Please answer from letter “e)” to letter “l)” Consider an individual with utility function c^al^1-a,

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Please answer from letter “e)” to letter “l)” Consider an individual with utility function c^αl^1−α, where cis consumption, l is leisure, and α ∈ (0, 1). The individual isendowed with R units of nonlabor income and T units of time. Theindividual earns wage w for each unit of time worked. The price ofa unit of consumption is p.

(a) What is the budget constraint for this individual?

(b) What is the price of leisure?

(c) Set up the appropriate Lagrangian for this agent’sproblem.

(d) Find the first order conditions.

(e) Solve the demand functions for l and c in terms of exogenouslygiven parameters.

(f) What did this procedure assume about the solution to ourproblem?

(g) Find the indirect utility function.

(h) Find the utility when the agent chooses not to work atall.

(i) Using the last two parts, set up an equation that describes thereservation wage.

(j) Using the slope of the indifference curve, find the reservationwage.

(k) Perform comparative statics on the reservation wage for T, α,and R

(l) sketch the budget set and the indifference curves. . . .

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