Paddy’s Pub produces hand-crafted wooden chairs in the perfectly competitive market for hand- crafted wooden chairs using woodshops (S) at rental rate $200 and labor (E) at wage rate $10 according to the production function f(S, E) = 5S3/4E1/4. Suppose that Paddy’s Pub currently has four woodshops, and the market price of a hand-crafted wooden chair is $125. The markets for labor and woodshops are also competitive. Note: When necessary, round to two decimals.

(a) What is the (approximate) marginal product of the 10th unit of labor? Explain the meaning of this number.

(b) What is the (approximate) value of the marginal product of the 10th unit of labor? Explain the meaning of this number.

(c) How many hours of labor should Paddy’s Pub employ in the short-run to maximize profits? The equation for the marginal product of labor is given by MPE = 5(S )3/4. Label this 4E number E0?. (Note: In this example, the number of woodshops is fixed in the short-run).

(d) Now suppose that the wage rate rises to $12. Assuming we’re still in the short-run, how many hours of labor should Paddy’s Pub employ at the new higher wage rate? Label this number E1?.

(e) From your calculations in (c) and (d), compute the company’s short-run elasticity of labor [2 pts] demand. If necessary, round to two decimals.

(f) In 2-3 sentences, explain why labor demand is more elastic in the long-run.