Question

2. Kyle owns a pizzeria. The number of pizzas he can make depends on his production function. q(E, K) = EK With this function, the marginal product of employment is K, and the marginal product of capital is E. He must use the markets price for labor, $8, and capital, $10.

(a) Assuming that he must make 80 pizzas per day, what is his optimal bundle of employees and capital?

(b) Now, the government implements a new living wage of $32. Assuming Kyle still needs to make 80 pizzas a day, what is his new optimal bundle?

(c) How did the bundles change from part a to part b? Explain. How does this relate to low-skilled labor that we talked about in class (Hint: Think about our discussion of minimum wage).

Answer 1

(a) Optimal bundle is that where MRS = Price of labor/Price of capital
MRS = marginal product of employment/marginal product of capital = K/E
Price of labor/Price of capital = 8/10 = 0.8
So, K/E = 0.8
So, K = 0.8E
And, Q = 80 = EK = E(0.8E)
So, E² = 80/0.8 = 100
So, E = 10
And, K = 0.8E = (0.8)(10) = 8
Optimal bundle: E = 10 and K = 8

(b) Now, Price of labor/Price of capital = 32/10 = 3.2
So, MRS = Price of labor/Price of capital gives,
K/E = 3.2
So, K = 3.2E
And, Q = 80 = EK = E(3.2E)
So, E² = 80/3.2 = 25
So, E = 5
And, K = 3.2E = (3.2)(5) = 16
Optimal bundle: E = 5 and K = 16

(c) Due to increase in price of labor from a to b, employment decreases from 10 to 5 and capital increases from 8 to 16. This tells that due to minimum wage legislation, employment of low skilled workers decreases and it is replaced by used of more capital.