ECONomics part5

Suppose a firm with a production function given by Q = 4K^0.25 L^0.75 produces 100 units of output. The firm pays a wage of $30 per units and pays a rental rate of capital of $10 per unit.

$1,000.

Suppose a firm's short-run production function is given by Q = 16L^0.8. What is the marginal product of the fourth worker?

10

A donut shop has a production function given by Q = 50K^1/3 L^1/2, 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

Suppose a firm with a production function given by Q = K^0.25 L^0.75 produces 1,500 units of output. The firm pays a wage of $50 per unit and pays a rental rate of capital of $50 per unit.

3 times as many units of labor as units of capital.

The short-run production function for a firm is given by Q = 10L 0.5. What is the marginal product?

A

The short-run production function for a firm is given by Q = 40L^2/3. What is the average product?

APL= 40/L^1/3

Between 1994 and 2008, the share of the workforce employed in manufacturing _____ and manufacturing output _____.

decreased; increased

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 = 25L + 50K.

Which of the following statements violates the basic assumptions of isoquants?

Diminishing marginal products imply that isoquants are concave to the origin.

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.

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

Which of the following statements is (are) TRUE, assuming the firm is choosing the optimal bundle of inputs that minimizes the cost of producing a given quantity of output? I. The marginal product per dollar spent on labor equals the marginal product per dollar spent on capital. II. APL = APK III. MPL/W = MPK/R IV. MPL × W = MPK × R

I and III

Which of the following is (are) example(s) of production functions? I. Q = 56K + 18L II. Q = 2K^0.8 L^0.2 III. Q = KL

I, II, and III

Consider the production function Q = Af(K, L). Which of the following statements is (are) TRUE? I. An increase in total factor productivity growth is represented by an increase in K or L. II. An increase in total factor productivity growth means that the same amount of output can be produced using fewer inputs. III. If A increases by 10%, the amount of output produced will increase by 10%, holding the quantity of inputs fixed.

II and III

Which of the following production functions exhibit(s) constant returns to scale? II. Q = 2K + L III. Q = K^0.8 L^0.2

II and III

Production is an extremely complicated task, so economists make a number of simplifying assumptions. Which of the following assumptions do economists make in their basic model of producer behavior? 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/L 0.5. 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

Suppose a firm with a production function given by Q = 30K^0.5 L^0.5 produces 1,500 units of output. The firm pays a wage of $40 per unit and pays a rental rate of capital of $640 per unit. How many units of labor and capital should the firm employ to minimize the cost of producing 1,500 units of output?

L = 200; K = 12.5

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?

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

Which of the following is a Cobb-Douglas production function?

Q = K^0.50 L^0.75

Which of the following statements best exemplifies the firm's constrained minimization problem?

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

A basic assumption of production is that the firm:

can buy as much labor and capital as it desires at fixed prices.

A basic assumption of the long run is that a firm:

can change the amount of labor and capital that it employs.

A basic assumption of the short run is that a firm:

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

The production function given by Q = 10(0.7K^2 + 0.3L^2)^0.5 has _____ returns to scale.

constant

Suppose a firm is currently minimizing costs in the long run with marginal product of labor and marginal product of capital given by K and L, respectively. If the price of capital falls by 50%, the capital-to-labor ratio will:

double.

If a firm is using a lot of capital and just a little labor, the marginal product of labor is_____ relative to the marginal product of capital making it _____ to substitute labor for capital.

high; easier

Brenda's Pastry employs three workers who produce 6 dozen pastries per hour. After Brenda hires a fourth worker, the number of pastries produced increases to 7 dozen per hour. Because the marginal product of the fourth worker is _____ than the average product of three workers the average product must _____.

less; fall

Suppose that a community health center finds that regardless of the number of physicians or nurse practitioners employed, it can always replace one family practice physician by using two additional nurse practitioners without affecting the quantity or quality of patient office visits. This finding implies that:

physicians and nurse practitioners are perfect substitutes in production.

In the long run, because firms can adjust both capital and labor:

the impact of diminishing marginal returns is lessened.

Capital cannot be adjusted in the short run because:

there is not sufficient time to adjust it.

In the short run, the marginal product of labor:

will eventually fall.