1. Determine: (1) whether there are diminishing marginal returns to labor in the short-run, and (2) the returns to scale.

f (L,K) = 2L + 3K

a. It is diminishing marginal returns to labor; it is decreasing returns to scale.

b.It is not diminishing marginal returns to labor; it is constant returns to scale.

c. It is not diminishing marginal returns to labor; it is increasing returns to scale.

d. It is diminishing marginal returns to labor; it is increasing returns to scale.

e.It is not diminishing marginal returns to labor; it is decreasing returns to scale.

f. It is diminishing marginal returns to labor; it is constant returns to scale.

2. Determine: (1) whether there are diminishing marginal returns to labor in the short-run, and (2) the returns to scale.

f (L,K) = 4L^0.75K^0.5

a. It is not diminishing marginal returns to labor; it is decreasing returns to scale.

b. It is diminishing marginal returns to labor; it is constant returns to scale.

c. It is not diminishing marginal returns to labor; it is increasing returns to scale.

d. It is diminishing marginal returns to labor; it is decreasing returns to scale.

e.It is diminishing marginal returns to labor; it is increasing returns to scale.

f. It is not diminishing marginal returns to labor; it is constant returns to scale.

3. Determine: (1) whether there are diminishing marginal returns to labor in the short-run, and (2) the returns to scale.

f (L,K) = min{0.5L , 0.5K}

Select one:

a. It is not diminishing marginal returns to labor; it is increasing returns to scale.

b.It is diminishing marginal returns to labor; it is decreasing returns to scale.

c. It is diminishing marginal returns to labor; it is constant returns to scale.

d. It is not diminishing marginal returns to labor; it is decreasing returns to scale.

e. It is not diminishing marginal returns to labor; it is constant returns to scale.

f. It is diminishing marginal returns to labor; it is increasing returns to scale.

For the next seven questions, assume a firm's production function is q = L^0.5 + K^0.5 . The cost of labor is fixed at w = 1 and the cost of capital is fixed at r = 8.

4. Suppose that capital is fixed at K = 9 in the short-run. Find the short-run cost function.

Select one:

a. Cost = q² + 6q + 81

b. Cost = q² - 6q + 72

c. Cost = q² - 6q + 81

d. Cost = q² - 6q - 81

5. Find the marginal cost function.

Select one:

a. MC = q² - 6q

b. MC = q - 6

c. MC = 2q + 6

d. MC = 2q - 6

6. Does the firm's production process exhibit diminishing marginal returns in the short-run?

Select one:

a. No

b. Yes

7. Find the long-run cost function.

Select one:

a. LRC = (8q² / 9)

b. LRC = (9q / 8)

c. LRC = (9q² / 8)

d. LRC = (8q / 9)

8. Assume a firm's production function is q = L^0.5 + K^0.5 . The cost of labor is fixed at w = 1 and the cost of capital is fixed at r = 8.

Find the long-run average cost function.

Select one:

a. LRAC = (8q / 9)

b. LRAC = (9q / 8)

c. LRAC = (8 / 9)

d. LRAC = (9 / 8)

9. What scale properties does this cost function display?

Select one:

a. diseconomies of scale

b. no economies of scale

c. economies of scale

For the next four questions, suppose a music publisher in medieval England pays $100 to prepare a plate for printing music. After the plate is prepared, the publisher can make as many copies of the music as she wants for $2 per copy.

10. Give an equation for the publisher's total cost function, where q is the number of copies.

Select one:

a. TC = 100 + 2q

b. TC = 100 + q

c. TC = 102q

d. TC = 2q

11.Give an equation for the publisher's AVC function.

Select one:

a. AVC = 2q

b. AVC = 102

c. AVC = 2

d. AVC = 1

12. Give an equation for the publisher's ATC function.

Select one:

a. ATC = 2

b. ATC = (100 / q) + 2 c. ATC = 102

d. ATC = (100 / q) + 1

13. Give an equation for the publisher's MC function.

Select one:

a.MC = 2q

b.MC = 102

c. MC = 2

d. MC = 1

For the next three questions, suppose a firm's production function is q = ln (L) + ln (K). The cost of labor is fixed at w = 1 and the cost of capital is fixed at r = 4.

14. Suppose that capital is fixed at K = 1 in the short-run. Does the production exhibit diminishing marginal returns to labor?

a. Yes

b. No

15. Find the long-run cost function.

Select one:

a.

LRC = 3 e^0.5q

b.

LRC = 6 e^0.5q

c.

LRC = 4 e^0.5q

d.

LRC = 5 e^0.5q

^16. Find the long-run average cost function. What scale properties does this cost function display when q > 2?

Select one:

a.

diseconomies of scale

b.

no economies of scale

c.

economies of scale