In a two-period model, suppose that a consumer's utility function is: U(C₁, C₂) = log(c₁) + log(c₂) where C₁, C₂ are the consumption of a good (orange) in the two periods. Let the endowment real income in the two periods be 2, 1 respectively. The real interest rate is unknown and is to be determined in the equilibrium. Assume that all consumers are identical. ** Part a

In a two-period model, suppose that a consumer's utility function is: U(C₁, C₂) = log(c₁) + log(c₂) where C₁, C₂ are the consumption of a good (orange) in the two periods. Let the endowment real income in the two periods be 2, 1 respectively. The real interest rate is unknown and is to be determined in the equilibrium. Assume that all consumers are identical. ** Part a

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter17: Capital And Time

Section: Chapter Questions

Problem 17.2P

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8. Consider the OLG model with capital. Each individual is endowed with y units of the consumption good when young and with nothing when old. Let N be the number of individuals in each generation. Suppose there is one asset available in the economy capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. One period after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Assume that each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U (C₁, C₂) = (C₁) (c₂) } . We focus on stationary allocations. (a) Write down the budget constraints faced by an individual when young and old. Combine the budget constraints to find the lifetime budget constraint for an individual (b) Solve for the optimal allocation of (c₁, c₂) for all future generations. What is the optimal k* ? Now suppose an…
8. Consider the OLG model with capital. Each individual is endowed with y units of the consumption good when young and with nothing when old. Let N be the number of individuals in each generation. Suppose there is one asset available in the economy - capital. A unit of capital can be created from a unit of the consumption good in any period t and capital can be created in any amount. One period after it is created, a unit of capital produces X units of the consumption good and then disintegrates. Assume that each initial old can produce Xko units of the consumption good in the first period. Now suppose that an individual's preference is given by U (C₁, C2) = (C₁) 1 (C₂) ¹. We focus on stationary allocations. (a) Write down the budget constraints faced by an individual when young and old. Combine the budget constraints to find the lifetime budget constraint for an individual ) (b) Solve for the optimal allocation of (c, c) for all future generations. What is the optimal k* ? Now suppose…
Consider the intertemporal consumption problem of Mr Cronus between two periods, say this yearand next year. His utility function takes the form U (c1; c2) = pc1 +0:97pc2, where c1 and c2 arehis consumption this and next year respectively. It can be shown (and you do not have to) thatthis utility function satises diminishing marginal rate of substitution.His yearly income is stable at 100 unit (let say a unit is ten-thousand). He faces di¤erent interestrates between borrowing and saving. Specically, the saving interest rate is 0:02, whereas theborrowing interest rate is 0:04.(a) Describe the budget set facing Mr Cronus.(b) Is Mr Cronus a borrower? Explain your answer.(c) Is Mr Cronus a saver? Explain your answer.
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Consider the problem of an individual that has Y dollars to spend on consuming over wo periods. Let c1 denote the amount of consumption that the individual would like co purchase in period 1 and c2 denote the amount of consumption that the individual would like to consume in period 2. The individual begins period 1 with Y dollars and can purchase ci units of the consumption good at a price P and can save any unspent wealth. Use s1 to denote the amount of savings the individual chooses to hold at the end of period 1. Any wealth that is saved earns interest at rate r so that the amount of wealth the ndividual has at his/her disposal to purchase consumption goods in period 2 is (1+r)s1. This principal and interest on savings is used to finance period 2 consumption. Again, for simplicity, we can assume that it costs P2 dollars to buy a unit of the consumption good in period 2.
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Now,suppose N=3 with a market clearing interest rate. The first two agents are the same as earlier. The third agent has an endowment of 20 in the first period and consumes 15 in the second period. If the first two agents each consumed 21 units in the first period, how much did the third agent consume in the first period? Plz do fast
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