Principles of Microeconomics

Problem Set 6

Principles of Microeconomics

Matthew Weinberg

Due: May 27, 2014

1. You produce widgets. Currently you produce 4 widgets at a total cost of $40.

(a) What is your average total cost?

(b) Suppose you could produce one more (the fifth) widget at a marginal cost of $5. If you do produce that fifth widget, what will your average total cost be? Has your average total cost increased or decreased? Why?

(c) Suppose instead that you could produce one more (the fifth) widget at a marginal cost of $20. If you do produce that fifth widget, what will your average total cost be? Has your average total cost increased or decreased, relative to part (a)? Why?

2. Explain whether each of the following statements is true or false, and explain your reasoning.

(a) At any given level of production, the short-run average total cost can never be less than the long-run average total cost.

(b) At any given level of production, the short-run average variable cost can never be less than the long-run average total cost.

3. Suppose that Kim owns a coffee shop, and the coffee business is perfectly competitive. On a daily basis, her fixed cost from machinery is $30. Her daily variable costs for labor and ingredients are described by Table 1, where Q is the number of cups of coffee sold.

(a) Calculate the total cost, average variable cost, average total cost, and marginal cost for each quantity of output.

(b) Suppose the market price of coffee is $0.70 per cup on Monday. If Kim decides to produce coffee on Monday, what is the profit-maximizing amount of coffee she should produce? How much profit does she earn?

(c) If the market price of coffee is $0.70 per cup on Monday, should she shut down or produce in the short run (i.e., on Monday)? Explain intuitively.

(d) In the long run, should Kim exit or stay in the coffee business if the market price stays at $0.70 per cup? What is the market price at which Kim should exit the industry? Compare your answer to that of part (c) and explain.

Q V C(Q) 0 0 10 2 20 4 30 10 40 18 50 35

Table 1: Kim’s daily variable costs

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4. Suppose that the laptop industry is perfectly competitive and the market is in long-run equilibrium. Assume that the long-run market supply curve is perfectly elastic.

(a) On two separate graphs, illustrate this initial equilibrium for (1) an individual producer, and (2) for the entire market. For the individual producer, be sure to include the average total cost curve and its optimal production level. For the entire market, be sure to include both the short-run and long-run industry supply curves.

(b) The popularity of laptops surges, causing demand to increase. Draw your graphs from part (a) again, and show the short-run impact of the increase in demand for laptops on (1) an individual firm’s profits, and (2) the entire market for laptops. Be sure to mark off the area that corresponds to an individual firm’s profits.

(c) The demand for laptops remains at its new level. Illustrate and describe the impact on laptop prices in the long run, both on (1) individual producers, and (2) the entire market. How does the quantity supplied by each individual firm compare to the original situation described in part (a)? How does the quantity supplied in the entire market compare to the original situation described in part (a), and why?

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