# Slutsky Equation - Labour Economics - Past Exam, Exams for Economics. Veer Bahadur Singh Purvanchal University

## Economics

Description: Slutsky Equation, Two Good Model, Dramatic Decline, Budget Share, Wealth and Wages, Economic Downturn, Payroll Taxes, Constant Returns, Scale Technology, International Capital Markets are some points from questions of this exam paper.
Showing pages  1  -  2  of  4
University of California Department of Economics
Field Exam August 2010
Labor Economics
There are three parts in the exam. Each part will be weighted equally and
should take approximately one hour. Make sure you allocate your time
carefully, answering all parts as fully as possible given the time constraint. Use
equations and graphs whenever possible to clarify your reasoning.
PART I Answer both questions in this part. Each question should take about 30
minutes.
Question 1: LABOR SUPPLY
a) Derive the Slutsky equation for hours of work in a standard two-good model with
leisure and consumption. Be sure to define your notation, and carefully state any
assumptions that you have used in your derivation.
b) The recent financial crisis led to a dramatic decline in the net worth of many American
households. Suppose that for a representative household the elasticity of hours worked
per year with respect to income is 0.1 and that the budget share of earned income in
total consumption is 0.8. How much of an increase in hours worked should we expect if
the crisis destroyed ten percent of lifetime wealth and wages remained constant? Using a
reasonable estimate of the compensated elasticity of labor supply, how much would
wages need to fall for total hours worked to be unaffected by the crisis?
Question 2: LABOR DEMAND
A pair of well known economists proposed cutting payroll taxes during the recent
economic downturn in order to boost employment. Note: Payroll taxes are federal taxes
levied on wages paid by firms to workers (e.g. firms pay an after tax wage of w(1+τ)).
a) Suppose firms produce output using a constant returns to scale technology F(K,L)
taking capital (K) and labor (L) as inputs. Assume the rate of return on capital r is fixed
exogenously by international capital markets. Derive an expression for the employment
effects of a 10% decrease in the federal payroll tax τ. Be sure to state any additional
2
b) Now consider a representative firm facing the following dynamic objective:
Π(A,K,L)= max AF(K,L) c1 1[L<L] c2(K-(1-δ)K) wL + β E Π (A,K,L)
K,L
where A is the firm's total factor productivity, which follows some stochastic process, F
is a production function, c1 represents the fixed cost of firing workers, 1[.] is an indicator
function for the expression in brackets being true, c2 is the cost of new capital, w is the
wage rate, and β<1 is a discount factor.
Using this model, discuss the dynamic effects of a small, temporary cut in the payroll tax
(e.g., a reduction in the tax rate that will last for 1 year).
c) How does your answer to b) depend on the firm's level of uncertainty regarding next
period's level of productivity A?
PART II Answer all parts of this question. The question is designed to take 1 hour. Use
equations and graphs whenever possible to clarify your reasoning.
In this question you will develop a variant of the Roback (JPE, 1982) model of the joint
determination of wages and cost of living. In particular, consider the case where there are
2 cities (A and B) and 2 skill groups: skilled workers and unskilled workers. Skilled and
unskilled workers are imperfect substitutes. Variation in the cost of living depends only
on variation in cost of land which is assumed to be the same for all workers in the same
city, irrespective skill.
1) State all the assumptions of the Roback model. (for example: what are you assuming
about workers' and firms' mobility? Which goods are traded and which goods are local?
What are you assuming about firms' profits?) . Full credit will be awarded for a full
description of all the assumptions.
2) Assume for now that the two cities are identical in terms of amenities and production
technology, and there are no externalities. Describe the equilibrium in words. Now,
describe the equilibrium graphically. (Hint: Draw two graphs side by side. The left
graph is for the skilled workers. The right graph is for the unskilled workers. Label the
axis and all the curves and explain in detail why each curve looks the way it does.)
3) Now suppose that city A is less attractive than city B because schools have lower
quality. For simplicity, assume that school quality directly enters workers' utility
functions. Assume also that schools are not financed locally and that skilled and
unskilled workers value schools equally. In a graph, show what happens to wages and
rents in equilibrium. Label all the curves. Explain what is happening in words.
4) In equilibrium, both skill groups are present in both cities. Since workers are free to