Professors Allen and Wessels

ECG 730

Fall 2001


Problems in Labor Demand


1.      True, false, or uncertain


a)      The elasticity of demand for a factor by a competitive industry must be lower when the quantities of other factors are held constant than when the prices of other factors are held constant.

b)      Labor demand is never more elastic than product demand.

c)      If labor demand is infinitely elastic, then product demand is also infinitely elastic.

d)      Suppose that personal computers are substitutes for clerical workers and complements for professional workers.  Then falling prices for personal computers should lead to reduced employment of clerical workers and increased employment of professional workers.

e)      France recently enacted laws reducing the length of the workweek from 40 to 35 hours.  In response employers will reduce hours and increase employment.

f)        Marye Anne Fox said in a recent talk that increased spending for higher education, which is financed through taxes paid by everyone in the state, is in the best interest of all in the state.


2.      Suppose that all employers were required to provide health insurance to all of their employees.  Explain what is likely to happen to


a)      total employment

b)      hours per worker

c)      total hours worked (a times b)

d)      employment of skilled relative to unskilled labor

e)      the odds that an employer will increase employment in response to a decrease in wages


3.      There currently is a ceiling on the amount of workers’ earnings that is subject to the payroll tax used to finance Unemployment Insurance (UI).  In most states the tax averages 3.4 percent of the first $8000 earned by each person on a firm’s payroll.  (The actual tax depends on the UI benefits received by its employees over the last three years.)


a)      Suppose the ceiling for this tax is removed, but the tax rate stays the same.  What will happen to the employment of skilled labor, unskilled labor, and capital in both relative and absolute terms?

b)      Suppose instead that the tax rate is reduced so that total payroll tax revenue for the UI system stays the same.  How does this change your answer?


4.      A profit maximizing firm operates in competitive markets with the production technology Q = [b(S)L]g1Kg2 where L = quantity of labor, K = quantity of capital, and the productivity of labor depends on its schooling level S according to b(S) = exp(0.3S – 0.01S2).  The output price is 1, the user cost of capital is r, and the price of labor is w(S) = exp(0.1S)


a)      What hiring standard S does the firm choose?  What wage does it pay?

b)      Now suppose a union organizes the firm’s work force and raises the wage to exp(1.15).  Given this wage, what hiring standard S will the firm desire?


5.      Santa Monica has become the first city in the US to pass a living wage ordinance that applies not just to city agencies and city contractors, but also to private firms working in certain areas of the city.  The living wage is defined as $12.50 per hour, less if health insurance is provided.  Click here for information about the ordinance in Santa Monica.  Discuss the most likely consequences of this ordinance on the labor market in and near Santa Monica, focusing on issues that can be analyzed through labor demand theory.


6.      The following exercise uses the KLEM data (in Excel or text format) from Berndt and Wood, AER, 1975 and is based upon exercises in Berndt, The Practice of Econometrics, ch. 9.  Variable definitions are as follows:


YEAR              Year, beginning with 47 for 1947 and ending with 71 for 1971

QY                   Quantity if Gross Output

PY                   Price Index of Gross Output

QK                   Quantity of Capital Services

PK                   Rental Price Index for Capital Services

QL                   Quantity of Labor Input

PL                    Price Index for Labor Input

QE                   Quantity of Aggregate Energy Input

PE                   Price Index for Aggregate Energy Input

QM                  Quantity of Non-Energy Intermediate Materials

            PM                   Price Index for Non-Energy Intermediate Materials

            QV                   Quantity of Value-Added Output

            PV                   Price Index of Value-Added Output


a)      Calculate real prices for K, L, E and M, using PY as a deflator.  What are the time trends of these prices?  Which prices seem to move together?  Which prices are most volatile?

b)      Calculate factor intensity ratios for each input (Qi/QY, for each input I).  Is the US becoming more or less labor-intensive over this time period?  What about energy and capital intensities?

c)      Calculate average labor productivity (QV/QL) and the capital-labor ratio (QK/QL), then estimate the Cobb-Douglas equation


ln(QV/QL) = ln A + aK ln(QK/QL)


and comment on your results.

d)      Consider three alternative estimates of the elasticity of substitution


ln(QV/QK) = a1 + s1 ln(PK/PV) + u1

ln(QV/QL) = a2 + s2 ln(PL/PV) + u2

ln(QK/QL) = a3 - s3 ln(PK/PL) + u3


Which of these values seem most reasonable?

e)      Estimate a translog model using the KLEM data.  Compare the results from a single equation OLS approach to a systems approach with symmetry restrictions, linear homogeneity in prices, and constant returns to scale imposed. 

f)        Calculate the own-price elasticities and the Allen-partial elasticities of substitution from the systems approach.  Do you find energy-capital complementarity?

g)      EXTRA CREDIT: How would you go about testing for energy-capital complementarity today?