hw 11 Soln

# hw 11 Soln - HOMEWORK 11 Sample Solution 1a Note the 100 is...

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Unformatted text preview: HOMEWORK 11 Sample Solution 1a. Note the 100 is an avoidable fixed cost, not sunk. Thus it must be included in the average cost calculation when we set marginal cost, 40 + 2g, equal to average [non—sunk] cost, (100/q) + 40 + q, to obtain the output, q = 10, at which average cost is minimized. The corresponding average cost is 60. For prices ab0ve 60, the firm chooses q to make marginal cost equal to the price, 40 + 2g :1). Solving for q, q = 0.5p — 20. Thus the supply function for a firm is 0ifp<60 s(p)= 00r10ifp=60 0.5p~—20 ifp>10 b. Because demand at price 60 is positive, the equilibrium price cannot be less than 60 (because aggregate supply there is zero). The equilibrium price cannot be above 60 because additional firms would want to enter. Thus the equilibrium price is p* = 60, with equilibrium quantity Q* = D(60) = 1800. Since each firm produces either 0 or 10 at price 60, there must be N* = Q*/ 10 = 180 firms active in the equilibrium. 0. In the short run, ﬁrms may not enter, but they may exit or change managers. If a firm used one of the new managers at salary 100, the firm’s optimal output at price 60 (the old equilibrium price) would be 30 and it would have surplus (and proﬁt, because there are no sunk costs) of 800. With all 10 of the new managers employed, the corresponding 10 firms would produce 300, which is less than demand at price 60. Thus the equilibrium price is p* = 60 (unchanged) and the corresponding aggregate output is Q* = D(60) =1800 (unchanged). Firms would compete to hire the 10 new managers until the salary paid was high enough (the originai 100 plus 800) that the firm would just break even. The 10 new managers prefer to work in this industry, so all 10 are employed in the industry displacing 30 original managers. Thus the number of firms is N* = 160 (150 with regular managers and 10 with new managers). All 10 new managers work in this industry for salary 900 each. d. CS and PS are unchanged. The regular managers are unaffected (even if they change industry, their salaries are unchanged). The 10 special managers are now paid 900 instead of 100, for a gain (economic rent) of 800 each, 8000 total. 2a. Note the 90,000 is an avoidable fixed cost, not sunk. Thus it must be included in the average cost calculation when we set marginal cost, 2c], equal to average [non—sunk] cost, (90000/q) + q, to obtain the output, q = 300, at which average cost is minimized. The corresponding average cost is 600. Because demand at price 600 is positive, the equilibrium price cannot be less than 600 (because aggregate supply there is zero). The equilibrium price cannot be above 600 because additional firms would want to enter. Thus the equilibrium price is p* = 600, with equilibrium quantity Q* = D(600) = 15000. Since each firm produces either 0 or 300 at price 600, there must be N* = Q*/300 = 50 firms active in the equilibrium. b. Yvonne works in this industry for salary \$135,000. Zane works elsewhere for salary \$90,000. This question is about longwrun equilibrium, but the approach and reasoning are similar to that in Problem 10. At price 600, a firm employing Yvonne [Zane] at the base salary of 90,000 3 l i l would have optimal output 900 [300] and profit \$45,000 [loss \$30,000]. Thus no firm would hire Zane, who would end up working elsewhere for \$90,000. Firms would compete to hire Yvonne until her salary was the \$90,000 base plus \$45,000 (economic rent). Because a firm employing Yvonne would produce 900 rather than the 300 produced when a regular manager is employed, Yvonne would displace 3 of the 50 regular managers who were previously employed in this industry, but the equilibrium price and aggregate quantity would not change. l l l l l l 1 a ...
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hw 11 Soln - HOMEWORK 11 Sample Solution 1a Note the 100 is...

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