3. Analytic Question on Durable ConsumptionIt is known that durable consumption is more sensitive to interest rates and expected income. In this question,we investigate if this is the case in the context of the model we have been studying. We investigate the followingdecision:U (c1, c2)1max{c1,c2} 2VCi + xo +subject to the following budget constraints:The time 1 budget constraint:a = Y1 - Ciand the time 2 budget constraint:C2 = Y2 + (1 +r) a.The novelty is that ro is now a variable to represents past purchases of goods 1. You can think of this as a car.In turn, we have that x1 = c1 so a1 is consumption derived utility in period 2 derived from past purchases. For thisquestion assume that B (1+ r) = 1.Answer the following questions.а.Substitute out a from both budget constraints, the one at time 1 and time 2, to write a singleintertemporal budget constraint.b.Show that the Euler equation (the equation that relates the marginal utility of consumptionto the interest rate and the discount factor 3), implies:C1 + xo = (B (1 +r))-²c2.Hint: form the Lagrangean of this problem, using your answer in (a). Then, obtain the first-order conditions andcombine them.с.Suppose that xo = 0. Then, argue that:C2 = (B (1 + r))² c1C1and substitute the condition into the intertemporal budget constraint to obtain the consumption shares:1Y2Y1 +C1 =1+ 32 (1 + r)1+rB2 (1+ r)1 + 32 (1 + r)Y2Yı +C21+r1+r

Intertemporal Utility function : U(c1 ,c2 ) = 0.5 (c1 + x0)0.5 + 0.5B (c2)0.5 Period 1 budget…

3. Analytic Question on Durable Consumption It is known that durable consumption is more sensitive to interest rates and expected income. In this question, ve investigate if this is the case in the context of the model we have been studying. We investigate the following lecision: 1 U (c1, c2) = max {c1,c2} 2 /C1 + o+ ubject to the following budget constraints: The time 1 budget constraint: a = Y1 - C nd the time 2 budget constraint: C2 = Y2 + (1 +r) a. The novelty is that ro is now a variable to represents past purchases of goods 1. You can think of this as a car. n turn, we have that a1 = c1 so a1 is consumption derived utility in period 2 derived from past purchases. For this juestion assume that B (1+r) = 1. Answer the following questions. а. Substitute out a from both budget constraints, the one at time 1 and time 2, to write a single

3. Analytic Question on Durable Consumption It is known that durable consumption is more sensitive to interest rates and expected income. In this question, ve investigate if this is the case in the context of the model we have been studying. We investigate the following lecision: 1 U (c1, c2) = max {c1,c2} 2 /C1 + o+ ubject to the following budget constraints: The time 1 budget constraint: a = Y1 - C nd the time 2 budget constraint: C2 = Y2 + (1 +r) a. The novelty is that ro is now a variable to represents past purchases of goods 1. You can think of this as a car. n turn, we have that a1 = c1 so a1 is consumption derived utility in period 2 derived from past purchases. For this juestion assume that B (1+r) = 1. Answer the following questions. а. Substitute out a from both budget constraints, the one at time 1 and time 2, to write a single

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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In class discussions about uncertainty we assumed that the utility levels in each state of nature depends on c, which we might interpret as some aggregate con- sumption and we expressed utility as U(c). Now, let's extend this to a case where the utility level depends on consumption of two goods (this was the type of utility we used mainly in this course). Ben is a farmer who grows wheat and barley. However, his harvest is uncertain. If weather is good, he gets 200 lbs of wheat and 200 lbs of barley. If weather is bad, he gets only 100 lbs of wheat and 100 lbs of barley. His utility in each state of nature is U(w, b) = w¹/4b³/4, where w and b represent his consumption of wheat and barley, respectively. Prices of wheat and barley are $1 in both state of nature. The probability of good weather is T. Question 3 Part a Express Ben's expected utility function. (Hint: find Ben's optimal consumption in each state of nature first) Question 3 Part b Let's assume = 0.5. Knowing that bad weather…