At a given output level, if the cost of capital is $50 per hour, the wage paid to employees is $30 per hour, the marginal product of capital is 120 units per hour, and the marginal product of labor is 60 units per hour, the firm is ________ .

Question

Quizplus · Accepted Answer

To determine whether the firm is on a short-run or long-run average total cost curve, we need to compare the marginal costs to the average costs. 
Marginal cost of capital (MCk) = Cost of capital = $50 per hour 
Marginal cost of labor (MCl) = Wage paid to employees = $30 per hour 
Marginal product of capital (MPk) = 120 units per hour 
Marginal product of labor (MPl) = 60 units per hour

Average product of capital (APk) = Total product / Units of capital = MPk / (Cost of capital / Price of output) = 120 / (50 / P) = 2.4P 
Average product of labor (APL) = Total product / Units of labor = MPl / Wage rate = 60 / 30 = 2

Average total cost (ATC) = Total cost / Total output = (Cost of capital × Units of capital + Wage rate × Units of labor) / Total output 
= (50 × K + 30 × L) / (MPk × K + MPl × L) 
= (50K + 30L) / (120K + 60L) 
= (5/12) × (10K + 6L) / (2K + L) 
= (5/12) × (5 + 3/APL)

Since APL = 2, 
ATC = (5/12) × (5 + 3/2) = 1.875P

Therefore, the short-run average total cost curve is: 
SRTAC = 1.875P, which is a U-shape since MC = ATC at the minimum point.

Since we are given only marginal products, we cannot determine the long-run average cost curve since it depends on the relationship between inputs and output in the long run. However, we know that the firm is currently experiencing increasing returns to scale (since MPk > APk and MPl > APL). This suggests that at higher levels of output, the firm will be able to produce even more efficiently, which would lead to a declining long-run average cost curve.

Therefore, the firm is on a short-run average total cost curve but not the long-run average cost curve (option A is correct).

At a Given Output Level, If the Cost of Capital