Question

Draw a graph showing the effect of a decrease in the price of capital on the combination of capital and labor that the firm selects, holding output constant at 10. Capital is on the y-axis (vertical axis) and labor on the x-axis (horizontal axis). Suppose that the production function is given by Q=min{K,5L}. Identify the amount of capital and labor that will be used to produce 10 units given the original price and label it A. Identify the amount of capital and labor given the decrease in the price of capital and label it B. Does the total cost of production increase/decrease/remain constant given the decrease in the price of capital? Briefly explain your answer.

Answer 1

Preferences are Perfect Complements

At eqm, K = 5L = Q

K*= Q, & L*= Q/5

if Q= 10

K*= 10, & L* = 2 : point A

if r falls, ( price of K), then since K & L are needed in a fixed proportion & for Q = 10, 10 units of K will be needed, irrespective of the price of K

Two inputs are not substitutable at all, both are complementary in Production

So point B : (K,L) = (10,2)

graph

isoquant is L shaped

so cost of production = 10r + 2w,

will fall, following a decrease in capital price