1 Consumption/Leisure Problem Consider a household only lives for one period. The household likes consumption and leisure. It's problem is to: max Ct,Lt U(Ct , θtLt) s.t. Lt = 1 − Nt Ct = wtNt 

Where 1 is household total time endowment. Nt is hours worked, and 1 − Nt is leisure. In this problem, the household receives no dividend from the firm.

 (a) In this utility function, what is the economic intuition of θt? 

(b) State the optimality condition characterizing the household problem. 

(c) Discuss the economic intuition of the optimality condition derived in part (b). 1 

(d) Suppose there is an increase in wage (wt), how does the optimal consumption (C ∗ t ) change? What about the optimal hours worked (N∗ t ) and leisure (L ∗ t )? Which two effects are at play? 

(e) Graphically represent your argument in part (d). 

(f) Suppose the household wins a sizeable lottery at the beginning of the period t. Graphically depict how C ∗ t , N∗ t , L ∗ t will change. (Here, wt holds fixed during t.)