Consider the following overlapping generations economy with two assets, capital and money. The number of consumers in each generation is Nt = 1. Consumers are endowed with y1 = 1 goods when young, and nothing (y2 = 0) when old. Suppose kt units of capital produce f (kt ) = 2vkt units of consumption good at t + 1. Let Mt = z Mt -1, where z > 1. The seigniorage revenue is used to ?nance a lump-sum transfer of at goods to each young person in period t.
(a) Write the consumer budget constraints when young and when old, the consumer lifetime budget constraint, the government budget constraint, and the market clearing conditions.
(b) Solve for the capital stock k in the stationary equilibrium.
(c) Consider a decrease in the money growth rate from z to z ' = 1. Determine the e?ect of this change on the capital stock k, real GDP, and the welfare (utility) of the future generations.