Answers To Chapter 3

Answers To Chapter 3

Review Questions

1. Answer d. Competition ensures that the firm will be a wage taker. If the firm pays less than the going wage, no one would work for the firm. If the firm pays more, it will be at a cost disadvantage relative to rivals that did pay the going wage, and as a result the firm will be forced to close. Since the wage does not change as employment changes, the additional cost associated with hiring an additional worker is just the going wage that the firm pays. 2. Answer d. Competition ensures that the firm will be a price taker. If the firm sells for more than the going price, no one would buy the product. If the firm sells for less, it will not be taking in the amount of revenue it could and so earns less than comparable firms. If this continues the firm will be forced to close. Since the price does not change as output changes, the additional revenue associated with an additional unit of output is just the going price that the firm receives. 3. Answer d. Answers a and c simply repeat the premise of the question, they do not give any economic reasons for the relationship. Answer b has the relationship backwards. A decrease in the wage will trigger a higher level of employment and, in turn, a lower marginal product since a larger number of workers will be spread over a fixed capital stock. 4. Answer b. When the MRL gets very close to the MEL, all the moves that add to profit have been made. 5. Answer a. Recall that a monopsonist chooses a wage and labor combination below its MRPL curve. Monopoly in the output market would only affect whether the MRPL expression could be simplified to P◊MPL. The expression MRPL = MR◊MPL is a definition and is always true. 6. Answer b. To survive in a competitive market, a firm must maximize profits. How it gets to that point (e.g., trial and error, luck, etc.) does not matter. However, since the MRPL = MEL rule does lead to maximum profits, a firm that is maximizing profits is acting as if it did follow that rule. Thus, even if no firm understands or actually follows the rule, it is useful to consider because it has predictive power. In the end we should see firms operating at this point because if they do not, they will not be maximizing profits, and can be driven out by firms that do. 7. Answer b. To find the market demand, add the individual quantities that are demanded at the real wage of 10. Since L1 = 2.5, L2 = 5, and L3 = 10, the market quantity is 17.5.

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Ehrenberg/Smith • Modern Labor Economics: Theory and Public Policy, Tenth Edition

8. Answer a. W $10 C $36 = =2< = = 3. MPL 5 MPK 12

The firm should increase L and decrease K to bring about an equality. As L increases, MPL will fall, increasing the left side of the equation. As K decreases, MPK will rise, decreasing the right side of the equation. Currently, the marginal cost of output produced by capital is $3, and only $2 for that produced by labor. Alternatively, an additional dollar spent on labor currently yields one-half unit of additional output, but the same dollar spent on additional capital only increases output by one-third unit. 9. Answer a. As C falls, the MC of the firm falls and the output of the firm increases. As output increases, the firm will use more of both capital and labor. This is called the scale effect of the price change. As long as this effect dominates the tendency of the firm to substitute capital for labor, the quantity of labor demanded should increase. 10. Answer d. In this question, capital and labor are used in fixed proportions in the production process. For example, if a firm uses one unit of labor and one unit of capital, it may be able to produce one unit of output, but if it adds another unit of capital without adding another unit of labor, output will not increase. In such a situation, the firm cannot substitute capital for labor when the price of capital falls, since this would take it away from the required proportion of labor and capital. The reduction in the price of capital, however, will reduce the marginal cost of production, leading to an increase in output (a scale effect) and an increase in the usage of both labor and capital. When the price of capital falls and labor usage increases, labor and capital are called gross complements. 11. Answer d. When the price of capital rises, in the long run the substitution and scale effects will combine to reduce the quantity of capital demanded. If the demand for labor shifts right as a result, that means labor usage is increasing. This occurs if the substitution effect of the capital price increase dominates the scale effect. In such a situation, labor and capital are called gross substitutes. 12. Answer d. The tax is the amount by which the demand curve is shifted down. 13. Answer c. As a result of the 4-unit tax, the equilibrium wage has been driven down by 2 (from 10 to 8). Therefore, the workers bear 50% of the tax in this example. 14. Answer a. In addition to the wage burden, workers see employment opportunities reduced by 1 (from 5 to 4) because of the tax. 15. Answer d. Who bears the burden of the tax is determined by which side of the market is least responsive to changes in the wage. When supply is perfectly vertical, the downward shift of the demand curve causes the wage to fall by the same amount. 16. Answer a. At the cost-minimizing combination of L and K, the isoquant is tangent to, and hence has the same slope as, the isoexpenditure line. Note that the slope of the isoexpenditure line is W/C = $16/$25 = 0.64. 17. Answer a. TC = $16(125) + $25(80) = $4,000. Notice also that the vertical intercept equals TC/C and the horizontal intercept equals TC/W.


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18. Answer d. If C increases to $40 holding all else constant, the isoexpenditure line would connect 250 on the labor axis with 100 on the capital axis. This would make an output of 100 unattainable. To produce along the old isoquant, the isoexpenditure line would have to move out parallel, reflecting an increase in cost. If it did so, notice that a tangency would occur with the Q = 100 isoquant at a point that involved less capital and more labor.

