Question

Suppose that the wage rate is $10 per hour and the rental rate of capital is $25 per hour.

* Write an equation for the isocost line for a firm.
* If TC = $800, what is the slope of the isocost line? What is the y-intercept (K-intercept)?

Answer 1

The equation for the isocost line for a firm can be written as:

w * L + r * K = C

where w is the wage rate, L is the quantity of labor used, r is the rental rate of capital, K is the quantity of capital used, and C is the total cost of production.

If we divide both sides of the equation by r, we get:

(K / r) + (w / r) * L = C / r

This equation tells us that the isocost line has a slope of -(w / r), which is the ratio of the wage rate to the rental rate of capital. The y-intercept (K-intercept) is C / r, which represents the quantity of capital that the firm can rent when it uses no labor.

If TC = $800, then the equation of the isocost line becomes:

(K / 25) + (10 / 25) * L = 800 / 25

Simplifying this equation, we get:

0.4 K + 0.4 L = 32

Thus, the slope of the isocost line is:

-(w / r) = - (10 / 25) = - 0.4

And the y-intercept (K-intercept) is:

C / r = 800 / 25 = 32