22. In a perfectly competitive market, market demand and supply functions are respectively: Demand: Q = 500 -0.5P, Supply: Q₁ = -800 +2P, where P is price while Qa and Q. are quantity demanded and supplied for the whole market respectively. (a) Solve the equilibrium price (P) and the market quantity (Q). (b) Suppose the supply side is composed of 1000 firms with identical cost functions. Assume that average variable cost (AVC) curve is below marginal cost (MC) for all q, where q is the output of a single firm. Find a typical firm's MC function. [Hint: If there are only two firms, whose MC functions are respectively MC₁ = a+bq₁ and MC₂ = a+bq2, then since firms produce at where P-MC, the quantity supplied by the two firms are respectively q₁ = (P-a)/b and q2 = (P-a)/b. The market supply is qi+q2 = 2(P-a)/b or Q₁ = -2a/b +2P/b. Using this logic, you can do the reverse: finding MC from market supply.] (c) (d) The typical firm's average total cost (ATC) is U-shaped. ATC is lowest when q = 0.2. Draw a diagram to indicate a typical firm's MC, ATC, the point where q = 0.2, and the profit-maximization output. Solve the typical firm's profit-maximizing output (q). You should provide a numerical value.

22. In a perfectly competitive market, market demand and supply functions are respectively: Demand: Q = 500 -0.5P, Supply: Q₁ = -800 +2P, where P is price while Qa and Q. are quantity demanded and supplied for the whole market respectively. (a) Solve the equilibrium price (P) and the market quantity (Q). (b) Suppose the supply side is composed of 1000 firms with identical cost functions. Assume that average variable cost (AVC) curve is below marginal cost (MC) for all q, where q is the output of a single firm. Find a typical firm's MC function. [Hint: If there are only two firms, whose MC functions are respectively MC₁ = a+bq₁ and MC₂ = a+bq2, then since firms produce at where P-MC, the quantity supplied by the two firms are respectively q₁ = (P-a)/b and q2 = (P-a)/b. The market supply is qi+q2 = 2(P-a)/b or Q₁ = -2a/b +2P/b. Using this logic, you can do the reverse: finding MC from market supply.] (c) (d) The typical firm's average total cost (ATC) is U-shaped. ATC is lowest when q = 0.2. Draw a diagram to indicate a typical firm's MC, ATC, the point where q = 0.2, and the profit-maximization output. Solve the typical firm's profit-maximizing output (q). You should provide a numerical value.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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