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Chapter 9: Q1. (page 363)

From time to time, Congress has raised the minimum wage. Some people suggested that a government subsidy could help employers finance the higher wage. This exercise examines the economics of minimum wage and wage subsidies. Suppose the supply of low-skilled labor is given by

LS= 10w

where, LS is the quantity of low-skilled labor (in millions of persons employed each year), and w is the wage rate(in dollars per hour). The demand for labor is given by

LD= 80 - 10w

a. What will be the free-market wage rate and employment level? Suppose the government sets a minimum wage of \(5 per hour. How many people would then be employed?

b. Suppose that instead of a minimum wage, the government pays a subsidy of \)1 per hour for each employee. What will the total level of employment be now? What will the equilibrium wage rate be?

Short Answer

Expert verified

  1. The free market wage rate would be $4 per hour and employment level 40 million. At a minimum wage rate of $5, the number of people employed would be 30 million.

  2. The total employment after the subsidy would be 45 million. The new wage rate would be $4.5 per hour.

Step by step solution

01

Step 1. Determining the free market wage rate and employment level and employment level after minimum wage.

  • Free market employment level.

The wage rate and employment level at which the quantity of demanded labor is equal to the quantity of supplied labor is the free market wage rate and employment level. The free market wage rate is calculated below:

Ls= LD

10w = 80-10w

20w=80

w=4

The free market wage rate is $4 per hour.

The free market employment level is calculated by putting the value of 鈥榳鈥� in the LS equation.

LS=10w=10脳4=40

The free market employment level is 40 million.

  • Employment level after the government sets a minimum wage rate of $5 per hour.

After implementing the minimum wage rate, the new employment level is calculated by determining the demanded quantity of laborers at this wage rate.

LD=80-105=80-50=30

The new employment level after the implementation of the wage rate is 30 million.

02

Step 2. Calculation of change in employment level and wage rate after the government subsidy

The subsidy of $1 by the government on wage rates will shift the demand curve for labor to its right. Thus, the demand for labor would increase, which will create a new equation for labor demand in the market. The new equation for labor demand (LD鈥�) is:

LD=80-10w+1=80-10w+10=90-10w

The shift in labor demand will create a new equilibrium position in the market where the demanded quantity of labor would equal the supplied quantity of labor.

LS=LD10w=90-10w20w=90w=4.5

The new wage rate after the government subsidy is $4.5 per hour.

By putting the value of wage rate in the labor supply equation, the new employment level is calculated below:

LS=10w=10脳4.5=45

The new employment level after the implementation of government subsidy on wage rate is 45 million.

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Most popular questions from this chapter

Japanese rice producers have extremely high production costs, due in part to the high opportunity cost of land and to their inability to take advantage of economies of large-scale production. Analyze two policies intended to maintain Japanese rice production:

(1) a per-pound subsidy to farmers for each pound of rice produced, or

(2) a per-pound tariff on imported rice.

Illustrate with supply-and-demand diagrams the equilibrium price and quantity, domestic rice production, government revenue or deficit, and deadweight loss from each policy. Which policy is the Japanese government likely to prefer? Which policy is Japanese farmers likely to prefer?

The domestic supply and demand curves for hula beans are as follows:

Supply: P = 50 + Q

Demand: P = 200 - 2Q

where P is the price in cents per pound and Q is the quantity in millions of pounds. The U.S. is a small producer in the world hula bean market, where the current price (which will not be affected by anything we do) is 60 cents per pound. Congress is considering a tariff of 40 cents per pound. Find the domestic price of hula beans that will result if the tariff is imposed. Also compute the dollar gain or loss to domestic consumers, domestic producers, and government revenue from the tariff.

In Example 9.1 (page 332), we calculated the gains and losses from price controls on natural gas and found that there was a deadweight loss of \(5.68 billion. This calculation was based on a price of oil of \)50 per barrel.

a. If the price of oil were \(60 per barrel, what would be the free-market price of gas? How large a deadweight loss would result if the maximum allowable price of natural gas were \)3.00 per thousand cubic feet?

b. What price of oil would yield a free-market price of natural gas of $3?

Suppose the market for widgets can be described by the following equations:

Demand: P = 10 - Q

Supply: P = Q 鈥� 4

where P is the price in dollars per unit and Q is the quantity in thousands of units. Then:

a. What is the equilibrium price and quantity?

b. Suppose the government imposes a tax of \(1 per unit to reduce widget consumption and raise government revenues. What will the new equilibrium quantity be? What price will the buyer pay? Whatamount per unit will the seller receive?

c. Suppose the government has a change of heart about the importance of widgets to the happiness of the American public. The tax is removed and a subsidy of \)1 per unit is granted to widget producers. What will the equilibrium quantity be? What price will the buyer pay? What amount per unit (including the subsidy) will the seller receive? What will be the total cost to the government?

In 1983, the Reagan administration introduced a new agricultural program called the Payment-in-Kind Program. To see how the program worked, let鈥檚 consider the wheat market:

  1. Suppose the demand function is QD = 28 - 2P and the supply function is QS = 4 + 4P, where P is the price of wheat in dollars per bushel, and Q is the quantity in billions of bushels. Find the free-market equilibrium price and quantity.

  2. Now suppose the government wants to lower the supply of wheat by 25 percent from the free-market equilibrium by paying farmers to withdraw land from production. However, the payment is made in wheat rather than in dollars鈥� hence the name of the program. The wheat comes from vast government reserves accumulated from previous price support programs. The amount of wheat paid is equal to the amount that could have been harvested on the land withdrawn from production. Farmers are free to sell this wheat on the market. How much is now produced by farmers?How much is indirectly supplied to the market by the government? What is the new market price? How much do farmers gain? Do consumers gain or lose?

  3. Had the government not given the wheat back to the farmers, it would have stored or destroyed it. Do taxpayers gain from the program? What potential problems does the program create?
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