Economics 0115 Homework #2

Table 1: The Market for Steelworkers

W L^D₀ L^S₀ L^D₁ L^D₂ L^S₁ L^S₂

$10 400 00 480 320 160 **

$12 360 40 440 280 200 **

$14 320 80 400 240 240 **

$16 280 120 360 200 280 **

$18 240 160 320 160 320 00

$20 200 200 280 120 360 40

$22 160 240 240 80 400 80

$24 120 280 200 40 440 120

$26 80 320 160 00 480 160

$28 40 360 120 ** 520 200

$30 00 400 80 ** 560 240

1. Given the original supply and demand curves in Table 1 (L^D₀ and L^S₀), do the following:

a. Find the equilibrium wage and quantity of labor hired.

w^e = $20 and L^e = 200

b. Calculate the total earnings of labor (TE) in this market.

TE = $20(200) = $4,000

c. Graph this situation and label all of the points and areas described above.

d. What situation occurs when the wage is $26? Explain how the market adjusts back to equilibrium when the wage is $26.

NOTE: Show all work for sections requiring calculations.

w = $26 means that w > w^e and ES = 320 - 80 = 240. ES mean that there is downward pressure on the wage. As wages fall, the quantity demand of labor increases and the quantity supplied decreases and the ES decreases. The wage will continue to fall until ES = 0.

2. Using the numbers in Table 1, start with the equilibrium established with L^D₀ and L^S₀, draw the indicated shift in demand or supply, and briefly explain your graph. Then repeat 1.a. through 1.e. for the following:

a. There is a decrease in demand for steel as producers use aluminum instead of steel in their cans.

A decrease in the demand for steel implies a decrease in the demand for steel workers. A decrease in demand for steelworkers is represented in L^D₂.

b. Legislation preserving the spotted owl reduces the supply of lumber and increases its price. As a consequence, many home-builders begin using structural steel frames to construct homes.

An increase in the price of lumber (a substitute for steel) decreases the quantity demanded for lumber and increases the demand for steel. An increase in the demand for steel increases the demand for steelworkers. This shift is represented in L^D₁.

c. Because younger workers see better possibilities elsewhere, the number of retiring steelworkers exceeds the number of new steelworkers.

A net outflow of workers implies a decrease in the supply of steelworkers. This is represented in L^S₂.

d. Unions negotiated a number of "givebacks" in the early 1980s which lowered the wages of steelworkers from $26 to $22.

Such "givebacks" represent a decrease in the relative wage of steelworkers (or an increase in the relative wage of non-steelworkers). If the union wage was $26 (ES = 240) and fell to $22 (ES = 240 - 160 = 80) then some workers (320 – 240 = 80) would move out of the union sector in search of other jobs in the non-union sector. That is, there is a decrease in the quantity supplied of steelworkers of x but the supply curve for non-steelworkers increase in non-steelworker labor markets. Since no numbers are given for non-steelworker labor markets then the graph above must use the numbers above for steelworkers.

3. Using the numbers in Table 1, start with the equilibrium established with L^D₀ and L^S₀ and do the following:

a. The government establishes a minimum wage for unskilled workers at $24. Draw this on a graph and briefly explain how this minimum wage will affect this labor market.

The w_min = $24 generates an ES = 280 - 120 = 160. If all unskilled workers are covered by this law then the ES = 160 (80 workers who are disemployed and 80 workers who have re-entered the labor force seeking work at the higher wage) represents permanently unemployed workers. If there is only partial coverage of unskilled workers, some unskilled workers move to the uncovered sector, lowering wages there because of the increase in supply of labor in that sector.

b. Calculate the welfare loss associated with the minimum wage and indicate the welfare loss on the graph. Briefly explain what a welfare loss is.

WL = ½(200 - 120)($24 - $16)

= 40($8) = $320

The welfare loss associated with this wage floor is shown in the graph.

The welfare loss occurs as follows: Workers who are displaced from the covered sector will move to the uncovered sector. Those displaced workers generated an amount of revenue for the firm equal to the area under the demand curve. These workers also have an opportunity cost equal to the area under the supply curve. Thus workers who are displaced move to their next best alternative use which is represented by the area under the supply curve. The area under the supply curve represents a gain to employers (in revenue) in the uncovered sector of the labor market. The loss in revenue outweighs the gain and therefore results in a net loss.

c. Graph and explain what happens when the minimum wage is raised to $26. What happens to the welfare loss? Explain.

