Question

Exercise 4. Cost Minimization Short and Long Run (Minimum Wage Workers)

McDonald’s employs minimum wage workers operating registers to take orders. Let y be the output of orders taken in an hour, L be the number of minimum wage workers working the registers, and let K be the number of registers. The production function is y=100∙L^½K^½.

1. Let the number of registers, K=4, be fixed. Are there diminishing marginal returns to labor? Explain why, and find ∂y/∂L.

2. Let the number of counter employees, L=4, be fixed. Are there diminishing marginal returns to capital? Explain why, and find ∂y/∂K.

3. If L=4 and K=4, how many customers are served in an hour? If both inputs are doubled, what happens to output, y? Does it double, more than double or less than double?

4. Consider minimum wage at w=$10/hr. Each register costs over $3,600, however, the daily amortization cost is r=$10, whether the register is used for one hour or several hours. What is the cost of serving y=400 customers?

5. What are the conditional factor demands, L(w,r,y) and K(w,r,y)? What is the minimized cost function C=(w,r,y)? Given w=10, r=10, and y=400, what is the minimum cost?

6. The minimum wage is raised to w’=$20/hr. What happens in the short run, with registers fixed at K=4? Find the new L(w,r,y) and the short-run cost function.

7. What happens in the long run, when McDonald’s can change K as well? McDonald’s automated kiosks allow for many registers to work directly with customers with minimum employee’s supervision. Do you think minimum wage laws are affecting technological change, or what other factor do you think might spur the introduction of automated kiosks?

Answer 1