ECON6007 – LABOUR ECONOMICS
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ECON6007 – LABOUR ECONOMICS
1. The individual’s utility function has the following form:
1 1
U (C, L) = 5 + C 2 L 2
Here C indicates the consumption good and L the leisure. The individual has non-labour income R and L0 hours that can be used to work (h) or leisure. P = 1 is the numeraire.
(a) Derive the Marshallian labour supply h* .
(b) Derive the Marshallian elasticity of labour supply with respect to wages ηM . (Note: this is a function of w , h and R)
(c) Derive the Hicksian labour supply 
.
(d) Derive the Hicksian elasticity of labour supply with respect to wages ηH . (Note: this is a function of w , h and 
)
(e) Assuming that w = 1, R = 8 and L0 = 24:
● Calculate the values of h* and 
(Hint: to do so, calculate before the optimal level of expenditure and of the utility.) What do you notice?
● Calculate the values of ηM and ηH ; comment and compare the sizes of the elasticities
● Verify that the Slutsky equation holds (recalling that ηM = ηH + 
ηR0 ).
2. Consider the paper “Labor supply response to the earned income tax credit” by Eissa and Liebman discussed in the lectures.
(a) Briefly summarise the differences-in-difference (DiD) methodology used in the paper and discuss why this technique is useful to estimate the causal impact of the policy on labour supply. In your summary, carefully state the assumptions of DiD and critically discuss whether these assumptions are satisfied in the case of the paper in question.
(b) Based on the results of the paper, discuss why policies such as the earned income tax credit can be used as a tool to increase work incentives. Compare this policy with an alternative intervention that provides a “cash grant” to subsidise disadvantaged workers.
3. Assume that the production function of a firm in a perfectly competitive market is:
1
Y = F (K, L) = 2L 2
(a) Compute the marginal product of labor and the marginal product of capital.
(b) Let P indicate the price of a unit of good and R the price of a unit of capital. Derive the profit-maximising level of labor demand L* .
(c) Derive the labour demand elasticity with respect to wages. (Note: this should be a function of L* , W and P .)
(d) Calculate the value of labour demand elasticity at L* when P = 2, W = 3 and R = 3.
(e) Based on the value of the elasticity above, what would happen to labour demand if the wage were to fall by 10%?
4. Consider the papers on the effects of minimum wages covered in the lectures
(a) Outline the major challenges in empirically identifying the effects of minimum wages on employment.
(b) Briefly summarise alternative strategies proposed in the literature. In your summary, in- clude a description of the different techniques, assumptions, and data used.
(c) Suppose that there are two countries (A and B) with identical perfectly competitive labour markets (i.e. equal equilibrium levels of employment and wages). Country A decides to introduce a minimum wage (MW) above the equilibrium wage. Describe (in words or analytically or graphically):
● What happens to employment in country A after the MW is introduced.
● What happens to employment and wages in country B after the MW is introduced in country A.
● Whether and how your answers above depend on the size of labour demand and labour supply elasticities (hint: compare scenarios of countries with different elasticities).
5. Consider the empirical estimation of the returns to schooling in the equation wi = α + ρsi + εi (where w = ln w and s represents the years of schooling of individuals i).
(a) Describe the ability bias problem. Briefly discuss how instrumental variable techniques could overcome ability bias. Carefully state the assumptions of the IV estimator and provide one example of instrument used in the literature.
(b) Suppose that, besides the years of schooling, you can observe some measures of the indi- vidual’s ability, such as results from an IQ test. You decide to include this measure in the OLS wage regression above. Explain whether and how this strategy can solve the ability bias problem. Would you recommend that IQ tests are used as instrument for schooling? Why or why not?
2022-03-22