1) Your utility function for consumption and leisure is u(C, L) = CL, The cost of consumption is $10/unit. You can make $25working for your Grandfather. You have personal and family responsibilities that leave you 60 hours/week to divide between leisure and work. What is your optimal choice of Consumption, Leisure and Work?

2) You are offered an opportunity to work for your Aunt (cleaning her barn) instead of for your Grandfather. But cleaning the barn for your Aunt is unpleasant; if you work W hours for your Aunt, spend L hours in Leisure and consume C units, your utility will be U(C,L,W) = CL10W. Because of that, your Aunt is willing to pay you more per hour than your Grandfather does.

(a)What wage w (per hour) would your Aunt have to offer in order that you would be willing to work for her instead of your Grandfather?

(b)If your Aunt offered a wage w > w and you worked for her, what would be your optimal choice of Consumption, Leisure and Work?

3.Your Aunt and your Grandfather get together and decide that it is OK if you work part-time for your Grandfather and part time for your Aunt. Your Grandfather will still pay you $25 for each hour you work for him and your Aunt will pay you $30 for each hour you work for her. If you choose to work WG hours for your Grandfather and WA hours for your Aunt you will be left with L = 60 (WG + WA) hours of Leisure and your utility will be CL 10WA. What should you do?

(a) How many hours per week should you work for your Grandfather? (b) How many hours per week should you work for your Aunt?

(c) How many hours per week of Leisure will you enjoy? (d) How much consumption will you buy?

(e) Will your utility be more/less/same as in Problem 1?