Assignment 5 solutions Q1-1

Assignment 5 solutions Q1-1 - Assignment 5 Solutions...

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Unformatted text preview: Assignment 5 Solutions November 3, 2011 Question [1] (A) To find an average cost, we first need the total cost. The total cost is the combination of fixed and variable costs. We are told fixed costs are 16 and variable costs are (12, so we can say total cost, TC, is: TC'(q) = 16 + (12. To find the average cost, we just divide the total by the number of units we want the average for (just like finding the average of anythingl), so we divide TC by q and we get AC(q) = TC(q)/q = 16/q + q. (B) The minimum point of the average cost curve is found where marginal cost (MC) is equal to average cost (AC). We are given marginal cost as 2q, so we have 2q 2 16/q + q which yields q = 4. (C) The long—run equilibrium price is found at the minimum point of the long—run average cost curve. Since the question tells us this minimum is the same as in the short run, we know the solution will be the average cost that exists at q=4 for the firm. Plug q = 4 into AC(q) to get AC(4) = 4 + 4 = 8. Thus, the long—run equilibrium price is 8. (D) Lond run equilibrium output will be the output that satisfies de— mand at the long—run equilibrium price (which we just found in part C). We are given demand as Q(P)=80—4P, so (2(8) 2 80 — 32 = 48. (E) In this chapter we assume all firms are identical and that the number of firms can be represented by n. Therefore, if we need to produce 48 units in the long—run and we know that each firm produces at its efficient scale of 4 units each then n = Q/q = 48/4 2 12. Thus, there will be 12 firms in long— run equilibrium. For more on the theory read pages 503—504 in the textbook. (F) We know that firms choose their quantity such that P = M C in perfectly competitive markets. Thus, P 2 2q <=> q = P/2. We know Q = mg 2 12(P/2) = 6P <=> P = (1/6)Q. (G) The long—run market supply curve is horizontal at P = 8. Firms do not make profit in the long run and they all produce at their minimum efficient scale, so the only no—profit price is where P28. The supply curve is necessarily a horizontal line at P28 because price does not vary with quan— tity in the long run in perfect competition. (H) In the short run, we can find consumer and producer surplus in the usual way by using the information provided in the demand and supply curves. See Figure 1 below. Since demand and supply curves are linear, we can use the formula for the area of a triangle to calculate the surpluses. CS 2 .5(48)(12) = 288 and PS 2 .5(48)(8) = 192. AS 2 CS + PS 2 480. (I) Now we have a new equation for the demand curve. Set it equal to the equation for short run supply that we calculated in to get 120—4P 2 GP <=> P = 12. (J) The number of firms must remain fixed in the short run; there is no time for new firms to enter. Now that the market demands 72 units, the existing 12 firms in operation will equally share in this production. q = Q/n = 72/12 = 6. So each firm will produce 6 units (and will do so at a higher average cost because they are no longer at the efficient scale of 4 units). (K) Here we are asked to calculate the profits of an individual firm (not the entire industry). Profits 2 Total Revenue — Total Costs 2 Pq — (16+q2) = (12)(6) — 16 — 62 = 20 (L) We found in part (C) that the price in the long run is P28; this is not affected by the increase in demand. So to find the new output we do what we did in part Demand is = 120 — 4P so = 120 — 32 = 88. (M) Now that we are in the long run again, we know that each firm will operate at its efficient scale. Since there has been no change in the cost function of the firms, the efficient scale continues to be at q = 4. So now that we have determined the market requires 88 units, we will need 22 firms each producing 4 units to satisfy the demand. (N) Now that the number of firms has changed7 we will have a new short—run market supply curve. We follow the same approach as in part We know q=P/ 2. As always7 total output can be found by the equation Q = mg 2 (22)(P/2) 2 HP <=> P = (1/11)Q. (O) The profit maximizing level of output for a firm remains at q = 4. This will not change as long as the cost function does not change. (P) We can use the same approach as we did in part again, the only difference is we now have new demand and supply curves. See Figure 2 below. CS 2 .5(88)(22) = 968 and PS 2 .5(88)(8) = 352. 20 P=(1/5)Q Figure 1: 30 Figure 2: 38 P=(1/11)Q ...
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This note was uploaded on 02/02/2012 for the course ECON 2410 taught by Professor Prescott during the Fall '11 term at University of Guelph.

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Assignment 5 solutions Q1-1 - Assignment 5 Solutions...

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