27. Suppose a consumer’s utility function is
U
(
F
0,
F
1) =
F
00.5
F
10.5, where
F
0 represents food
consumed this year and
F
1 represents food consumed next year. For that utility function, the
marginal utility of food consumed this year is 0.5 × (
F
1/
F
0)0.5 and the marginal utility of food
consumed next year is 0.5 × (
F
0/
F
1)0.5. Suppose the consumer earns $100 this year and nothing in
the next, food costs $1 per unit in both years, and the interest rate is 10%. How much food does
she consume this year, and how much does consume tomorrow?
A. She consumes 45 units of food this year and 55 units of food next year.
28. Suppose a consumer’s utility function is
U
(
F
0,
F
1) =
F
00.6
F
10.4, where
F
0 represents food
consumed this year and
F
1 represents food consumed next year. For that utility function, the
marginal utility of food consumed this year is 0.6 × (
F
1/
F
0)0.4 and the marginal utility of food
consumed next year is 0.4 × (
F
0/
F
1)0.6. Which of the following expressions gives the consumer’s
marginal rate of substitution for food this year with food next year (
MRS
01)?
A.
MRS
01 =
F
1/
F
0