B. If the firm wanted to minimize the average total cost, would it choose to be very large or very small? Explain.

The firm should choose a very large output because average total cost will continue to decrease as q is increased. As q becomes infinitely large, ATC will equal $500.

4. Suppose a firm must pay an annual tax, which is a fixed sum, independent of whether it produces any output.

a. How does this tax affect the firm’s fixed, marginal, and average costs?

Total cost, TC, is equal to fixed cost, FC, plus variable cost, VC. Fixed costs do not vary with the quantity of output. Because the franchise fee, FF, is a fixed sum, the firm’s fixed costs increase by this fee. Thus, average cost, equal to , and average fixed cost, equal to , increase by the average franchise fee . Note that the franchise fee does not affect average variable cost. Also, because marginal cost is the change in total cost with the production of an additional unit and because the fee is constant, marginal cost is unchanged.

B. Now suppose the firm is charged a tax that is proportional to the number of items it produces. Again, how does this tax affect the firm’s fixed, marginal, and average costs?

Let t equal the per unit tax. When a tax is imposed on each unit produced, variable costs increase by tq. Average variable costs increase by t, and because fixed costs are constant, average (total) costs also increase by t. Further, because total cost increases by t with each additional unit, marginal costs increase by t.

5. A recent issue of Business Week reported the following:

During the recent auto sales slump, GM, Ford, and Chrysler decided it was cheaper to sell cars to rental companies at a loss than to lay off workers. That’s because closing and reopening plants is expensive, partly because the auto makers’ current union contracts obligate them to pay many workers even if they’re not working.

When the article discusses selling cars “at a loss,” is it referring to accounting profit or economic profit? How will the two differ in this case? Explain briefly.

When the article refers to the car companies selling at a loss, it is referring to accounting profit. The article is stating that the price obtained for the sale of the cars to the rental companies was less than their accounting cost. Economic profit would be measured by the difference of the price with the opportunity cost of the cars. This opportunity cost represents the market value of all the inputs used by the companies to produce the cars. The article mentions that the car companies must pay workers even if they are not working (and thus producing cars). This implies that the wages paid to these workers are sunk and are thus not part of the opportunity cost of production. On the other hand, the wages would still be included in the accounting costs. These accounting costs would then be higher than the opportunity costs and would make the accounting profit lower than the economic profit.

6. Suppose the economy takes a downturn, and that labor costs fall by 50 percent and are expected to stay at that level for a long time. Show graphically how this change in the relative price of labor and capital affects the firm’s expansion path.

Figure 7.6 shows a family of isoquants and two isocost curves. Units of capital are on the vertical axis and units of labor are on the horizontal axis. (Note: In drawing this figure we have assumed that the production function underlying the isoquants exhibits constant returns to scale, resulting in linear expansion paths. However, the results do not depend on this assumption.)

If the price of labor decreases while the price of capital is constant, the isocost curve pivots outward around its intersection with the capital axis. Because the expansion path is the set of points where the MRTS is equal to the ratio of prices, as the isocost curves pivot outward, the expansion path pivots toward the labor axis. As the price of labor falls relative to capital, the firm uses more labor as output increases.

Figure 7.6

8.7. The cost of flying a passenger plane from point A to point B is $50,000. The airline flies this route four times per day at 7am, 10am, 1pm, and 4pm. The first and last flights are fulfilled l to capacity with 240 people. The second and third flights are only half full. Find the average cost per passenger for each flight. Suppose the airline hires you as a marketing consultant and wants to know which type of customer it should try to attract, the off-peak customer (the middle two flights) or the rush-hour customer (the first and last flights). What advice would you offer?

The average cost per passenger is $50,000/240 for the full flights and $50,000/120 for the half full flights. The airline should focus on attracting more off-peak customers in order to reduce the average cost per passenger on those flights. The average cost per passenger is already minimized for the two peak time flights.

8. You manage a plant that mass produces engines by teams of workers using assembly machines. The technology is summarized by the production function.

q = 5 KL

A. What is the cost function for your plant — namely, how much would it cost to produce q engines? What are average and marginal costs for producing q engines? How do average costs vary with output?

K is fixed at 5. The short-run production function then becomes q = 25L. This implies that for any level of output q, the number of labor teams hired will be . The total cost function is thus given by the sum of the costs of capital, labor, and raw materials:

The average cost function is then given by:

and the marginal cost function is given by:

Marginal costs are constant and average costs will decrease as quantity increases (due to the fixed cost of capital).

b. How many teams are required to produce 250 engines? What is the average cost per engine?

To produce q = 250 engines we need labor teams or L=10. Average costs are given by

C. You are asked to make recommendations for the design of a new production facility. What capital/labor (K/L) ratio should the new plant accommodate if it wants to minimize the total cost of producing any level of output q?

We no longer assume that K is fixed at 5. We need to find the combination of K and L that minimizes costs at any level of output q. The cost-minimization rule is given by

To find the marginal product of capital, observe that increasing K by 1 unit increases q by 5L, so MP_K= 5L. Similarly, observe that increasing L by 1 unit increases Q by 5K, so MP_L= 5K. Mathematically,

.

Using these formulas in the cost-minimization rule, we obtain:

.

The new plant should accommodate a capital to labor ratio of 1 to 2. Note that the current firm is presently operating at this capital-labor ratio.

9. The short-run cost function of a company is given by the equation TC=200+55q, where TC is the total cost and q is the total quantity of output, both measured in thousands.

a. What is the company’s fixed cost?

When q = 0, TC = 200, so fixed cost is equal to 200 (or $200,000).

Date: 2015-12-24; view: 1265