Question

Assignment Three - Chapter 4

16. Suppose labor demand is given by the equation

L = 50 −2W,

where L is the number of workers and W is the wage rate.

16a. The slope of the demand curve can be viewed as the amount by which Lchanges for every 1 unit     change in W. This can be expressed formally as

Slope ₌    ∆^∆LWL _,

where∆refers to a small change in the value of L or W. Using this definition, find the slope associated with a wage change from $5 to $6. Would your answer be different if the wage rose from $20 to $21?

16b. Calculate the own-wage elasticity of labor demand as the wage changes from $5 to $6. How would your answer be different if the wage rose from $20 to $21?

16c. How does the slope change as one moves up this labor demand curve? How does the elasticity change as one moves up this labor demand curve? Graph this labor demand curve.

16d. The firm’s total expenditures on labor (the total income received by labor) equals the wage multiplied by the number of workers employed. Calculate the change in the firm’s total expenditures on labor when the wage changes from $5 to $6. Do the same for a change from $20 to $21.

16e. Considering your answer to 16b and 16d, what relationship can you find between the own-wage elasticity of labor demand and the change in a firm’s total expenditures on labor (the total income received by labor)?

16f. Suppose each worker at this firm always works 40 hours a week. If Lwere expressed in terms of labor hours instead of the number of workers, the labor demand curve would be represented by the equation

L = 2000 − 80W.

Find the slope of the curve and the elasticity as the wage rises from $5 to $6. Does the change in the units in which L is measured make any difference to your answers (when compared to the answers in 16a and 16b)?

16g. Why do you think the economists prefer the elasticity when compared to the slope as a measure of labor’s responsiveness to wage changes?

Answer 1

Solving first 4 as per Chegg policy.

A. Slope is given by deltaL/deltaW

When wage increases from 5 to 6,

L when wage 5= 50-2w=50-10=40

L when wage 6= 50-2w=50-12=38

Slope=38-40/6-5=-2

Calculating same when wage changes from 20 to 21

L when wage 20= 50-2*20=50-40=10

L when wage 21= 50-42=8

Slope=8-10/21-20=-2

The answer does not change.

B.

Wage elasticity of demand can be given by

e=(Cange in L/change in w)*w/L

elasticity when wage changes from 5 to 6

=-2*5/10=-.25

elasticity when wage changes from 20 to 21

=-2*20/10=-4

c.

Given, L=50-2w

as established in part A, slope=-2

and slope remains same as move up the demand curve.

elasticity=(Change in L/change in w)*w/L

As we move upwards in the demand curve, w increases and L falls. Hence, from the above formula, its clear that elasticity increases.

The demand curve has been plotted below

D. When the wage changes from 5 to 6

change in expenditure=6*38-5*40

=228-200

=28 (increases by 28)

when wage changes from 20 to 21

Change in expenditure=21*8-10*20

=168-200

=-32 (falls by 32)