(a)Construct a model of an individual who has an interior endowment of intertemporal receipts and an associated intertemporal consumption plan. Imagine that there is a fall in the interest rate.
(1) Under what conditions will the person's planned consumption rise?
(2) Under what conditions will planned savings rise?
(3) Is it possible for both to rise? Explain.
(b) Explain how the following imply that a change in the rate of interest may have occurred and note the direction of change.
(1) A rise in the price of raisins relative to the price of grapes.
(2) An increase in the "spot" price of soybeans on the Chicago futures market.
(3) Young people are better off relative to old people.
(1) It implies the interest rate has risen. Raisins are equivalent to an investment of grapes. The present value of raisins (grapes) have fallen in price relative to future raisins, implying a higher discount rate.
Contrast to Christmas tree story: This is an identical product at a different time. If trees are shorter, they are being harvested earlier which implies that their future value is decreased relative to their current price. Since current goods are worth relatively more, they will be harvested earlier. This implies the interest rate has gone up.
(2)The formula: -- A spot price reflects the present value of the contract. If the Spot price increases, the interest rate has decreased.
(3)Young people tend to be borrowers, as their wealth rests in the future. The value of future goods increases when the interest rate decreases. Old people tend to be lenders as their wealth is all in the present. As lenders, they benefit from a rise in interest rates. The discounted present value of the future wealth of young people is reduced by higher interest rates.
In this second graph the endowments are shown with respect to each group. Old have all their endowment now (in the current period), and Young have their whole endowment in the future (in the next period). When the interest rate decreases the old who are living off of savings are relatively poorer. They cannot finance as much current spending with the principle plus the interest. The young, alternatively find it cheaper to borrow money to finance consumption. As a result of this increased availability of funds the young are now relatively wealthier.
