. (20 points) Prior to the recent COVID-19 pandemic, Melman had the following utiltiy function to describe his labour-leisure trade-off:

U(C, N) = (N)(1/3)(C)(2/3)

Additionally, Melman slept for 6 hours a day and was paid a wage ofw= $100.

(Reminder:Y=Chere.)

(a)(4 points) Set up Melman's problem. What is his optimal consumption of leisure

Nand incomeY?

(b)(6 points) If his previous job is no longer available and the only option available has a wage ofw= $20, then how does this change Melman's optimal outcome? Provide a sketch of the income consumption curve for Melman (Reminder: Do not forget to label your axis and curves and consider a wage rate $20< w <$100). What does your result forNimply about Melman's Labour Supply Curve? Briefly explain your answer (one sentence is sufficient).

(c)(4 points) Instead of using the Canadian Emergency Response Benefit (CERB) program like Canada did, suppose the government implemented a program that providedconsumption to each person who lost income where >0 could not be bought or sold. Furthermore suppose this makes Melman's utility function:

U(C, N;) = (N)(1/3)(C+)(2/3)

What is Melman's new choice of of leisureNand incomeYwith the wage rate ofwand Melman continuing to sleep 6 hours a day? (Hint: both will be a function ofand you can useY=Cstill.)

(d)(2 points) What is the own-price (or point) elasticity of leisure whenw= 20 and= 9? (Reminder: wagewis the price of leisure.)

(e)(4 points) Based on your answer above, what can you say about Melman's Labour Supply Curve now? An explaination in words is sufficient. If you feel it is neces- sary to derive the Labour Supply Curve, then full marks will be awarded for that as well.