Calculate the own-wage elasticity of labor demand
Question 1. Using the mid-point method, calculate the own-wage elasticity of demand for Occupations a, b, and c below. E’D and W’ are the original employment and wage. and E’D and W’ are the new employment and wage. State whether the demand is elastic, inelastic, or unitary elastic.
a) %ΔED = 5, %ΔW = -10
b) ED = 50, W = 7
ED’ = 40, W’ = 8
c) ED = 80, W = 8
D E’D = 100, W’ = 6
Question 2. Suppose labor demand is given by the equation L = 50 -2W, where L is the number of workers and W is the wage rate
a. The slope of the demand curve can be viewed as the amount by which L changes for every 1 unit change in W. This can be expressed formally as Slope = ΔL/ Δ W, where Δ 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?
b. 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?
c. 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.
d. 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.
e. Considering your answer to (b) and (d), 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)?
f. Suppose each worker at this firm always works 40 hours a week. If L were 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 (a) and (b)?
g. Why do you think the economists prefer the elasticity in comparison to the slope as a measure of labor’s responsiveness to wage changes?
Question 3. Union A faces a demand curve in which a wage of $4 per hour leads to demand for 20,000 person hours and a wage of $5 per hour leads to demand for 10,000 person hours. Union B faces a demand curve in which a wage of $6 per hour leads to demand for 30,000 person hours, while a wage of $5 per hour leads to demand for 33,000 person hours.
a. Which union faces the more elastic demand curve?
b. Which union will be more successful in increasing the total income (wages times person hours) of its membership? Explain. Why?
Question 4. The public utilities commission in a state lifts price controls on the sale of natural gas to manufacturing plants and allows utilities to charge market prices (which are 30% higher). What conditions would minimize the extent of manufacturing job loss associated with this price increase?
Question 5. In 1942 the government promulgated regulations that prohibited the manufacture of many types of garments by workers who did the sewing, stitching, and knitting in their homes. If these prohibitions are repealed, so that clothing items may now be made either by workers in factories or by independent contractors doing work in their homes, what effect will repealing the prohibitions have on the labor demand curve for factory workers in the garment industry?
Question 6. One approach to health care reform is the so called “play or pay” approach. Under this approach, employers are required to either provide health insurance to their employees or contribute to a fund which the government would use to provide insurance for all those lacking coverage. Consider three competing proposals for how these contributions could be determined.
Plan A: Contributions would be required for every hour an employee works (e.g., 10 cents per hour).
Plan B: Contributions would be some percentage of the value of the firm’s buildings, land, and machinery (e.g., 2% of the total property value).
Plan C: Contributions would be required for every unit of output a firm produces (e.g., 50 cents per unit of output).
a. While all the plans have the potential to reduce employment opportunities, which plan would probably have the least impact on employment? Explain your reasoning.
b. For each plan, list the conditions that would lead to the largest reduction in employment.
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