The output of workers at a factory depends on the number of supervisors hired (see Table 3P.4). The factory sells its output for $0.50 each, it hires 50 production workers at a wage of $100 per day, and it needs to decide how many supervisors to hire. The daily wage of supervisors is $500, but output rises as more supervisors are hired, as shown in Table 3P.4. How many supervisors should it hire?

Table 3P.4 Supervisors and Output

Supervisors Output (units per day)

1. 11,000
2. 14,800
3. 18,000
4. 19,500
5. 20,200
6. 20,600

a. Calculate the MPL.

b. Do you observe the law of diminishing marginal returns? Explain.

Bakers and Cake Production

Number of bakers Number of cakes

0 0

1 10

2 18

3 23

4 27

c. Suppose each cake sells for $10. Calculate the MRPL.

d. Draw the MRPL curve, which is the demand curve for bakers.

e. If each baker is paid $80 per day, how many bakers will the bakery owner hire, given that the goal is to maximize profits? How many cakes will be baked and sold each day?

The demand curve for gardeners is GD = 19 W, where G = the number of gardeners, and W = the hourly wage. The supply curve is GS = 4 + 2W. Graph the demand curve and the supply curve. What is the equilibrium wage and equilibrium number of gardeners hired? Suppose that the town government imposes a $2 per hour tax on all gardeners. Indicate the effect of the tax on the market for gardeners. What is the effect on the equilibrium wage and the equilibrium number of gardeners hired? How much does the gardener receive? How much does the customer pay? How much does the government receive as tax revenue?

A production process using two inputs, labor and capital, can be written as: Q = 5LK MPL= 5L MPK = 5K where Q represents output per day (tons). The unit costs of inputs are $150 for labor (L) and $1,000 for capital (K). Determine the least cost combination of L and K when output is produced at the rate of 1,000 tons per day. Determine the required outlay for Q=1,000 tons per day