Perfect competition problem set - questions 1, 3, 5, 13, 18, 20 and 21 from McGraw Hill Microeconomics and Behaviour PDF

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questions 1, 3, 5, 13, 18, 20 and 21 from McGraw Hill Microeconomics and Behaviour by Frank and Cartwright EMEA, 3rd edition....

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Chapter 12 Review Questions

1.

! hat is the difference between economic profit and W accounting profit, and how does this difference matter for actual business decisions? Economic profit includes all costs – both explicit and implicit - while accounting profit looks only at explicit costs. The firm should take into account implicit costs and hence focus on economic profit only. 3. !Would the market for dry cleaning be perfectly competitive in large cities such as Paris or London? Why or why not? How about in a small town? The dry-cleaning markets would be nearly perfect except that many people do not want to drive far for their clothing pickups and drop-offs. In small towns there may only be one or two cleaners so less competition will be present. 5. !Does the fact that a business manager may not know the definition of marginal cost contradict the theory of perfect competition? No, because managers often relate to their competition by trial and error actions moving in the direction of what succeeds for them. This moves the firm to the quantity of output that is consistent with perfect competition outcomes.

Problems

2.

!If the short-run marginal and average variable cost curves for a competitive firm are given by SMC = 2 + 4Q and AVC = 2 + 2Q, how many units of output will it produce at a market price of 10? At what level of fixed cost will this firm earn zero economic profit? Setting price P = 10 equal to marginal cost of SMC = 2 + 4Q, solve for quantity 10 = 2 + 4Q or 8 = 4Q or Q = 2. The fixed cost that leads to zero economic profit is calculated by solving p = (P – AVC)Q – FC = 0 or (10 – 6)2 – FC = 0 for FC = 8.

3.

! ach of 1,000 identical firms in the competitive peanut E butter industry has a short-run marginal cost curve given by SMC = 4 + Q. If the demand curve for this industry is

what will be the short-run loss in producer and consumer surplus if an outbreak of aflatoxin suddenly makes it impossible to produce any peanut butter? SR supply = !

!

MCi = 4 + Qi Qi = MCi – 4 = P-4 = Q =1,000P - 4,000 which means that industry supply is given by P = 4 + Q/1,000. SR equilibrium Q: 4 + Q/1,000 = 10 - 2Q/1,000 3Q/1,000 = 6, Q = 2,000, P = 6.

! onsumer surplus = area of upper triangle = (10C 6)*2000/2 = 4,000. !Producer surplus = area of lower triangle = (6-4)*2000/2 = 2,000. !Total loss in surplus = 6,000.

5.

!A perfectly competitive firm faces a price of 10 and is currently producing a level of output at which marginal cost is equal to 10 on a rising portion of its short-run marginal cost curve. Its long-run marginal cost is equal to 12. Its short-run average variable cost is equal to 8. The minimum point on its long-run average cost curve is equal to 10. Is this firm earning an economic profit in the short run? Should it alter its output in the short run? In the long run, what should this firm do?

Since P = SMC > AVC, the firm should continue at its current level of output in the short run. In the long run, it should select the plant size for which P = LMC = SMC. We cannot tell, however, whether the firm is making a profit because we do not know the extent of fixed costs. In the long run, it should select the plant size for which P = LMC = SMC. As indicated in the diagram below, this means it should switch to a smaller plant size in the long run.

13.

!A firm in a competitive industry has a total cost function of TC = 0.2Q - 5Q + 30, whose corresponding marginal cost curve is MC = 0.4Q - 5. If the firm faces a price of 6, what quantity should it sell? What profit does the firm make at this price? Should the firm shut down? TC = 0.2 Q2 - 5Q + 30 - >. Taking the derivative yields MC = MC = dTC/dQ = 0.4 Q - 5. 2

In equilibrium MC = P, which implies 0.4Q - 5 = 6, which solves for Q = 27.5. Profit = revenue – cost = 27.5x6 - [0.2(27.5)2 -5(27.5) + 30] = 121.25. Since the firm earns positive profit, it should stay open. 18.

!An Australian researcher has discovered a drug that weakens a sheep’s wool fibres just above the sheep’s skin. The drug sharply reduces the cost of shearing (cutting the wool off) sheep because the entire coat pulls off easily in one piece. The world wool market is reasonably close to the model of perfect competition in both the product and factor sides. Trace out all of the effects of the introduction of this new drug. (i) Costs will fall for all existing firms. At existing prices, the firms will make positive economic profits and increase output.

(ii) New firms will enter the industry because of profits. (iii) The industry supply curve will shift out until profits are again driven down to zero. The final result is that prices

fall, quantity increases, and there are more firms than before. In other words, consumers reap all the surplus from this innovation.

0.5

20. A firm in a perfectly competitive industry has short-run production function Q = 10L . The price of labour is w = 500. Derive the firm’s short-run supply curve. The firm’s profit function is . The FOC yields which implies and thus the short-run supply curve is .

21. All firms in a perfectly competitive industry have production function Q =2K L . The price of labour is w = 4 and that of capital is r =1. Derive the industry long-run supply curve. 0.5

0.5

The firm’s profit function is given by: The FOCs to the profit maximization problem of the firm can be written as These imply in turn that in the long run the firm will choose its capital/labour ratio so that the ratio of the marginal products of the two inputs is equal to the ratio of their prices: Replacing this condition in the production function to derive the optimal demand of capital and labour yields K(Q)=Q and L(Q)=Q. The firm’s total cost function is thus TC(Q) (=4L+K) = 4Q+Q = 5Q. The associated LAC is thus equal to 5. As this is a constant, it is minimized for any value of Q. Thus, in this world firms (and thus the market) are willing to supply any quantity to the market at P=5. This is a result that is always obtained under perfect competition when firms produce with a production function that exhibits constant returns to scale (indeed, the FOC for profit maximization does not depend on Q, as it is given by, in the specific case we have here: P=5). To be fully precise, the supply of this market is given by:...