Question

2. Suppose you can hire workers for $15 per hour or rent capital for $5.

(a) Write an expression for the total cost of production as a function of how many workers, L, you hire and K, capital, you use. (1 point)

(b) Assume that you want to keep your total cost at $200. Use your answer from part (a) to find the equation for an isocost line that corresponds to $200 in total cost. Rearrange the equation to isolate capital, i.e. your equation should be of the form K = .... (1 point)

(c) What does the slope of the line represent? (2 points) (d) What do the intercept points represent? (2 points)

Answer 1

2. We are given that wage rate = $15 per hour and rental price of capital = $5.

(a) Total cost of production C = wL + rK = 15L + 5K

(b) Now total cost is fixed at C = $200. The equation for an isocost line that corresponds to $200 in total cost is given as 200 = 15L + 5K

5K = 200 - 15L

K = 200/5 - 15L/5

K = 40 - 3L

This is the equation where we see the isolated capital K in terms of L

(c) The slope of the line represent the relative price of capital in terms of labor.

(d) Intercept points represent the maximum units of capital and labor firm can adopt. The intercept for capital is 40 and 40/3 for labor. The maximum capital units affordable are 40 units and maximum labor units affordable are 40/3 units.