Question

In: Economics

Consider a two-period model, inhabited by two individuals, Anna and Bob (or as they like to...

Consider a two-period model, inhabited by two individuals, Anna and Bob (or as they like to be called, A, and B). A has the following preferences

uA(c0,A cA1 ) = ln(cA0 ) + 0.9 ln(cA1 ), while B has the following preferences

u B ( c 0 , B c B1 ) = l n ( c B0 ) + 0 . 8 l n ( c B1 ) .

Consumer A receives an income Y0A = 100 in period 0 and Y1A = 150 in period 1. On the other side, Consumer B receives an income Y0B = 125 in period 0 and Y1B = 100 in period 1. Assume the interest rate is r. The government wants to spend G0 = 50 in period 0 and G1 = 75 in period 1. These spendings are financed through lump-sum taxes. It is assumed that the government collects the necessary tax to finance its spending in each period and the tax burden is equally supported by the consumers in each period.

1. Compute the optimal consumption (c0, c1) for each individual as a function of the interest rate r.

2. Find the equilibrium interest rate that clears the credit market.

Solutions

Expert Solution

Rahul Sunny answered 7 months ago
Next > < Previous

Related Solutions

Consider a two-period model, inhabited by two individuals, Anna and Bob (or as they like to...
Consider a two-period model, inhabited by two individuals, Anna and Bob (or as they like to be called, A, and B). A has the following preferences uA(cA0, cA 1 ) = ln(cA 0 )+0.9 ln(cA 1 ), while B has the following preferences uB(cB0, cB 1 ) = ln(cB0)+0.8 ln(cB1 ). Consumer A receives an income YA0 = 100 in period 0 and YA1 = 150 in period 1. On the other side, Consumer B receives an income YB0 =...
Consider an economy with two goods, x and y, and two agents, Anna and Bert. Anna...
Consider an economy with two goods, x and y, and two agents, Anna and Bert. Anna and Bert wish to trade with one another in order to maximize their individual utilities. We will consider how their trading decisions depend on the initial endowments of X and Y and on their utility functions. Suppose Anna is endowed with one unit of X and half a unit of Y and Bert is endowed with one unit of X and one and a...
Assume the existence of a two-period Diamond Model. Individuals may live for up to two periods...
Assume the existence of a two-period Diamond Model. Individuals may live for up to two periods t and t + 1. All individuals both live and work in period t. Some proportion γ of individuals die at the end of the first period, and do not consume in the second period. The remaining proportion (1 − γ) will will live and consume in period 2. Expected lifetime utility is given by: 2 U(C1t , C2t+1) = ln(C1t) + (1 −...
Consider a two-period model in which the consumer receives income of y in the current period...
Consider a two-period model in which the consumer receives income of y in the current period and y' in the future period. Rather than imposing lump-sum taxes, the government imposes a proportional tax on consumption. In the current period the tax rate is σ and in the future period the tax rate is σ'. As a result, the government collects σc in goods in the current period and σ'c' in goods in the future period. Since G and G' are...
Consider a two-period consumption model where an individual has income It > 0 in period t...
Consider a two-period consumption model where an individual has income It > 0 in period t and the (net) interest rate is r > 0. However, suppose the price levels are not assumed to be 1. Instead, let p2 ≥ p1 > 0. (a) Derive the lifetime budget constraint. (b) What is the slope of the lifetime budget line? Letting 1 + π = p2/p1 bethe gross inflation rate, given an interpretation of the magnitude of them budget line. (c)...
Consider the following two-period Fisher model of consumption. Jamil earns $600 in the first period and...
Consider the following two-period Fisher model of consumption. Jamil earns $600 in the first period and $0 in the second period. The interest rate is 10 percent. His lifetime utility function is log(?1 ) + 0.5log(?2). a) Find the optimal values of ?1 and ?2. Answer: ?? = ???, ?? = ??? b) Suppose that the lifetime utility function changes to log(?1 ) + log(?2). Calculate the new optimal values of ?1 and ?2. How is the optimal value of...
Bob learns that his income in the second period of this two period existence will now...
Bob learns that his income in the second period of this two period existence will now be $100 greater than he previously expected. Assuming he perfectly smooths his consumption (so that consumption will be the same in both his periods), he isn't borrowing constrained, and the interest rate is 16%: a) What will happen to his consumption in the future period? b) what will happen to his savings in the current period?
Consider a model in which individuals live for two periods and have utility functions of the...
Consider a model in which individuals live for two periods and have utility functions of the form ? = ??(?1) + .5??(?2). They earn income of $10,000 in the first period and save S to finance consumption in the second period. The interest rate, r, is 20. a. Set up the individual’s lifetime utility maximization problem. Solve for the optimal C1, C2, and S. (Hint: ????1,?2 = −.5?2/?1 and the budget line is given by C2= (10,000-C1)(1+r) hence the slope...
Consider the following shocks in the two-period model with money. Suppose there is an impatience shock...
Consider the following shocks in the two-period model with money. Suppose there is an impatience shock that causes the discount factor ? to decrease. i. What are the e?ects on the competitive equilibrium? Explain in words and with diagrams. ii. Explain the extent to which the model driven by an impatience shock can or cannot replicate the key business cycle facts (see Chapter 3 for a review!). Be sure to reference which speci?c facts the model can or cannot explain
Consider a two-period model of a closed economy with government. Assume that the representative agent is...
Consider a two-period model of a closed economy with government. Assume that the representative agent is endowed with ?1 and ?2 as initial endowments in period 1 and period 2 respectively, and has the utility function ? = ln ?1 + ? ln ?2, where ?1 and ?2 denote consumption and ? is the discount rate. Suppose that the government spends ?1 and ?2 in period 1 and period 2 and finances its expenditure through lump-sum taxes ?1and ?2 in...
ADVERTISEMENT
Subjects
ADVERTISEMENT
Latest Questions
ADVERTISEMENT