tsts
nΔwiΔxi ≤ 0, where Δwi = w ?wand Δxi = x?xi=1 iiii.
21 Cost Curves
1. Which of the following are true?
(1) Average ?xed costs never increase with output;
(2) average total costs are always greater than or equal to average variable costs;
(3) average cost can never rise while marginal costs are declining. 21.1. True, true, false.
2. A ?rm produces identical outputs at two di?erent plants. If the marginal cost at the ?rst plant exceeds the marginal cost at the second plant, how can the ?rm reduce costs and maintain the same level of output?
21.2. By simultaneously producing more output at the second plant and reducing production at the ?rst plant, the ?rm can reduce costs.
3. True or false? In the long run a ?rm always operates at the mini- mum level of average costs for the optimally sized plant to produce a given amount of output. 21.3. False.
22 Firm Supply
1. A ?rm has a cost function given by c(y) = 10 ????+ 1000. What is its
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supply curve?
22.1. The inverse supply curve is p = 20 y, so the supply curve is y = p/20.
2. A ?rm has a cost function given by c(y) = 10 ???? +1000. At what output is average cost minimized?
22.2. Set AC = MC to ?nd 10y + 1000/y = 20 y. Solve to get y? = 10.
3. If the supply curve is given by S(p) = 100+20p, what is the formula for the inverse supply curve?
22.3. Solve for p to get Ps(y)=( y?100)/20.
4. A ?rm has a supply function given by S(p)=4 p. Its ?xed costs are 100. If the price changes from 10 to 20, what is the change in its pro?ts? 22.4. At 10 the supply is 40 and at 20 the supply is 80. The producer’s surplus is composed of a rectangle of area 10×40 plus a triangle of area 1 2 ×10×40, which gives a total change in producer’s surplus of 600. This is the same as the change in pro?ts, since the ?xed costs don’t change.
5. If the long-run cost function is c(y)= ????+1, what is the long-run supply curve of the ?rm?
22.5. The supply curve is given by y = p/2 for all p ≥ 2, and y = 0 for all p ≤ 2. At p = 2 the ?rm is indi?erent between supplying 1 unit of
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output or not supplying it.
6. Classify each of the following as either technological or market constraints: the price of inputs, the number of other ?rms in the market, the quantity of output produced, and the ability to produce more given the current input levels.
22.6. Mostly technical (in more advanced models this could be market), market, could be either market or technical, technical.
7. What is the major assumption that characterizes a purely competitive market?
22.7. That all ?rms in the industry take the market price as given.
8. In a purely competitive market a ?rm’s marginal revenue is always equal to what? A pro?t-maximizing ?rm in such a market will operate at what level of output?
22.8. The market price. A pro?t-maximizing ?rm will set its output such that the marginal cost of producing the last unit of output is equal to its marginal revenue, which in the case of pure competition is equal to the market price.
9. If average variable costs exceed the market price, what level of
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output should the ?rm produce? What if there are no ?xed costs? 22.9. The ?rm should produce zero output (with or without ?xed costs).
10. Is it ever better for a perfectly competitive ?rm to produce output even though it is losing money? If so, when?
22.10. In the short run, if the market price is greater than the average variable cost, a ?rm should produce some output even though it is losing money. This is true because the ?rm would have lost more had it not produced since it must still pay ?xed costs. However, in the long run there are no ?xed costs, and therefore any ?rm that is losing money can produce zero output and lose a maximum of zero dollars.
11. In a perfectly competitive market what is the relationship between the market price and the cost of production for all ?rms in the industry?
22.11. The market price must be equal to the marginal cost of production for all ?rms in the industry.
23 Industry Supply
1. If S1(p)=p?10 and S2(p)=p?15, then at what price does the industry supply curve have a kink in it?
23.1. The inverse supply curves are P1(y1) = 10+y1 and P2(y2) = 15+y2. When the price is below 10 neither ?rm supplies output. When the price
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is 15 ?rm 2 will enter the market, and at any price above 15, both ?rms are in the market. Thus the kink occurs at a price of 15.
2. In the short run the demand for cigarettes is totally inelastic. In the long run, suppose that it is perfectly elastic. What is the impact of a cigarette tax on the price that consumers pay in the short run and in the long run?
23.2. In the short run, the consumers pay the entire amount of the tax. In the long run it is paid by the producers.
3. True or false? Convenience stores near the campus have high prices because they have to pay high rents.
23.3. False. A better statement would be: convenience stores can charge high prices because they are near the campus. Because of the high prices the stores are able to charge, the landowners can in turn charge high rents for the use of the convenient location.
4. True or false? In long-run industry equilibrium no ?rm will be losing money. 23.4. True.
5. According to the model presented in this chapter, what determines
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