Question

1. If the absolute value of the Technical Rate of Substitution is increasing:
a. A firm will have a concave isoquant.
b. The value of the |TRS| does not depend on the quantity of inputs.
c. A firm will be likely to use a mix inputs rather than use all of one or the other. d. All of the above.

2. If MPL/MPK = 2.
a. the last machine is two times as productive as the last worker. b. the last worker is two times as productive as the last machine. c. the firm will produce with two times as much capital as labor. d. the firm will produce with two times as much labor as capital.

3. A firm is said to be operating in the long run if
a. it can’t change its production decision within a fiscal year. b. all inputs are variable.
c. all inputs are fixed
d. at least one input is fixed.

4. If a firm can sell its output at $4, the MPL of the last worker hired is 3, and the wage is $10 a. the firm should lay off workers.
b. the firm should hire more workers.
c. the firm should shut down.

d. total revenue is less than total cost.

5. If a firm is producing according the production function q = min{L, 2K} a. a firm will produce with all capital and no labor.
b. a firm will produce with all capital and no labor.
c. a firm will produce two goods with two machines and one worker.

d. a firm will produce two goods with one machine and two workers.

II. Short answer (10 pts).

6. For the following two functions prove whether each of the production functions has increasing, decreasing, or constant returns to scale. Then find whether the MPL is increasing, decreasing or constant with L.

A. ? = ?^1/3?1/3

B. ? = 3?^3/2

Answer 1

1 Option A

Since MRTS must diminish, the isoquants must be convex to the origin. If MRTS of labor for capital increases then Isouant is concave. This is typically not common since it means a consumer would consume more of one good for the increased consumption of other good and vice versa.

2. Option B

The marginal rate of technical substitution shows the rate at which you can substitute one input, such as labor, for another input, such as capital, without changing the level of resulting output.

MRTS = MPL / MPK = 2

It means that last labour is two times as productive as last capital or machine

3. Option B

Long run is a period of time in which no input is fixed. In long run all inputs are variable.

4.Option B

Here MPL = $3, P = $4 MRPL = $3 * 4 = $12. As long as Marginal Revenue Product of Labour, MRPL > Wage Rate the firm can hire more labourers. Here 12 > $10.