Graphical representation of indifference curves and optimal consumption bundle.

This exercise was first assigned by Nobel Prize Gary Becker to his students at the University of Chicago. Here goes:

"Sally has bought a summer lake cottage in Minnesota. She really likes spending the summer in her new cabin and only consumes hotdish and lutefisk (a peculiar type of Minnesotan fish). Lutefisk is sold in an unusual way in Minnesota: there is only one supplier, and the more lutefisk you buy from him, the higher the price you have to pay per unit. In fact, l units of lutefisk will cost Sally l2 dollars. Hotdish is sold in the usual way at a price of 2 dollars per unit. Sally's income is 20 $ per week and her utility function is U (l, h) = h + 2l, where h is her consumption of hotdish per week and l is her consumption of lutefisk per week.

1.Sketch Sally's opportunity sets and shade it in (measure hotdish along the horizontal axis).

2. Draw some of her indifference curves also show with a small arrow the direction of increasing utility. Label on the graph the optimal consumption bundle that she chooses.