Consider worker 1 with non-labour income Y facing a wage offer w and a utility function defined over consumption and leisure U(c,l) = lnC + 4lnl 1) Compare worker 1 with worker 2 whose utility function is described by U(c,l) = cl. Which worker places a higher value on labour market work? 1 2) Suppose the worker participates in the labour market. Derive worker’s compensated labor supply function and the compensated labour supply elasticity with respect to wage as a function of utility level and wage. 3) Derive worker’s uncompensated labour supply function (for labour market participants and non-participants) and the uncompensated labour supply elasticity (for labor market participants) with respect to wage as a function of non-labour income and wage. 4) Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker?
Consider worker 1 with non-labour income Y facing a wage offer w and a utility function
defined over consumption and leisure
U(c,l) = lnC + 4lnl
1) Compare worker 1 with worker 2 whose utility function is described by U(c,l) = cl. Which
worker places a higher value on labour market work?
1
2) Suppose the worker participates in the labour market. Derive worker’s compensated labor
supply function and the compensated labour supply elasticity with respect to wage as a function
of utility level and wage.
3) Derive worker’s uncompensated labour supply function (for labour market participants and
non-participants) and the uncompensated labour supply elasticity (for labor market participants)
with respect to wage as a function of non-labour income and wage.
4) Derive worker’s income elasticity. Is leisure a normal or inferior good for this worker?
5) Provide the functional form of the income effect from a marginal decrease in income.
6) Provide the functional form of the substitution and total income effects of a marginal increase
in wage.
8) Show that the Slutsky equation holds for this worker.
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