Reference no: EM132445010

Suppose that the representative consumer's preferences are given by the utility function U(C,l)= lnC +α lnl, where C is consumption and l is leisure. The consumer's budgetconstraint is given by C = w(h-l)+π -T , where w is the real wage, h is the quantity of time the consumer has available, π is dividend income, and T is the lump-sum tax.

a) Set up the consumer's optimization problem.

b) Write down the Lagrangian associated with this consumer's optimization problem.

c) Assume that there is an interior solution to the consumer's problem. Determine the consumer's optimal choice of consumption and leisure. Illustrate your results on a diagram. [Notes/Hints: Show all steps of your calculations//derivations to get full marks.]

d) Suppose that there is an increase in the real wage rate, w. Determine mathematically the effects of this increase in w on the consumer's optimal choice of consumption and leisure. Provide an intuition for each of these effects. Illustrate the effects of this increase in w on a diagram. [Notes/Hints: Show all steps of your calculations to get full marks. You have to take a partial derivative of the endogenous variables with respect to w and determine whether the result is positive or negative. Clearly label each axis of the diagram and clearly identify the intercepts and the equilibrium.]