# hw 11 - HOMEWORK 11 DUE AT START OF CLASS MONDAY FEBRUARY...

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Unformatted text preview: HOMEWORK 11 DUE AT START OF CLASS MONDAY, FEBRUARY 21 1. Consider a market in which all firms have access to a technology with cost function C(q) = 100 + 40g + q2 for q > 0 and 0(0) = 0, where q is the firm’s output. This cost function applies in both the short and long run, but in the short run ﬁrms cannot enter the market. Aggregate demand is D(p) = 3600 — 30p. a. What is the supply function for a single firm? b. What are the long run competitive equilibrium price, quantity and number of firms? Suppose the 100 in the cost function represents the salary paid to a manager needed to coordinate production. The number of potential managers with this skill level is unlimited, and all have the option of working in a different industry in which they could obtain wage 100 per period. Starting from the long—run equilibrium in Part (b), suppose that a testing service reveals that ten potential managers, who work in a different industry, have special skills when working in this industry. All ten of these potential managers are identical, and identical to the original managers, in their abilities outside this industry. However, these ten potential managers are now known to have a different level of skill when organizing production in this industry. When any of this group of ten runs a firm in this industry, the firm’s cost function (ignoring the manager— salary portion) is qz. The skill level has been publicly announced by the testing service, so it is observable by firms. Firms may change managers in the short run. c. What is the new short-run equilibrium and how does it differ from the short run equilibrium without the new information about these ten potential managers? Where do these managers work, and what are their salaries? d. What are the changes in surplus due to the new information about these potential managers? 2a. What is the long—run competitive equilibrium for a market in which firms have cost function C(q) = 90,000 + q2 for q > 0 and C(0) = 0, where q is the firm’s output, and aggregate demand is D(p) = 21,000 — 10p, where p is the perwunit price? b. Suppose the 90,000 in the cost function represents the salary paid to a manager needed to coordinate production. The number of potential managers with this skill level is unlimited, and all have the Option of working in a different industry in which they could obtain wage 90,000 per period. Starting from the long—run equilibrium specified above, suppose that a new group of potential managers becomes available. All the new potential managers are identical, and identical to the original managers in their abilities outside this industry and all but two are identical to the original managers in terms of their skills in this industry as well. However, two of the new potential managers, Yvonne and Zane, are known to have a different level of skill when organizing production in this industry. When Yvonne runs a firm in this industry, its cost function (ignoring the manager—salary portion) is 3009' + (qr2 /6) while the corresponding cost when Zane runs a firm is 200q + (qu2 3). In the new long-run equilibrium, where do Yvonne and Zane work and what are their salaries? READING ASSIGNMENT for Monday, February 21st Part of text Chapter 10 Efficiency of equilibrium: pages 362 — 4 Excise taxes: pages 364 — 71 Subsidies: pages 372 — 4 Price ceilings: pages 374 — 82 Price floors: pages 382 — 9 ...
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hw 11 - HOMEWORK 11 DUE AT START OF CLASS MONDAY FEBRUARY...

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