Problem Set No. 4
1. Annie grows apples on her farm. Her production costs are as follows:
Quantity (tons) Total Cost (dollars) 0 2.00 1 2.70 2 3.20 3 3.60 4 4.10 5 4.70 6 5.70 7 7.20 8 9.20 9 11.70
a. Calculate Annie's fixed costs (FC), total variable costs (TVC), average total costs (ATC), average variable costs (AVC), and marginal costs (MC). Arrange these in a well-organized table.
b. Plot MC, ATC, and AVC on one graph. Explain the shape of each of the curves. On the same graph, show Annie's supply curve.
c. Suppose that the price of apples is .60 cents per ton. How much does Annie produce? Why?
d. What is the relationship between a firm's MC and its short-run and long-run supply curves?
e. Suppose that the apple industry consists of 100 growers, each having the same costs as given above (i.e., the industry is composed of Annie and another 99 identical producers). How many tons of apples will be produced by the apple industry when the price per ton is .40 cents, .50 cents, $1.00, and $2.00? Explain. Graph the industry's supply curve.
f. Calculate Annie's (i.e., one firm's) profit for each of the above prices.
g. Imagine that Annie hits upon a way to decrease her fixed costs to only $1.00. Graph her new cost curves. What would be her short-run profit at a price of $2.00 per ton? Give an example of a way that Annie could reduce her fixed costs.
2. Briefly answer the following questions about a competitive firm's average, marginal, and fixed costs.
a. If a firm's average cost curve is U-shaped, what do we know about the firm's marginal cost curve? Specifically, what point on the U-shaped average cost curve will the marginal cost curve cross? Why?
b. Suppose that, at the quantity where P = MC, price is greater than average variable cost but less than average total cost. In the short run, should the firm continue to produce or shut down? Why? Will profits be positive or negative?
c. Why does it make sense for a change in a firm's fixed cost not to change the output level that maximizes its profits?
3. Read the following article from Newsweek. Answer each of the following questions in words and using clearly labelled graphs of firms' cost curves and industry supply and demand curves.
a. Did the price fall because demand decreased (i.e., a demand curve shift to the left)?
b. Is the price decline, in and of itself, evidence of "overplanting," i.e., a level of production greater than the long-run equilibrium level?
c. The article states that some vineyards are "bankrupt." What does this mean in terms of their ability to cover their fixed costs? Their variable costs? Which firms will be going bankrupt (compare cost curves)? What should these firms produce in the short run? In the long run?
d. Should the government have intervened to prevent the initial price rise? The price fall? Why or why not?
California: Sour Grapes
"This ought to be a time of rejoicing in the vineyards of California. The crop of wine grapes has rarely been richer, the harvest is nearly complete, and Americans are drinking more California wine than ever before. But not quite enough, as it turns out. Because of overplanting during the past five years of unprecedented boom, the graph crop this year is simply too big to squeeze. As a result, a number of growers were licking their financial wounds last week, while wine lovers were licking their chops in anticipation of what one expert predicts will be five years of top-quality California wine offered at bargain-basement prices.
The cycle started back in the early 1970s when Americans suddenly turned to wine, particularly moderate-priced brands from California. Sales began to skyrocket, and wholesale grape prices began to rise as well. Cabernet Sauvignon grapes, California's finest black variety, climbed to a peak of $810 per ton in 1973. The Bank of America confidently predicted that the decade would bring 'the strongest growth in wine markets ever recorded.' Industrial conglomerates began buying vineyards, and so did hastily organized partnerships of airline pilots, doctors, lawyers, and other professional people with money to invest. Since it takes at least three years to bring a vineyard to maturity, the new growers began planting as fast as they could. In 1969, there were 450,000 acres of grapes in California; this year, there are 650,000.
The cork finally popped. Even though the sale of California wine will increase by 9 percent this year, that is not enough to soak up the added production, and prices for grapes and wine alike are tumbling. Chardonnay grapes, for example, went for $815 per ton two years ago; they are now selling for $350 to $400. The result is a number of bankrupt vineyards and a slash in winery profits. Prudential Insurance Company of America recently foreclosed on 2,000 acres of wine grapes in the Fresno area, and Roger Hoag, a company official, predicts that it will be three years before many investors have any hope of getting back in the black. 'There will be a lot of vineyards pulled out,' Hoag said. 'This is the only way the overplanting can be rectified.'"
Newsweek, November 17, 1975.