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?

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.

7) Show that the Slutsky equation holds 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?

Consider the following economy with production.  There is a worker endowed with 1 unit of time, which can be allocated either to leisure or labor.  There is a firm with a technology that turns a worker’s labor (the complement of his leisure) into bread.  That technology satisfies: b(l)=l^(1/2)

Where l∈[0,1]  denotes the worker’s labor and b(l) is the amount of bread produced as a function of labor input. The  worker’s  utility  function  from  labor  supplied  and bread consumed is: u(l,b) =αln(b)−l,0< α <2

1. What is the set of Pareto optimal allocations in this economy? 

2. Provide prices and an allocation that, together, constitute a competitive equilibrium in this economy. 

Willy the Worker has unavoidable personal commitments taking 8 hours per day. He can choose to work or to play (i.e., take leisure, a normal good) in the remaining hours. Being a graduate in Economics, he can charge $100 per hour for his consulting services when he chooses to work. The government's income tax system has a 0% tax rate for daily incomes from $0 to $ $600 per day; above $600 per day, the tax rate is 20%. Willy has a certain Utility Function U(L, I) where L = leisure play time and I = Income. His Marginal Rate of Substitution is known to be derived from this equation: MRSLI = 21/L . [Note that the "price" of Income is $1.] 1.1 (4) Willy thinks he pays enough taxes via the excise taxes on things he buys. So he decides to work the maximum number of hours he can without paying any income taxes. According to our Indifference Theory model, is Willy maximizing his satisfaction with his "no tax" choice, or should he work fewer hours? Explain your answer. [No diagram; use "the logic" of the model only.] At equilibrium, MRSLA = price ratio =PL/P1 = 100/1 = slope of BL = wage rate = 100 At "no tax” point, L = 10 and I = $600, hence MRS = 1200/10 = 120 Since MRS > P ratio, he must reduce MRS by taking more Leisure and working less He should (be at the "no tax" point / work fewer hours than the "no tax" point*)