Problems

19a. MR is the change in total revenue (R) associated with a one-unit change in output (Q), holding all else constant. More formally, if ΔQ represents a small change in output, and ΔR represents the resulting change in revenue, then MR =

ΔR . ΔQ

Similarly, MPL is the change in output associated with a one-unit change in labor, holding all else constant. Formally, the MPL can be written as MPL =

ΔQ . ΔL

By definition, MR◊MPL is the marginal revenue product (MRPL). Substituting the above expressions for MR and MPL yields ΔR ΔQ ΔR , × = ΔQ ΔL ΔL

which is by definition MRL, the additional revenue associated with a one-unit change in labor. 19b. If there is perfect competition in the output market, MR simplifies to P in the MRPL expression. With P constant, the MRPL slopes downward because MPL is assumed to diminish. With P constant, MRPL reaches zero when the MPL reaches zero. When the firm has monopoly power in the output market, the MRPL is downward sloping because both MR and MPL diminish as L increases. (For a monopoly, MR falls as Q increases, and Q increases as L increases.) 20a. The new MRPL (demand) curve has the equation MRPL = 40 − L. It is shown as curve D2 in Figure 3-7. Notice that the shift is not parallel, since the curve reaches zero when the MPL reaches zero (at L = 40). If W stays at $10, the optimal level of labor to demand is 30.

Figure 3-7

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20b. The changes are identical to those in 25a. 20c. The changes are identical to those in 25a and 25b. 21a. See Figure 3-8.

Figure 3-8 21b. The marginal product of labor curve now serves as the firm’s demand curve for labor. 22a. See Figure 3-9.

Figure 3-9 22b. Let L standard for the total quantity demanded in the market. Then, L = L1 + L2 = 50 − (W/P) + 25 − 0.5(W/P) = 75 − 1.5(W/P) or W/P = 50 − (2/3)L. 23. The inequality suggests that if the firm produced one less unit of output by using less capital, its total cost of production would go down by $5. If the firm then proceeded to produce that same unit of output using labor, its total costs would only go up by $4. In other words, the firm could produce the same total output by changing its mix of labor and capital. If the firm can produce the same output at a lower cost with a different input mix, it could not have been at the optimal mix of labor and capital.


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*24a. If P = 56 − 2Q, then MR = 56 − 4Q. As W increases from $4 to $9 again, the MC will still rise from $16 to $24. What will be the change in optimal output? Originally, MR = MC ⇒ 56 − 4Q = * * 16 ⇒ Q = 10. After the rise in MC, MR = MC ⇒ 56 − 4Q = 24 ⇒ Q = 8. So originally, with an * * output of 10, L = 20 and K = 5. Holding output constant at 10, the change in W will lead to * * * L = 13.33 and K = 7.5. Allowing output to adjust downward to 8 yields L = (4/3)8 = 10.67 and * K = (3/4)8 = 6. The net result of W increasing from $4 to $9 was that L* fell from 20 to 10.67 (a reduction of * 9.33 units), and K rose from 5 to 6 units (an increase of one unit). This net result, however, can be explained by a substitution effect where L* fell from 20 to 13.33 (a reduction of 6.67) and a scale * effect where L fell even further from 13.33 to 10.67 (an additional reduction of 2.67). Similarly, * * the increase in K can be explained by a substitution effect where K increased from 5 to 7.5 * (a 2.5 unit increase), and also a scale effect where K fell from 7.5 to 6 (a 1.5 unit decrease). 24b. Since the substitution effect on capital of the wage increase dominated the scale effect, labor and capital are gross substitutes, and the demand for capital will shift right (increase) as the wage increases. *25a.

* * Originally, L = 20 and K = 5. After the change in C, the expressions for the optimal levels of * * L and K become L = 3Q and K = (1/3) Q. If the original output level of 10 were maintained, the * * firm would substitute labor for capital so that L = 30 and K = 3.33. However, output does not * remain at 10 since MC rises from $16 to $24. As the MC rises to $24, output falls to Q = 6. * * At the new level of output, L = (3)6 = 18 and K = (1/3) 6 = 2.

The net result of C increasing from $16 to $36 was that L* fell from 20 to 18 (a reduction of * 2 units), and K fell from 5 to 2 (an decrease of 3 units). This net result can be explained by a * substitution effect where L rose from 20 to 30 (an increase of 10) and a scale effect where * L fell from 30 to 18 (a reduction of 12). Similarly, the decrease in K * can be explained by a * substitution effect where K fell from 5 to 3.33 (a 1.67-unit decrease), and also a scale effect * where K fell from 3.33 to 2 (a 1.33-unit decrease). 25b. Since the scale effect on labor of the capital price increase dominated the substitution effect, labor and capital are gross complements, and the demand for labor will shift left (decrease) as the price of capital increases. 26a. MPL is the change in output associated with a one-unit change in labor, holding all else constant. More formally, if ΔL represents a small change in labor, and ΔQ represents the resulting change in output, then ΔQ . MPL = ΔL Using this formula, the movement from point a to b implies MPL = 2/4 = 0.5. For the movement from b to c, MPL = 2/5 = 0.4. 26b. The diagram does show a diminishing marginal product of labor. It does not help to explain why the MPL falls, however. The diagram is drawn assuming a diminishing MPL and so simply reflects that assumption.

