Man 503                                              Homework VII                                    Fall 2009

 

1.  In 1996, the U.S. Congress raised the minimum wage from $4.25 per hour to $5.15 per hour.  Some people suggested that a government subsidy could help employers finance the higher wage.  This exercise examines the economics of a minimum wage and wage subsidies.  Suppose the supply of low-skilled labor is given by, 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.

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

In a free-market equilibrium, LS = LD.  Solving yields w = $4 and LS = LD = 40.  If the minimum wage is $5, then LS = 50 and LD = 30.  The number of people employed will be given by the labor demand, so employers will hire 30 million workers. 

Figure 9.1.a


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?

Let w denote the wage received by the employee.  Then the employer receiving the $1 subsidy per worker hour only pays w-1 for each worker hour.  As shown in Figure 9.1.b, the labor demand curve shifts to:

LD = 80 - 10 (w-1) = 90 - 10w,

where w represents the wage received by the employee.

The new equilibrium will be given by the intersection of the old supply curve with the new demand curve, and therefore, 90-10W** = 10W**, or w** = $4.5 per hour and  L** = 10(4.5) = 45 million persons employed.  The real cost to the employer is $3.5 per hour. 

2.  About 100 million pounds of jelly beans are consumed in the United States each year, and the price has been about 50 cents per pound.  However, jelly bean producers feel that their incomes are too low, and they have convinced the government that price supports are in order.  The government will therefore buy up as many jelly beans as necessary to keep the price at $1 per pound.  However, government economists are worried about the impact of this program, because they have no estimates of the elasticities of jelly bean demand or supply.

a.         Could this program cost the government more than $50 million per year?  Under what conditions?  Could it cost less than $50 million per year?  Under what conditions?  Illustrate with a diagram.

If the quantities demanded and supplied are very responsive to price changes, then a government program that doubles the price of jelly beans could easily cost more than $50 million.  In this case, the change in price will cause a large change in quantity supplied, and a large change in quantity demanded.  In Figure 9.5.a.i, the cost of the program is (QS-QD)*$1.  Given QS-QD is larger than 50 million, then the government will pay more than 50 million dollars.  If instead supply and demand were relatively price inelastic, then the change in price would result in very  small changes in quantity supplied and quantity demanded and (QS-QD) would be less than $50 million, as illustrated in figure 9.5.a.ii.

b.        Could this program cost consumers (in terms of lost consumer surplus) more than $50 million per year?  Under what conditions?  Could it cost consumers less than $50 million per year?  Under what conditions?  Again, use a diagram to illustrate.

When the demand curve is perfectly inelastic, the loss in consumer surplus is $50 million, equal to ($0.5)(100 million pounds).  This represents the highest possible loss in consumer surplus.  If the demand curve has any elasticity at all, the loss in consumer surplus would be less then $50 million.  In Figure 9.5.b, the loss in consumer surplus is area A plus area B if the demand curve is D and only area A if the demand curve is D’.

Figure 9.5.a.i

 

Figure 9.5.a.ii

 

Figure 9.5.b

 

3.  In Exercise 4 of Chapter 2, we examined a vegetable fiber traded in a competitive world market and imported into the United States at a world price of $9 per pound. U.S. domestic supply and demand for various price levels are shown in the following table.

Price

U.S. Supply

(million pounds)

U.S. Demand

(million pounds)

 3

 2

34

 6

 4

28

 9

 6

22

12

 8

16

15

10

10

18

12

 4

Answer the following about the U.S. market:

a.         Confirm that the demand curve is given by , and that the supply curve is given by .

To find the equation for demand, we need to find a linear function QD= a + bP such that the line it represents passes through two of the points in the table such as (15,10) and (12,16).  First, the slope, b, is equal to the “rise” divided by the “run,”

Second, we substitute for b and one point, e.g., (15, 10), into our linear function to solve for the constant, a:

, or a = 40.

Therefore,

Similarly, we may solve for the supply equation QS= c + dP passing through two points such as (6,4) and (3,2).  The slope, d, is

 

.

Solving for c:

 or c = 0.

Therefore,

b.         Confirm that if there were no restrictions on trade, the U.S. would import 16 million pounds.

If there are no trade restrictions, the world price of $9.00 will prevail in the U.S.  From the table, we see that at $9.00 domestic supply will be 6 million pounds.  Similarly, domestic demand will be 22 million pounds.  Imports will provide the difference between domestic demand and domestic supply: 22 - 6 = 16 million pounds.


c.         If the United States imposes a tariff of $3 per pound, what will be the U.S. price and level of imports?  How much revenue will the government earn from the tariff?  How large is the deadweight loss?

With a $3.00 tariff, the U.S. price will be $12 (the world price plus the tariff).  At this price, demand is 16 million pounds and supply is 8 million pounds, so imports are 8 million pounds (16-8).   The government will collect $3*8=$24 million.  The deadweight loss is equal to

0.5(12-9)(8-6)+0.5(12-9)(22-16)=$12 million.

d.         If the United States has no tariff but imposes an import quota of 8 million pounds, what will be the U.S. domestic price?  What is the cost of this quota for U.S. consumers of the fiber?  What is the gain for U.S. producers?

With an import quota of 8 million pounds, the domestic price will be $12. At $12, the difference between domestic demand and domestic supply is 8 million pounds, i.e., 16 million pounds minus 8 million pounds.  Note you can also find the equilibrium price by setting demand equal to supply plus the quota so that

The cost of the quota to consumers is equal to area A+B+C+D in Figure 9.6.d, which is

(12 - 9)(16) + (0.5)(12 - 9)(22 - 16) = $57 million.

The gain to domestic producers is equal to area A in Figure 9.6.d, which is

 (12 - 9)(6) + (0.5)(8 - 6)(12 - 9) = $21 million.

 

Figure 9.6.d