Consider a consumer who contemplates his optimal consumption plan for two period. Assume that the interest rate at which all consumers can borrow and lend is 10%. This consumer has income 60 in period 1 and income 39 in period 2.

(i) If the consumer would like to consume equal amounts in the two periods, how much does he need to save in period 1? How much will he end up consuming in both periods?

Suppose now that economy is populated by lots of copies of such consumers (whose income and optimal choices are as described above). The government decides to offer a deficit-financed transfer of 10 in period 1 to all consumers. Assume that the government can borrow and lend at the same rate (10%) as consumers, and that the deficit is repaid by lump-sum taxes in period 2.
(ii) How do optimal savings respond to this government policy?

(iii) What is the optimal consumption sequence for consumers faced with this policy?

Assume now that the government offers the mirror image of this policy, raising lump-sum taxes of 10 for all consumers in the first period, and giving transfers of 11 in the second.
(iv) How do optimal savings respond to this government policy?

(vi) What is the optimal consumption sequence for consumers faced with this policy?