Question #58167

Suppose that the production function for iPods is Q = 20K0.5L0.5. The marginal product of labor is 10(K/L)0.5, and the marginal product of capital is 10(L/K)0.5. Suppose that labor can be hired for $6, and capital can be rented for $9. If the firm has exactly $300 to spend on producing iPods, what is the maximum number of iPods it can produce?

Expert's answer

Q = 20K^0.5*L^0.5, MPL = 10(K/L)^0.5, MPK = 10(L/K)^0.5.

PL = $6, PK = $9.

In microeconomic theory, the Marginal Rate of Technical Substitution (MRTS) is the amount by which the quantity of one input has to be reduced when one extra unit of another input is used, so that output remains constant.

The firm's marginal rate of technical substitution will be:

MRTS = MPL/MPK = (10(K/L)^0.5) / ((10(L/K)^0.5) = (K/L)^0.5 / (L/K)^0.5 = (K/L)^0.5*(K/L)^0.5 = K/L

In this case the highest amount of output is produced, when K = L, so 6L + 9K = 300,

6L + 9L = 300,

15L = 300

L = K = 20 units.

Q = 20*20^0.5*20^0.5 = 400 iPods.

PL = $6, PK = $9.

In microeconomic theory, the Marginal Rate of Technical Substitution (MRTS) is the amount by which the quantity of one input has to be reduced when one extra unit of another input is used, so that output remains constant.

The firm's marginal rate of technical substitution will be:

MRTS = MPL/MPK = (10(K/L)^0.5) / ((10(L/K)^0.5) = (K/L)^0.5 / (L/K)^0.5 = (K/L)^0.5*(K/L)^0.5 = K/L

In this case the highest amount of output is produced, when K = L, so 6L + 9K = 300,

6L + 9L = 300,

15L = 300

L = K = 20 units.

Q = 20*20^0.5*20^0.5 = 400 iPods.

## Comments

Assignment Expert23.11.17, 13:05Dear visitor,

please use panel for submitting new questions

Nik22.11.17, 19:57Supppose that a farm's production function is determined by two factors: land area (K) and labour (L). The

production function is specified as follows:

Q = 64K^0.5 L^>5

The farm's land area is 500 acres

The unit cost of capital and labour is as follows:

- land $10 per acre

- labour $500 per labour

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