Department of Agricultural and Resource Economics ENV ECON 1 University of California at Berkeley

Transcription

1 Department of Agricultural and Resource Economics ENV ECON 1 University of California at Berkeley P. Berck INTRODUCTION TO ENVIRONMENTAL ECONOMICS AND POLICY Solutions to Problem Set No. 4 by Atanu Dey (Revised by Susan Stratton) 1) Note: The answers to this problem set used Peter s convention MC(q) = C(q+1) C(q). As mentioned during section, either convention is okay as long as you are consistent. (I.e., answers using the convention MC(q) = C(q) C(q-1) were marked correct as well). a) See Table 1. Table 1 Q TC(Q) FC(Q) TVC(Q) ATC(Q) AVC(Q) MC(Q) b) See Figure 1. The average cost (also called the total average cost) curve is U- shaped because, for the initial range of output, average costs decline and subsequently increase. The initial decline is due to economies of scale, indivisibility of inputs, etc. Later, diseconomies of scale set in and average costs increase. The average variable cost curve follows the shape of the average cost curve with the difference being the average fixed cost (which is decreasing continuously). The marginal cost is assumed to be increasing and so the upwardsloping MC curve. Annie s supply curve is that portion of the MC curve above the AVC curve.

2 Figure 1: Annie's Cost Curves 3.00 Dollars/Ton AC MC 0.50 AVC Quantity 10 c) With 60 cents per ton as the price, the quantity supplied is 4 tons since, at that quantity, the marginal cost is equal to the price. P = MC(5). d) In the short run, the portion of the MC curve above the AVC curve is the firm s supply curve. In the long run entry drives the price down to minimum average cost which is where marginal cost hits average cost. Therefore, the industry s long run supply curve is tangent to the average cost curve at its minimum. e) The minimum AVC is 53 cents. So 53 cents per ton is the shut-down price, and the supply is therefore zero for prices below 53 cents. For $1.00 per ton, each firm supplies 5 tons since P = MC(5). Therefore, the industry supply is 500 tons. For $2.00 per ton, the industry supply is 700 tons. f) When prices are below the shut-down price, the revenue is zero but fixed costs are $2.00. So the profits are -$2.00. With P = $1.00, the revenue is $5.00 and the costs are $4.70. So the profit is 30 cents. With P = $2.00, revenue is $14, costs are $7.20, and profit is $6.80. g) With FC decreasing from $2.00 to $1.00, the MC and the AVC curves do not change. Only the AC curve shifts down so that the gap between the AC and the AVC is the lower AFC. The total cost decreases by $1.00 at each point. For a price of $2.00 per ton, the profit-maximizing quantity is still 7 tons (since the MC does not change). So the revenue is still $14, but the total cost is only $6.20. Therefore, the profit is $7.80. This means that any reduction of the fixed cost is reflected in the bottom line of the firm.

3 Suppose that Annie was renting the land to grow the apples. If the rent were negotiated down, then the fixed cost would come down. Or suppose that Annie hired a consultant each season for advice. She could move to a less expensive consultant. Or suppose that she rented an apple-harvesting machine each season. If she found a better deal, she could cut down on that fixed cost. 2) a) If the average cost curve is U-shaped, then the marginal cost curve for the firm is below the AC curve in the portion where the AC curve is downward sloping and the MC cost curve is above the AC curve in the portion where the AC is upward sloping. The MC curve will cross the AC curve at the minimum point of the AC curve. If the marginal is less than the average, the average declines. If the marginal is greater than the average, the average increases. If the marginal is equal to the average, the average stays the same. Therefore, the AC must have a minimum and the marginal must cross the average at this point. b) In the short run, the firm should continue to produce since it is covering all of its variable costs of production. The profits at this point will be negative since the revenue (P x Q) is less than the total cost, which is AC(Q) x Q. c) A change in the firm s fixed cost affects the profits. But the profit-maximizing quantity depends on the marginal costs of the firm and the price that the firm faces. Therefore, the profit-maximizing quantity changes only if the firm s MC changes or if the price changes or both. Since the fixed cost has no effect on either the MC or the price, the result follows. 3) a) No, the demand did not decrease. Initially, the industry was in a long-run equilibrium where p=mc=ac. Demand shifted out causing a rise in price. This allowed the incumbent producers to earn profits and induced new firms to enter. Therefore, the supply did shift outward (200,000 acres extra in production between 1969 and 1975 an increase of 44 percent.) This resulted in the price decline. (See Figure 2)

4 Figure 2 S1 S3 S2 P1 Min AC P2 D2 D1 b) No, the price decline from its high point is simply evidence of new supply entering. However, vineyards going bankrupt does suggest overplanting (i.e. the price fell too far.) Again, the decline may be a temporary phenomenon. If in a few years demand grows adequately, then the added capacity would be required to meet the demand without moving above the long-run equilibrium again. c) There are three types of vineyards we need to consider. The vineyards with highest costs of production might have average variable costs that exceed the price. These vineyards should shut down immediately. As we know, firms who are not covering their total costs (i.e. p<ac) but are covering their variable costs (p>avc) should continue to produce in the short run. Some of these vineyards may have borrowed from banks to cover their fixed costs. If they are not earning enough to pay back their loans, they will have to declare bankruptcy. However, they should still produce in the short run to minimize the amount of loan default. Vineyards that were financed with private savings or selling stocks will also be unable to cover their fixed costs, but won t go bankrupt because they have no obligations that have to be paid. Vineyards in the last two categories will leave the industry in the long-run if demand conditions remain the same. However, the long-run for vineyards may be very long and if demand increases they may be able to get back in the black before too long. d) Government intervention in the initial price rise by instituting price ceilings would have led to shortages. Grape growers would have been inhibited from

5 planting more acres seeing little profit in the business. Consumer surplus would have been reduced because of shortage of wine in the markets. Therefore, government is well advised to keep out of meddling with the market. In the event of the price fall, a similar argument can be made with the appropriate changes, e.g., instituting price floors would lead to excess supply. Moreover, the article talks about producers going out of business. This is evidence of the market correcting. Left alone, the market will reach an equilibrium were demand = supply and firms are making normal profits (i.e. zero economic profit). If the government were to intervene (perhaps using a tax or quota to control production and prevent overplanting), the government would have to know BEFORE the vineyards started planting how much wine would be demanded in several years. There is no reason to expect the government to be any better at predicting this than the vineyard owners.