Question

Firm ABC uses two inputs, blue workers and purple workers (measured in number of workers) to produce output. At Firm ABC’s current input bundle, the marginal product of blue workers is two times the marginal product of purple workers. The wage for a purple worker is one third of the wage for a blue worker. Is the firm currently minimizing its cost of production?

Answer 1

Cost minimisation has the condition that Marginal product per wage of factor should be equal for all the units of production.

Given,

Marginal product of blue workers is two times the marginal product of purple workers.

• Let, Marginal product of purple worker = MP
• So, Marginal product of blue worker = 2*MP

The wage for a purple worker is one third of the wage for a blue worker

• Let, Wage of Blue worker = W
• So, Wage of Purple worker = 1/3 * W

Based on the above information :-

Marginal product per wage for Purple workers = MP/(1/3 * W) = 3MP/W

Marginal product per wage for Blue workers = 2MP/W

As we can see,

3MP/W ≠ 2MP/W

So, The marginal product per wage is not equal for each type of workers. This violates the condition of cost minimisation.

Hence, Firm is currently not minimizing it's cost of production.

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