Consider an economy in which a representative household lives for two periods (year t and year t l 1). The representative household derives utility from consumption and discount the future at rate ,8. The household's life time utility is given by: U =1nc; + lncHl The household receives income from work in both period y; and 3;!\" respec- tively and has no nancial wealth. The intertemporal budget constraint for an household can be written in present discounted values as Ct+1 yt+1 c + = + ' 1+ R m 1+ R where you can interpret 39;\" as expected income. Write down the maximization problem in detail? Derive the optimal conditions to obtain the Euler Equation? Interpret the Euler Equation? 1 . . . If we let gc = c': c' be the growth rate of consumption, under what conditions i: consumption is the growth rate of consumption constant or increases/decreases over time? Solve for consumption c; and ("+1 as a function of income, the discount factor, and the interest rate (37;, \"+1, [2, R). How ctand c+1are affected by individual changes in any of by, yHl, 3, R)? (e.g., is crincreasing, constant or decreasing in all else constant?)