Question . Time is discrete and denoted t = 1, 2, 3...oo. The economy is populated by a sequence of two-period-lived overlapping generations. As usual, Na denotes the number of people born in time t and population grows at rate 72., N, = nNt_1. The population of initial old is given by: No. Individuals only care about their consumption when old: u(c1,g,02,+1) 2 cu\". Given this utility function, we know that agents will save all of their income. By assuming this type of utility, we are abstracting from the consumption-savings decision problem, however, we will focus on the portfolio-choice problem. The young are endowed with :9 units of output. The young also possess an investment technology, where kg units of invested at date if yields asf(kt) units at date t+ 1. f' > 0, f\" 1 and the yield on reserves zero Rm = 1. For this return structure, the demand for reserves would fall to zero in our model. To generate a demand for reserves when they are dominated in rate of return, we assume that investors structure their wealth portfolios in a manner that respects a \"reserve requiremen \Utkt S Utmt (2) a E (0, 1) is a parameter that may be interpreted as either a legislated minimum reserve requirement (investors are required to hold a minimum amount of cash against their private sector investments). . Combine the young and old constraints into a single constraint [3 points] [HINTz solve the young BC for 1):] . Using the constraint above and the reserve requirement constraint Gib, write down the Lagrangian and then take rstorder conditions with respect to Is: and mi [3 points] Page 2 . When is the Reserve requirements @ constraint binding? [3 points] Combining both FOCs, we may nd the Fisher equation belowE which equates the real interest rate (marginal product of capital) to the inationadjusted rate of return on government debt. :1: mat) = ((1 + 0)Rb aRm) \"\"1 (3) \"t We may assume a stationary equilibrium from now on: . Find the ination rate pt+1/pt (or v: /vt+1). [3 points] In equilibrium, the old must pay taxes 1",: consistent with satisfying the government budget constraint Gib