described by Assume the representative consumer lives in two periods, and his preferences can be U (c, c') = c/2 + B (c)/, where c is the current consumption, c'is next period consumption, and = 0.95. The consumer receives an income y = 100 in the current period and y' = 110 in the next period. The government wants to spend G = 30 in the current period and G' = 35 in the future period. a) Solve the consumer's problem by finding the optimal allocations c* and c'* as a function of interest rate r. b) Is the economy at equilibrium when the interest rate equals 10%? Explain. c) What are the equilibrium values of c and c'? d) What is the equilibrium interest rate? e) How will the equilibrium interest rate response to an increase in G?