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Unformatted text preview: Chapter 10 Long-run Equilibrium and Short-run Changes. All firms have identical cost functions. a. Consider the following cost function for the production of DVDs. TC = 2500 + q 2 b. Using this function we can determine marginal costs and average costs. i. AC = 2500 q + q ii. MC = 2 q c. We can find the q that minimizes average costs either by differentiating the first expression or by setting average costs equal to marginal costs. i. AC = 2500 q + q = 2 q = MC ii. q * = 50 This is the quantity that minimizes average costs. This will be the firm size in any long run equilibrium (it is the only firm size that minimizes average costs). d. Substituting this number into the average cost function, we get min( AC ) = 2500 50 + 50 = 100 e. We know that the long run price equals the minimum average cost. f. In order to find the equilibrium quantity, we need a demand function. Consider the following Q D = 1000- 2 P + 5 P BR If P BR = 200 this simplifies to Q D = 2000- 2 P g. We know the price is 100 in the long run. Plugging this into the demand function, we getg....
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- Fall '08
- Economics, minimizes average costs