Lou's preferences over food (F) and other goods (C) are given by U(F, C) = F 0.5C 0.5. His income is $1024 per month to buy F and C.

a) Calculate his optimal basket when PF = 8 and PC = 8.

b) Calculate his income and price effects of a decrease in the price of food to $2.

Answer:

a) At the initial basket, Lou consumes?units of F.

b) To find the income effect and the price effect, first we need the decomposition basket. The decomposition basket would satisfy the new tangency condition, C/F =?and would give him as much utility as the initial basket, i.e. F 0.5 C0.5 =?. At the decomposition basket, he consumes?units of F. Now we need the final basket, which satisfies the same tangency condition as the decomposition basket and also the new budget constraint: 2F+8C = ?. After calculating the initial basket, decomposition basket, and the final basket, we find that in this example, the price effect is?units of F and the income effect is? units of F.