Worker 1 with non-labour income Y is facing a wage offer, w and a utility function defined over consumption and leisure

U (c,l) = lnC + 4lnl

a) When comparing 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?

b) Assuming the worker participates in the labour market. Derive the worker's compensated labour supply function and the compensated labour supply elasticity with respect to wage as a function of utility level and wage

c) Derive worker's uncompensated labour supply function (for labour market participants and non-participants) and the uncompensated labour supply elasticity (for labour market participants) with respect to wage as a function of non-labour income and wage

d) Derive worker's income elasticity. Is leisure a normal or inferior good for this worker?

e) What is the functional form of the income effect from a marginal decrease in income

f) What is the functional form of the substitution and total income effects of a marginal increase

g) Prove that the Slutsky equation holds for this worker