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Unformatted text preview: Problem 3 (a) The demand functions for the two consumer groups are
X 1 = 200  P if P 200 , and X 1 = 0 if P 200.
X 2 = 50  1 P if P 100 , and X 2 = 0 if P 100 2 First consider the case when P 200. In this case, X 1 = 0 and X 2 = 0 , implying X 1+ X 2 = 0 Now, consider 100 < P 200 . In this case, X 1 = 200  P , and X 2 = 0 , implying X 1 + X 2 = 200  P .
1 Next, consider 0 P 100 . In this case, X 1 = 200  P and X 2 = 50  P , implying 2 X 1 + X 2 = 250  3 P 2 (b) First consider the case when P 200. In this case, X 1+ X 2 = 0 , implying = 0 . Now, consider 100 < P 200 . In this case, X 1 + X 2 = 200  P . Therefore, Next, consider 0 P 100 . In this case, X 1 + X 2 = 250  1.5P . Therefore, But this solution violates the assumption that P is less than 100, so is not viable. If P is 100, the X = 100 and profits will be 6000. This is less than 6400. The maximum is then for the second case with no sales to group 2. Total profits are equal to 6400. Consumer surplus is obtained by using the first market only. It is given by Problem 7 (a) With price discrimination
PT = 18  QT MRT = 18  2QT Now, equate marginal revenue in Toronto with marginal cost.
18  2QT = 3 QT = 7.5 PT = 10.5 where the marginal cost of producing and delivering cough syrup to each town is 3, since the total cost is 2 + 3Qi where i = T, M.
PM = 14  QM MRM = 14  2QM Now, equate marginal revenue in Montreal with marginal cost.
14  2QM = 3 QM = 5.5 PM = 8.5 Thus, the optimal price of Buckley's cough medicine is 10.5 in Toronto and 8.5 in Montreal if the two markets are separate. (b) Without price discrimination If Toronto and Montreal are treated as a common market, then the aggregate demand faced by Buckley is
Q A = QT + QM = ( 18  P ) + ( 14  P ) = 32  2 P MR A = 16  Q A Now, equate marginal revenue with marginal cost
16  Q A = 3 Q A = 13 P = $9.5 Thus, the optimal price if Buckley's medicine for a common market is $9.5 Problem 8 If the MSAC charges the same price per hour regardless of type of player, then the aggregate demand faced by MSAC is
Q = 1000Q A + 1000Q N = 1000( 6  P ) + 1000( 3  P / 2 ) = 9000  1500 P P = 6  Q / 1500 MR = 6  Q / 750 Now, equate marginal revenue with marginal cost 6  Q / 750 = 0 Q = 4500 P = 3 Thus, the price is 3 it should charge to maximize club revenue. ...
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 Spring '07
 Hopenhayn

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