In each of the following four cases, MRP L and MRP C refer to the marginal revenue products of labor and capital, respectively, and P L and P C refer to their prices. Indicate in each case whether the conditions are consistent with maximum profits for the firm. If not, state which resource(s) should be used in larger amounts and which resource(s) should be used in smaller amounts. a. MRPL = $8; PL = $4; MRPC = $8; PC = $4
1. These conditions are consistent with maximum profits for the firm.
True or False
2. Which resource should be used in larger and/or smaller amounts?
a- Use less of both
b. Conditions are already consistent
c. Use more of both
d. Use less labor and more capital
e. Use more labor and less capital
b. MRPL = $10; PL = $12; MRPC = $14; PC = $9
1. These conditions are consistent with maximum profits for the firm.
True / False
2. Which resource should be used in larger and/or smaller amounts?
a- Use less of both
b- Conditions are already consistent
c- Use more of both
d- Use less labor and more capital
e- Use more labor and less capital
c. MRPL = $6; PL = $6; MRPC = $12; PC = $12

a-1. True, these conditions are consistent with maximum profits for the firm.

a-2. The correct option is b. Conditions are already consistent.

b-1. False, these conditions are NOT consistent with maximum profits for the firm.

b-2. The correct option is e- Use more labor and less capital.

c-1. True, these conditions are consistent with maximum profits for the firm.

c-2. The correct option is b. Conditions are already consistent.

d-1. False, these conditions are NOT consistent with maximum profits for the firm.

d-2. The correct option is d- Use less labor and more capital.

Explanation:

Note: This question is not complete as question c is not complete and question d is omitted completely. To complete this question, questions c and d are therefore provided before answering the question as follows:

c. MRPL = $6; PL = $6; MRPC = $12; PC = $12

1. These conditions are consistent with maximum profits for the firm.

True / False

2. Which resource should be used in larger and/or smaller amounts?

a- Use less of both

b- Conditions are already consistent

c- Use more of both

d- Use less labor and more capital

e- Use more labor and less capital

d. MRPL = $22; PL = $26; MRPC = $16; PC = $19

1. These conditions are consistent with maximum profits for the firm.

True / False

2. Which resource should be used in larger and/or smaller amounts?

a- Use less of both

b- Conditions are already consistent

c- Use more of both

d- Use less labor and more capital

e- Use more labor and less capital

The explanation of the answers is now provided as follows:

The condition for the profit maximization of a firm is as follows:

MRPL / PL = MRPC / PC ……………………………. (1)

Therefore, we have:

a. MRPL = $8; PL = $4; MRPC = $8; PC = $4

MRPL / PL = $8 / $4 = 2

MRPC / PC = $8 / $4 = 2

Using equation (1), we have:

MRPL / PL = MRPC / PC = 2

a-1. These conditions are consistent with maximum profits for the firm.

True, these conditions are consistent with maximum profits for the firm. This is because MRPL / PL = MRPC / PC = 2.

a-2. Which resource should be used in larger and/or smaller amounts?

The correct option is b. Conditions are already consistent.

b. MRPL = $10; PL = $12; MRPC = $14; PC = $9

MRPL / PL = $10 / $12 = 0.83

MRPC / PC = $14 / $9 = 1.56

Using equation (1), we have:

0.83 = MRPL / PL <  MRPC / PC = 1.56

b-1. These conditions are consistent with maximum profits for the firm.

False, these conditions are NOT consistent with maximum profits for the firm. This is because 0.83 = MRPL / PL <  MRPC / PC = 1.56.

b-2. Which resource should be used in larger and/or smaller amounts?

The correct option is e- Use more labor and less capital. If this is done, it will result in MRPL / PL = MRPC / PC where the conditions will be consistent with maximum profits for the firm.

c. MRPL = $6; PL = $6; MRPC = $12; PC = $12

MRPL / PL = $6 / $6 = 1.00

MRPC / PC = $12 / $12 = 1.00

Using equation (1), we have:

MRPL / PL = MRPC / PC = 1

c-1. These conditions are consistent with maximum profits for the firm.

True, these conditions are consistent with maximum profits for the firm. This is because MRPL / PL = MRPC / PC = 1.

c-2. Which resource should be used in larger and/or smaller amounts?

The correct option is b. Conditions are already consistent.

d. MRPL = $22; PL = $26; MRPC = $16; PC = $19

MRPL / PL = $22 / $26 = 0.85

MRPC / PC = $16 / $19 = 0.84

Using equation (1), we have:

0.85 = MRPL / PL >  MRPC / PC = 0.84

d-1. These conditions are consistent with maximum profits for the firm.

False, these conditions are NOT consistent with maximum profits for the firm. This is because 0.85 = MRPL / PL >  MRPC / PC = 0.84.

d-2. Which resource should be used in larger and/or smaller amounts?

The correct option is d- Use less labor and more capital. If this is done, it will result in MRPL / PL = MRPC / PC where the conditions will be consistent with maximum profits for the firm.