Question

Consider two firms, X and Y in the same industry who use the same production technology. To produce the same level of output, say 1000 pairs of bars, X uses more capital than Y and Y uses more labor than X. Suppose both companies pay the same wage to their employees: w = 15:

(Unless otherwise stated, assume that all firms choose their input levels optimally)

(a) Which company is paying a lower rent? Why? & Which company has a higher cost? Why?

(b) At their current optimal input bundles, the marginal product of labor is higher for which firm? Why?

(c) At their current optimal input bundles, the marginal product of labor is higher for which firm? Why?

(d) Circle the correct answer and provide a brief explanation.
If the wage rate doubles, firms' costs will MORE THAN / LESS THAN / EXACTLY double.

Answer 1

We can make out that X is a capital intensive firm (or relies more on capital), whereas Y is a labour intensive firm (or relies more on labour).

a) rental rate is inversly proportional to capital. And since X used more capital, it pays lesser rent.

also since,   in the short run,

as w is same for both, X gets away by paying their employees the same amount as paid by Y, without having to hire as many people, so Y has higher cost.

b) Marginal product of labour is higher for Y, as it is a labour intensive firm, and increment in output should be more per unit addition of input.

d) If the wage rate doubles, the firms cost will be less than double. Because the capital factor of the cost function remains unchanged