Consider a two-period consumption saving model and let f1 and f2 denote the first and second period consumption, respectively. Assume that the interest rate at which the consumer may lend or borrow is 10%. Suppose that a consumer’s utility function is x (f1> f2) = f1 + 20√f2= The consumer first period income is L1 = $100 and the present value of her income stream is $330= (a) What is the optimal consumption stream (consumption bundle) of this consumer? (b) Is this consumer borrower or lender? How much does she borrow or lend? (c) What is the effect of a reduction of the interest rate to 5% on the consumer’s optimal first-period saving? (Make sure to take into account the effect of the decline in the interest rate on the present value of the consumer’s income stream.)
Consider a two-period consumption saving model and let f1 and f2 denote the first and second
period consumption, respectively. Assume that the interest rate at which the consumer may lend or borrow
is 10%. Suppose that a consumer’s utility function is x (f1> f2) = f1 + 20√f2= The consumer first period
income is L1 = $100 and the present value of her income stream is $330=
(a) What is the optimal consumption stream (consumption bundle) of this consumer?
(b) Is this consumer borrower or lender? How much does she borrow or lend?
(c) What is the effect of a reduction of the interest rate to 5% on the consumer’s optimal first-period
saving? (Make sure to take into account the effect of the decline in the interest rate on the present value of
the consumer’s income stream.)
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