Minimum Wage Labor Subsidy (cont’d): In exercise 13.10, we investigated the firm’s decisions in the presence of a government subsidy for hiring minimum wage workers. Implicitly, we assumed that the policy has no impact on the prices faced by the firm in question.
A: Suppose again that you operate a business that uses minimum wage workers ℓ and capital k. The minimum wage is w, the rental rate for capital is r and you are one of many identical businesses in the industry, each using a homothetic, decreasing returns to scale production process and each facing a recurring fixed cost F.
(a) Begin by drawing the average cost curve of one firm and relating it to the (short run) supply and demand in the industry assuming we are in long run equilibrium.
(b) Now the government introduces a wage subsidy s that lowers the effective cost of hiring min mum wage workers from w to (1 − s)w. What happens in the firm and in the industry in the short run?
(c) What happens to price and output (in the firm and the market) in the long run compared to the original quantities?
(d) Is it possible to tell whether there will be more or fewer firms in the new long run equilibrium?
(e) Is it possible to tell whether the long run price will be higher or lower than the short run price? How does this relate to your answer to part (d)?
B: Suppose that the firms in the industry use the production technology x = f (ℓ, k) = 100ℓ0.25k0.25 and pay a recurring fixed cost of F = 2, 210. Suppose further that the minimum wage is $10 and the rental rate of capital is r = 20.
(a) What is the initial long run equilibrium price and firm output level?
(b) Suppose that s = 0.5 — implying that the cost of hiring minimum wage labor falls to $5. How does your answer to (a) change?
(c) How much more or less of each input does the firm buy in the new long run equilibrium compared to the original one? (The input demand functions for a Cobb-Douglas production process were previously derived and given in equation (13.50) of exercise 13.8.)
(d) If price does not affect the quantity of x demanded very much, will the number of firms in- crease or decrease in the long run?
(e) Suppose that demand is given by x(d) = 200, 048 − 2, 000p. How many firms are there in the initial long run equilibrium?
(f) Derive the short run market supply function and illustrate that it results in the initial long run equilibrium price.
(g) Verify that the short run equilibrium price falls to approximately $2.69 when the wage is subsidized.
(h) How much does each firm’s output change in the short run?
(i) Determine the change in the long run equilibrium number of firms when the wage is subsidized and make sense of this in light of the short run equilibrium results.