Question

The current market wage rate is $\backslash (10$, the rental rate of land is $\backslash )1,000$per unit, and the rental rate of capital is $\$500$. Production managers at a firm find that under their current allocation of factors of production, the marginal product of labor is $100$, the marginal product of land is $10,000$, and the marginal product of capital is $4,000$. Is the firm minimizing costs? Why or why not?

Short answer

Since the MPP of land as well as the price of land are not equal to the MPP of labour and the price of labour, and the MPP of capital and also the price of capital, the firm is not minimizing costs.

Step-by-step solution

Introduction.

The marginal product of capital is the extra output produced by adding one unit of capital, usually cash. This metric is frequently applied to start-ups that rely on private investment to get their operations off the ground.

The marginal product of labour is the extra output generated by hiring another worker.

Given Information.

The following are the given information:

Current market wage rate is $\$10$

Rental rate of land is $\$1000$per unit.

Rental rate of capital is $\$500$

The marginal product of labor is $100$

The marginal product of land is $10000$

The marginal product of capital is$4000$

The Marginal physical product of Labor.

The company will hire various production factors until the marginal physical product equals the value money spent on factors. Symbolically, it could be stated as follows.

$\frac{MPPofLabor}{PriceofLabor}=\frac{MPPofCapital}{PriceofCapital}=\frac{MPPofLand}{PriceofLand}$

When calculating a firm's cost, the marginal physical product of labour and capital is taken into account.

Find the the firm minimizing costs or not.

Labor costs $\$10$, and the marginal physical product (MPP) is $100$.

The capital price is $\$500$, and the capital MPP is $4,000$.

The cost of land is $\$1,000$, and the MPP is $\$10,000$. Therefore,

$\frac{100}{10}=\frac{10,000}{1,000}\ne \frac{4,000}{500}$

As a result, the firm is not minimizing costs because the MPP of land and the price of land are not equal to the MPP of labour, the price of labour, and the MPP of capital and the price of capital.