Question

5. Suppose that the demand equation for a monopolist's product is p = 400 - 2q and the average cost function is c = 0.29 + 4 + toº, where q is number of units, and both p and c are expressed in dollars per unit. a) Determine the level of output at which profit is maximized b) Determine the price at which maximum profit occurs c) Determine the maximum profit d) If, as a regulatory device, the government imposes a tax of $22 per unit on the monopolist, what is the new price for profit maximization?

Answer 1

0 5. we have f- 400-29 p. 9 400g - 292. Total Reserve 500 margind Rerence - Charen Tota a TR aq - MR = a (400g - 2q2) = 400 - 49 - Ako, we have AC- 0,2q + 4 it (400) 2 TC = Ac. q = 0.2 g 2 + 4 q + 400 - Me @ TC - 0.49 + 4 ag a) At profit merimizing level, 27 it MR - 14c or Yoo - Ug = 0.49 tu 200 Yoo-4 = 0.49 +49 = q = 396. - 90 4.4 :00 (6) At this profit maximizing output f. 907 - yoo - 2190) = 480-180 - $220 16 Now Profit function is given as T 12) = TR (9) - TC (a) T - You q - 2q² - 0.2q² - 4q - 400 T-3969 - 2.29 2 - 400 At 9 - 90 mokinun profit is I 396690) -2.2 (90)'-400 I, 35640 17820 - 400 T = $ 17, 420

• .!! Torper unt d Due to tax f $ & ar per unit the total cost curl & the mondha mie and become in Tec (0.2q² + "q t "oo) + (229) duzina te This me bromes i ate 09 rices 0.49 + 4 +22= 0.49 + 26 New equilibrith is rectijest at HEHE or 0.49 & 26 = 400 - 49 st 4:49 = 374 . ! - q-374 85 units - Si q= 85 , equilibrin faze is given en ps Hoorid(85) l 40o 170 SUNDAY fa$d30... UNDAY