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Question 2 (22 pts.) Consider a representative agent with preferences over consumption c and leisure I represented by Uel)Inc + InI. Her budget constraint is c S wN, where w is the wage rate and N -the number of hours worked. The representative agent also chooses how to allocate her time between work and leisure activities given her time constraint 1 + N = h, where h is the total number of hours. a) (2 pt.) Combine the budget constraint and the time constraint of the representative agent into a single constraint b) (2 pts.) List all endogenous and exogenous variables. c) (1 pt.) Set up the Lagrangean function. d) (3 pts.) Find the first order conditions ro C e) (2 pts.) Use t order conditions to find an expression for MRScJ. Briefly interpret it. t.
f) (4 pts.) Solve for the optimal allocation bundle (c. L, N). (3 pts.) Suppose that h decreases due to the representative agent being sick. Find the effect of h decreasing on (c, I, N). g) h) (2 pts.) Suppose that w 1,h 1. Find numerical values for the optimal allocation bundle (c, L, N) i) (4 pts.) Draw a graph that depicts the optimal bundle in h).
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Answer tiventhat utility unctio o Buaget Constrant -) e LwN- (b) exog enaug Varia ble ejk endo jenouaableb irs ordev Con dition

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