Consider Hitoshi who lives for two periods. In period 1, he is young and in period 2 he is old. He enjoys consuming, ct, and experiences distutility from labour, nt, according to the following preference function: U(C1, C2, n1, n2) = 2c1.+ 2Bc2-5 - 0.5n; -0.5Bn? He earns income from supplying labour in period 1 of win and in period 2 of w2n2. Any saving he earns in period 1 can earn a return of (1 + r1) that is paid out to him at the beginning of period 2. He also knows when he is young that he will receive an inheritence of a2 in period 2. a) Write out Hitoshi's one and two-period budget constraints. Combine these to form an intertemporal budget constraint. b) What is Hitoshi's choice problem? What variables does he have control over? What variables does he take as given? c) Solve Hitoshi's two-period optimization problem by taking FOCs and deriving his intertemporal and intra-temporal tradeoff conditions. d) Does Hitoshi's inheritence affect his intra-temporal tradeoffs? What about his inter-temporal tradeoffs? Explain why or why not. e) Does the amount that Hitoshi expects to inherit in period 2 change how much Hitoshi would spend in Period 1? Why or why not? Explain and show your math