Joe’s coffee house operates under the production function Q(L,K)= LK + (LK)1/2. In the short-run, capital (K) is fixed while labor (L) is variable. Which statement correctly describes Joe’s short-run total product of labor curve?

Production functions MRTS labor and capital

Multiple Choice Questions (5 points each)

1. Consider the production function 𝑄(𝐿,𝐾)=(𝐿1/2 + 𝐾1/2)2/3, where L denotes labor and K denotes capital. This production function exhibits

a. constant returns to scale.
b. decreasing returns to scale.
c. increasing returns to scale.

(See Besanko 6.19, 6.20, 6.24 and 6.25 and Production Practice Problems #1, 2 and 3.)

2. Suppose the production of paved roadways is represented as Q(L,K) = LK + L. Based on this production function, which of the following statements is (are) TRUE?

a. In the short-run when capital is held constant, labor exhibits the law of diminishing returns.

b. The isoquants for paved roadways are downward sloping and convex to the origin.

c. The production function exhibits constant returns to scale.

d. Both a and b are true.

e. Both b and c are true.

f. None of the above statements are true.

(See Besanko 6.13, 6.14, 6.24 and 6.25 and Production Practice Problems #1, 2 and 3.)

3. A firm’s technology of production can be described by Q(𝐿,𝐾)=𝐿2𝐾2. Labor exhibits
_______ marginal product, and the corresponding isoquants slope downward at _______rate as
the firm moves from left to right along an isoquant.
a. an increasing; an increasing
b. a constant; an increasing
c. an increasing; a decreasing
d. a decreasing; a decreasing
e. none of the above

(See Besanko 4, 6.13, 6.14 and 6.25 and Production Practice Problems #2, 3 and 4.)

4. Consider the following statements:

I. If the marginal product of capital is substantially higher than the marginal product of labor, the isoquants are relatively steep when labor is on the horizontal axis and capital is
on the vertical axis.

II. Diminishing MRTS means a firm must add increasing amounts of labor in order to give up each additional unit of capital while maintaining output.

a. Only I is false
b. Only II is false
c. Both I and II are false
d. Neither I nor II is false

(See Production Practice Problems #2, 3 and 4.)

5. A firm’s production function is represented by Q(M,R) = 4M 3/4R1/3, where Q denotes output, M raw materials, and R robots. The firm is currently using 3 units of raw materials and 8 robots.

According to the MRTS, if the firm adds 1 more unit of raw materials, how many robots will it need to give up to maintain output?

a. 6
b. 1/6
c. 2/3
d. 3/2
e. 8/3
f. 3/8

(See Production Practice Problems #3 and 5.)

6. Suppose that worker hours (L) and machine hours (K) are perfect substitute inputs in the production of widgets (Q). Moreover, to produce an additional widget, the firm can either
employ 50 more worker hours OR 10 more machine hours. Which of the following correctly represents the production of widgets?
a. 𝑄(𝐿,𝐾)=10𝐿+50𝐾
b. 𝑄(𝐿,𝐾)=50𝐿+10𝐾
c. 𝑄(𝐿,𝐾)=0.1𝐿+0.02𝐾
d. 𝑄(𝐿,𝐾)=0.02𝐿+0.1𝐾

(See Production Practice Problem #6.)

7. Joe’s coffee house operates under the production function Q(L,K)= LK + (LK)1/2. In the short-run, capital (K) is fixed while labor (L) is variable. Which statement correctly describes Joe’s short-run total product of labor curve?

a. Total product of labor everywhere increases at a decreasing rate.

b. Total product of labor everywhere increases at an increasing rate.

c. Total product of labor everywhere increases at a constant rate.

d. Total product of labor initially increases at an increasing rate, then increases at a decreasing rate, and eventually decreases.

e. Total product of labor initially increases at a decreasing rate and then eventually increases at an increasing rate.

(See Production Practice Problem #7.)

8. The production of customers served (Q) at a convenience store is determined by the function Q(L,K) = LK + K, where L is labor and K is checkout stands.

Which statement correctly describes the corresponding short-run average product of labor curve, where the number of  checkout stands is fixed?

a. APL decreases at a decreasing rate.
b. APL decreases at an increasing rate.
c. APL decreases at a constant rate.
d. APL increases at a decreasing rate.
e. APL increases at an increasing rate.

(See Production Practice Problem #8.)

9. Suppose you observe that MPL > APL and MPL is decreasing but positive as more labor is used.
Based on this, you can say that TP is ______ at______ rate, and APL must be ______.

a. increasing; a decreasing; increasing
b. increasing; a decreasing; decreasing
c. increasing; an increasing; decreasing
d. decreasing; a decreasing; decreasing
e. decreasing; increasing; increasing

(See Besanko 4 and 6.5 and Production Practice Problem #9.)

10. Consider the truthfulness of the following statement.

I. When total product increases with labor at a decreasing rate, marginal product of labor is negative.

II. If total product of labor is increasing, marginal product of labor must be increasing too.
a. Only statement I is true.
b. Only statement II is true.
c. Both statements I and II are true.
d. Neither statement is true.

(See Besanko 4 and 6.5 and Production Practice Problem #9.)

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