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

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter3: Preferences And Utility

Section: Chapter Questions

Problem 3.13P

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On a given evening, J. P. enjoys the consumption of cigars (c) and brandy (b) according tothe functionU(c, b) = 20c− c²+ 18b − 3b²a. How many cigars and glasses of brandy does he consume during an evening? (Cost isno object to J. P.)b. Lately, however, J. P. has been advised by his doctors that he should limit the sum ofglasses of brandy and cigars consumed to 5. How many glasses of brandy and cigarswill he consume under these circumstances?
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