# optimal level of output

Making dresses is a labor-intensive process. Indeed, the production function of a dressmaking firm is well described by the equation Q=L-L^2/800, where Q denotes the number of dresses per week and L is the number of labor hours per week. The firm's additional cost of hiring an extra hour of labor is about $20 per hour (wage plus fringe benefits). The firm faces the fixed selling price, P=$40.

a. how much labor should the firm employ? What are its resulting output and profit?

b. Over the next two years, labor costs are expected to be unchanged, but dress prices are expected to increase to $50. What effect will this have on the firm's optimal output? Explain. Suppose instead that inflation is expected to increase the firm's labor cost and output price by identical (percentage) amounts. What effect would this have on the firm's output?

c. Finally, suppose once again that MCl=$20 and P=$50 but that labor productivity (i.e. output per labor-hour) is expected to increase by 25 percent over the next five years. What effect would this have on the firm's optimal output? Explain.

#### Solution Preview

How much labor should the firm employ? What is its resulting output and profit?

Q=L-L^2/800

Marginal Product of labor=MP=dQ/dL=1-L/400

Marginal Revenue of labor=MP*Price=(1-L/400)*40=40-L/10

Marginal Cost of labor=20 per hour

For optimal level of output, Put Marginal Cost equal to Marginal Revenue of labor

40-L/10=20

L/10=20

L=200 hours

Total output at L=200 hours=200-200^2/800=150 units

Total revenue=Price*optimal output=40*150=$6000

Total cost=L*wage rate=200*20=$4000

Profit=6000-4000=$2000

Over the next two years, labor costs are ...

#### Solution Summary

The optimal level of output is determined.