Exercise 4

Part 1: Sally has just 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 (the unit price she pays is equal to the number of units she buys). 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.

a) Sketch Sally's budget set and shade it in (measure lutefisk along the horizontal axis).

b) Sketch some of her indifference curves and show with a small arrow the direction of increasing utility.

c) Using the Lagrangian method, find Sally's optimal amount of hotdish and lutefisk.

Part 2: At the lake, Sally has $10 to spend on Diet Coke or Diet Pepsi that she considers perfect substitutes. Suppose the price of a can of Diet Pepsi is $1.

d) Find Sally's optimal consumption of Diet Coke as a function of the unit price of Diet Coke (PC).

e) In a graph where you measure the number of cans of Diet Coke along the horizontal axis and the unit price along the vertical axis, draw Sally's demand curve for Diet Coke.