If w_min = $26 the ES = 320 - 80 = 240, an increase of 80 workers (40 additional workers are disemployed and 40 additional workers reenter the labor force). The new welfare loss is:

WL = ½($26 - $14)(200 - 80)

= $6(120) = $720

This represents a 125% increase ($720/$320) in the WL from a $2 increase in the minimum wage.

d. Graph and explain what happens to minimum wage workers in a recession. Then compare this result to what happens to workers who are not affected by the minimum wage.

Note that a recession will cause the demand for unskilled workers to decrease. When unskilled workers work in markets covered by the minimum wage, the wage cannot adjust downward so that a large number of workers (80) become unemployed.

Comparatively speaking, workers not covered by the minimum wage experience less employment loss because employers can reduce the wage for some workers instead of laying them off. Some workers in the uncovered market will decide to drop out of the labor force but this will be a smaller number of workers compared to the number of unemployed created in the covered market.

Table 2

Taxed Sector (1)

W $12 $14 $16 $18 $20 $22 $24 $26 $28

L^D₀ 110 100 90 80 70 60 50 40 30

L^S₀ 30 40 50 60 70 80 90 100 110

L^D₁

Untaxed Sector (2)

W $12 $14 $16 $18 $20 $22 $24 $26 $28

L^D₀ 110 100 90 80 70 60 50 40 30

L^S₀ 30 40 50 60 70 80 90 100 110

L^S₁

4. Given the numbers in Table 2, do the following:

a. Graph the supply and demand for the taxed sector and label all relevant points with numbers.

b. A tax of $4 per worker is levied on employers. Place the proper numbers in the row for L^D₁ and draw a new graph with this tax on it. Be sure to label the new equilibrium.

Table 2

Taxed Sector (1)

W $12 $14 $16 $18 $20 $22 $24 $26 $28

L^D₀ 110 100 90 80 70 60 50 40 30

L^S₀ 30 40 50 60 70 80 90 100 110

L^D₁ 90 80 70 60 50 40 30 20 10

The numbers for L^D₁ are derived as follows: Take some wage such as $16 and note that the quantity demanded of labor there is 90. Since the demand curve decreases because of the tax we must subtract $4 from $16 getting $12: the new point on the new demand curve is $12 and 90 units of labor.

c. Extra Credit: Calculate the final burden for employer and worker and indicate each area on the graph.

Employers' Final Burden: ($22 - $20)60 = $120

Workers' Final Burden: ($20 - $18)60 = $120

d. Calculate the welfare loss and explain how it arose.

WL = ½(70 - 60)($22 - $18) = $20

Because the taxes displace (or disemploy) 10 workers they must now seek their next best alternative employment in another part of the economy. These additional resources produce additional output whose value is represented by the area under the supply curve. Employers lose a value of output equivalent to the area underneath the demand curve between 60 and 70 workers. Adding these two areas produces a net loss of output to the economy (our WL). In effect, 10 workers have been reallocated to lower valued uses.

e. Graph the supply and demand curves for the untaxed sector and label all relevant points with numbers.

f. Show and explain what happens in the untaxed sector when those workers who were displaced by the tax attempt to find jobs in that sector. Fill in the second part of Table 2 for the new supply curve and label the new equilibrium.

Table 2

Untaxed Sector (2)

W $12 $14 $16 $18 $20 $22 $24 $26 $28

L^D₀ 110 100 90 80 70 60 50 40 30

L^S₀ 30 40 50 60 70 80 90 100 110

L^S₁ 40 50 60 70 80 90 100 110 120

The supply curve increases by the number of workers displaced in the taxed sector. That is, 10 workers move to the untaxed sector, increasing the quantity supplied at each wage by 10 workers. Because this produces an ES in the untaxed sector, wages will fall to $19 and employment will rise to 75. As a result, 5 workers (of the 10 who were displaced from the taxed sector) drop out of the labor force (become part of NILF). That is, the new equilibrium is $19 and 75 units of labor.