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27a. The substitution effect is zero on both inputs, since holding output constant, the increase in the price of capital has no effect on the optimal input mix. The firm will remain at point a as long as it wishes to produce 70 units of output. 27b. The scale effect is a reduction in 20 units of both labor and capital. The firm moves from point a to point b. 27c. Labor and capital are gross complements since labor has been reduced in response to an increase in the price of capital. 27d. The total cost level has increased. Originally TC = $5(70) + $10(70) = $1,050. After the price change and the adjustment in the input mix, TC = $5(50) + $20(50) = $1,250. Without the scale adjustment, however, the increase in cost would have been much worse.

Applications

28a. Equilibrium occurs where WD = WS. 30 − 0.04L = 0.05L − 15 ⇒ 0.09L = 45 * * ⇒ L = 500 ⇒ W = $10.

28b. The $9 per unit payroll tax shifts the demand curve down vertically by $9. 30 − 0.04L − 9 = 0.05L − 15 ⇒ 0.09L = 36 ⇒ L* = 400 ⇒ W * = $5. The cost of labor (per unit) to the employer is the $5 wage plus the $9 tax for a total of $14. 28c. Since workers see their wage reduced from $10 to $5, they bear five-ninths of the tax. The firm sees its labor costs per unit rise from $10 to $14, so they bear the remaining four-ninths of the tax. 28d. Like the payroll tax, mandated benefits impose real per-unit labor costs on firms. The effect of such costs would be to shift the demand for labor down and thereby reduce wages and employment levels. When all adjustments required by the market have been made, workers are likely to have borne a significant share of the cost of such programs. *29a. The demand curve is the MRPL curve. MRPL = MR◊MPL . K = 16 ⇒ Q = 4 L . MR = 20 − Q = 20 − 4 L . 2 40 MRPL 20 − 4 L = − 8. L L

(

)


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29b. Profit maximization occurs where MRPL = W. 40 − 8 = 10 ⇒ L* = 4.94 L Q* = 4 4.94 = 8.89 ⇒ P* = $15.56.

*29c.

MRPL = 15

2 L

=

30 L Profit maximization ⇒

30

= 10 L ⇒ L* = 9 ⇒ Q* = 12.

*29d. See Figure 3-10.

Figure 3-10 29e. In the long run the increase in output should lead to a scale effect that would increase the usage of both capital and labor. 29f.

Regulations usually allow the firm a normal rate of return over its costs. As a result it has no incentive to control costs. If the firm pays higher wages, workers will be happier and the best new workers can be hired, making life smoother for the mangers of the firm, and the firm’s rate of return will not be affected.

30a. At W = $4, L = 120. See the line ab in Figure 3-11 for a plot of the original demand curve. *30b. The subsidy is 50% of the difference between the target wage ($8) and the actual wage ($4). Therefore, the subsidy is $2 for each eligible worker. The effective cost to the firm of a new worker is $4 − $2 = $2. *30c.

Since the effective cost of new labor is $2, the firm should be willing to hire out to L = 140. It is as if the firm is moving to the employment level associated with point e while the wage remains at $4. The intersection of the $4 wage and the new employment level creates the point f. Repeating this process for wage rates other than $4 creates the line segment dg. The new demand curve in its entirety would be the line bdg.

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Figure 3-11 *30d. At a wage of $4, the new demand curve is flatter (the slope as it appears on the graph changes from −0.1 to −0.067). The curve would be even flatter if the percentage of the subsidy increased to 75%. Point f would lie further to the right at L = 150 (and the slope would become −0.057). *30e.

The total payment would be $2 times the number of new hires (20) for a total of $40. If the subsidy applied to all workers, the payment would be $2 times 140 for a total of $280.

*30f.

If the original demand were steeper, the subsidy would have a smaller effect on employment. If the demand were steeper, point e would lie to the left of its current position. Since the employment level associated with point e determines the employment level associated with point f, point f would lie to the left of its current position.

*30g.

Targeted programs like this do not always work as well as the model predicts because there may be a stigmatizing effect associated with being eligible for the subsidy. The employer may feel there is something wrong with a worker who needs the government’s help to be hired, and so judge the worker’s marginal revenue product to be even lower than it actually is. If the employer devalues the employee’s worth as much as the subsidy reduces the employer’s cost of hiring this worker, there may be no increase in employment.