QUESTION 4.4 and 4.5 PLEASE Consider a household that maximizes utility from con
ID: 1115832 • Letter: Q
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QUESTION 4.4 and 4.5 PLEASE
Consider a household that maximizes utility from consumption over two periods max u (G) + «G) subject to the intertemporal budget constraint C2 C1+ Question 4.1 What is the economic reason for why we assume that the utility function is concave? Question 4.2 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 4.3 Assume that the household can leave bequests in the amount of B 2 0 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 4.4 Assume that the household still maximizes utility given by equation (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 (1) that would make the household leave behind a positive amount of bequests 4 Question 4.5 Imagine that the government needs to spend G in period 1. This spending must be paid for by taxing the houschold. The government can either tax the houschold in period 1, or borrow the necessary amount through international financial market at interest rate Rc and repay the loan (including interest) by taxing the household in period 2 Assume RG R. Is it better for the household if the government taxes in period 1, or period 2? Show it mathematically Does the Ricardian equivalence hold? Explain why or why notExplanation / Answer
Answer 4.1 - A utility is twice differentiable function of wealth such that U'(w)>0 and U"(w)<0 where w>0. U'(w)>0 implies non satiation property which indicates utility increases as wealth increases. On the other hand U"(w)<0 implies risk aversion property that is the utility function is concave, that the marginal utility of wealth decreases as wealth increases. If the utility function is convex then the consumer will be risk lover.
Answer 4.2 - The given utilty function of the consumer U(c1,c2)=u(c1)+u(c2) The budget constraint is c1+c2/(1+R)=W. Now we form lagrangian for maximisation, L=u(c1)+u(c2)+(W-c1-c2/(1+R)). Now F.O.C. conditions are dL/dc1=u'(c1) - = 0, dL/dc2=u'(c2) - /(1+R) and dL/d = W - c1-c2/(1+R). Now by combining them we get u'(c1)/u'(c2)=(1+R). This optimality condition is refer to as the Euler equation. It is an dynamic optimality condition we take optimum decision of consumption based on both current and future. It is MRS equals price ratio. Based on interst rate, R and we can get optimum consumption bundel.
Answer 4.3 - When we include B>0, bequest in period 2 we get the budget constraint as c1+c2/(1+R)=y1+(y2-B)/(1+R). where yi is the income in ith period.
Answer 4.4 - In first condition we do not consider B, bequest value. Since optimum consumption in period 2 is higher than if we consider bequest value. Due to adding B term it will shift the budget line inwards as result at optimum point consumers will have to reduce their current and future consumption. But if we make consumptions without considering this then no amount will be left in period 2.
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