3 Bequests and taxation in the intertemporal consumption model Consider a household that maximizes utility from consumption over two periods maxC1,C2u(C1)+u(C2) 2 subject to the intertemporal budget constraint C1+1+RC2=W Question 3.1 What is the economic reason for why we assume that the utility function is concave? Question 3.2 Derive the Euler equation for the household. The Euler equation relates the marginal utility of consumption in periods 1 and 2 under the optimal consumption choice. Make sure you provide the derivation so that it is clear how you did it (just the final answer is not enough). Question 3.3 Assume that the household can leave bequests in the amount of B0 at the end of period 2, maybe for the children or for charity. Modify the intertemporal budget constraint appropriately to allow for this possibility. Question 3.4 Assume that the household still maximizes utility given by equation (3.1) above. Will it leave a strictly positive amount of bequests? If yes, determine this amount. If no, propose a modification of the utility function in equation (3.1) that would make the household leave behind a positive amount of bequests. Question 3.5 Imagine that the government needs to spend G in period 1. This spending must be paid for by taxing the household. The government can either tax the household in period 1, or borrow the necessary amount through international financial market at interest rate RG and repay the loan (including interest) by taxing the household in period 2. Assume RG