 + 10 & 50 = 1000 Thus the change in cost is 125. (d) In the long run, the restaurant can adjust k . With the new input costs, l = 250 10 r 1 5 = 5 p 5 = 11 : 18 k = 250 10 p 5 = 25 p 5 = 55 : 9 The long-run total cost is c 2 = w 0 & l + k & r = 50 & 5 p 5 + 10 & 25 p 5 = 500 p 5 = 1118 : 03 ; and total cost increases by 118.03 relative to the short-run. Question 2 (a) The demand side: Q GP = 200 ± 25 P Q S = 150 ± 10 P Summing horizontally gives total demand: Q = & 150 ± 10 P if 8 < P ² 15 350 ± 35 P if P ² 8 (b) Set supply equal to total demand: 65 P ± 250 = 350 ± 35 P P = 6 At P = 6 , total demand is Q = 140 . Substituting P = 6 into the demand functions for students and the general public yields: Q GP = 50 Q S = 90 : We can verify that this is the only solution by setting supply equal to 150 ± 10 P (total demand if 8 < P ² 15 ). This yields a price of P = 5 1 3 . Since this price is outside of the relevant price range for this portion of the total demand curve, this is not a solution. 2

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(c) When there is a \$2 discount for students and the theaters continue to set only one price, the students&demand function is Q S = 150 & 10( P & 2) = 170 & 10 P Total demand is: Q = & 170 & 10 P if 8 < P ± 17 370 & 35 P if P ± 8 Setting the new aggregate demand of 370 & 35 P equal to the old supply function results in a price of P = 6 : 2 The associated aggregate demand equals Q = 153 ; with Q GP = 45 and Q S = 108 . Again, setting 65 P & 250 = 170 & 10 P yields a price outside of the price range for this part of aggregate demand and is not a solution. (d) Consumer surplus is calculated as the area of the triangle below the de- mand curve and above the market price. CS before S = (15 & 6) ² 90 2 = 405 after S = (17 & 6 : 2) ² 108 2 = 583 : 2 Students gain a total of 178 : 2 from the introduction of the discount. 3
(e) Graphical representation of e/ect of \$1 tax: (f) To determine the amount of the tax borne by producers, we need to &nd the price paid by consumers under the tax and the price received by pro- ducers. With the tax, the supply curve becomes Q = 65( P & 1) & 250 = 65 P & 315 Total demand is, as before: Q = & 150 & 10 P if 8 < P ± 15 350 & 35 P if P ± 8 Setting aggregate demand equal to the new supply curve yields the price 4

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paid by consumers: 350 & 35 P = 65 P & 315 P cons = 6 : 65 Producers receive a price of P prod = 6 : 65 & 1 = 5 : 65 . Producers thus pay 6 & 5 : 65 = \$0 : 35 of every \$1 of taxes.
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## This note was uploaded on 04/04/2012 for the course BPUB 250 taught by Professor Seim during the Spring '08 term at UPenn.

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MIDTERM_TESTBANK_NEW - BPUB 250 Midterm Answers Spring 2006...

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