Question

Suppose labor is on the horizontal axis and capital is on the vertical axis. If the wage rate is $15 per worker per hour and the rental rate of capital is $10 per unit per hour, what is the slope of the isocost curve?

A. Option A: –0.667

B. Option B: –15

C. Option C: –10

D. Option D: –1.5

Answer 1

Answer: D. -1.5

On the graph, the labor is measured on the horizontal axis and capital is measured on the vertical axis. The price of labor or wage rate is $15 per worker per hour and the price of capital or rental rate of capital is $10 per capital per hour.

In the above figure, the quantity of labor(L) is measured on the horizontal axis, and the quantity of capital(K) is measured on the vertical axis. The curve 'C' is the isocost curve.

C = wL + rK

Or, C = 15L + 10K

If the firm hires only labor and no capital, then cost equation would be,

C = 15L

So, the maximum number of labor, the firm could hire would be,

L = C / 15

If the firm hires only capital and no labor, then cost equation would be,

C = 10K

So, the maximum number of capital, the firm could hire would be,

K = C / 10

The isocost curve is negatively sloped.

Thus, the slope of the isocost curve = -OA / OB

Or, The slope of the isocost curve = - (C/10) / (C/15) , [ OA = C/10 ; OB = C/15]

Or, The slope of the isocost curve = - (C/10) * (15/C)

Or, The slope of the isocost curve = - 15/10

The slope of the isocost curve = -1.5

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