Chapter 6 Homework Examples

Suppose the wage rate is $25 per hour and the rent on capital is $50 per hour. The equation for the isocost line is given by: C = 75LK. C = 25L + 50K. C = 75(L + K). C = 2K/L.

C = 25L + 50K

In the long run, because firms can adjust both capital and labor: firms fire workers, replacing the labor productivity with capital. firms will grow. production is more expensive because firms must invest in both labor and capital. the impact of diminishing marginal returns is lessened.

the impact of diminishing marginal returns is lessened.

or the production function Q(K,L) = K0.5L0.5, the marginal product of capital is: 0.5K0.5L-0.5 0.5K^-0.5L^0.5 K-0.5L0.5 0.25X-0.5Y-0.5

0.5K^-0.5L^0.5

Suppose a firm's short-run production function is given by Q = 16L0.8. What is the marginal product of the fourth worker? 1.85 49 10 36

10

For the production function Q(K,L) = 3K + 2L, the marginal product of labor is: 2L. 3. 3K. 2.

2

For the production function Q(K,L) = 3K + 2L, the marginal rate of technical substitution MRTSlk is: 2L/3K. 3/2. 2/3. 3K/2L.

2/3.

A donut shop has a production function given by Q = 50K1/3L1/2, where Q is the number of donuts produced per hour, K is the number of donut fryers (which is fixed at eight in the short run), and L is the number of employed workers. How many donuts can be produced per hour with four workers in the short run? 200 167 84 320

200

Which situation will likely give rise to diminishing marginal product of labor? Hell's Kitchen, which has enough counter space for three cooks per shift, decides to hire a fourth cook per shift. A landscaping firm replaces all of its self-propelled lawnmowers with push mowers. Plasma television manufacturers are going out of business because of increased competition from LCD televisions. Nevaeh's Kitchen undertakes a massive expansion, doubling both the size of its kitchen and number of cooks.

Hell's Kitchen, which has enough counter space for three cooks per shift, decides to hire a fourth cook per shift.

Which of the following statements is (are) TRUE? I. If labor and capital are perfect substitutes in production, the isoquant is a downward-sloping line. II. If a company needs to use inputs in fixed proportion such that the capital to labor ratio is always 2, the firm's isoquants are L-shaped. III. If the production function is given by Q = min(14, 7), the firm can produce, at minimum, 21 units of output.

I and II

MRTSLK decreases as the firm substitutes labor for capital along the isoquant for all production functions below EXCEPT: I. Multiproduct firms: All firms produce at least two goods. II. Firms only use two inputs in the production process: capital and labor. III. Cost minimization: Firms attempt to produce a fixed quantity of output at the lowest possible total cost. IV. Firms can produce more output by using more inputs.

II, III, and IV

Suppose the slope of a short-run production function is given by 2/L0.5. Which of the following statements is (are) TRUE? I. The marginal product of the fifth worker is 0.20. II. The production function exhibits increasing marginal returns. III. The marginal product of the sixteenth worker is 0.50. IV. The production function's slope eventually changes from positive to negative as the firm produces more and more.

III. The marginal product of the sixteenth worker is 0.50.

For the production function Q(K,L) = K0.5L0.5, the marginal rate of technical substitution MRTSlk is: K/L. 0.25L/K. 0.25K/L. L/K.

K/L.

Suppose a firm is producing 2,475 units of output by hiring 50 workers (W = $20 per hour) and 25 units of capital (R = $10 per hour). The marginal product of labor and marginal product of capital are 40 and 25, respectively. Is the firm minimizing the cost of producing 2,475 units of output? Yes, the ratio of the number of workers to the wage equals the ratio of the number of units of capital to the rental rate. No, the firm should use more labor and less capital. No, the firm should use more of both labor and capital. No, the firm should use more capital and less labor.

No, the firm should use more capital and less labor.

Which of the following is a Cobb-Douglas production function? Q = 2K/3L Q = f(K, L) Q = K^0.50L^0.75 Q = 5K + 2.5L

Q = K0.50L0.75

Which of the following statements best exemplifies the firm's constrained minimization problem? The firm desires to produce as much output as possible by choosing values of L and K that minimize RK + WL. The firm desires to produce as much output as possible subject to the constraint that C = RK + WL. The firm desires to produce a given quantity of output by choosing values of L and K that minimize RK + WL. The firm desires to produce a given quantity of output by choosing values of W and R that minimize RK + WL.

The firm desires to produce a given quantity of output by choosing values of L and K that minimize RK + WL.

Why are the slopes of isocost lines constant? because firms must use less labor if employing more capital because the marginal rate of technical substitution of labor for capital is constant because firms must use capital and labor inputs in fixed proportions because firms can hire as much of an input as they desire without changing wages or rental rates

because firms can hire as much of an input as they desire without changing wages or rental rates

A basic assumption of the short run is that a firm: cannot adjust its workforce or the amount of capital it uses. can employ more workers and add more capital to the production process. can freely adjust the amount of labor and capital that it employs. can reduce the number of workers it uses, but it cannot adjust how much capital it uses.

can reduce the number of workers it uses, but it cannot adjust how much capital it uses.

In the short run, the marginal product of labor: continues to increase so long as the firm adds labor slowly. will eventually fall. is always diminishing. always increases because laborers become more efficient with experience.

will eventually fall.