Levinn’s utility function is expressed as the following: U= C1 C2 0.3 where C1 is his first period consumption and C2 is his second period consumption. His income in the first period is $2500 and interest rate is at 10%. If at equilibrium, Levinn is neither a borrower nor a lender, then what is his expected income in the second period?
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APPLIED ECONOMICS
Topic: Intertemporal Choice
Levinn’s utility function is expressed as the following: U= C1 C2 0.3 where C1 is his first period
consumption and C2 is his second period consumption. His income in the first period is
$2500 and interest rate is at 10%. If at equilibrium, Levinn is neither a borrower nor a lender,
then what is his expected income in the second period? Do not copy from others
Step by step
Solved in 3 steps
- In the two-period Fisher model of consumption, suppose that the first period income is $5,000 and the second period income is $5,000 for both Matt and Paola. The interest rate is 10 percent. Matt’s lifetime utility function is C1 + C2 while Paola’s lifetime utility function is C1 + 0.8C2. If there is a borrowing constraint, whose consumption is affected by that?Q1. Consider the following two-period model of consumption and saving: Utility = C1^0.5 + B*C2^0.5 C1 + C2/(1+r) = Y1 + Y2/(1+r) where Y1 = 4, Y2 = 1, r = 0.17 and B = 0.5. Find a numerical solution for period 1 consumption, C1. (State your answer to 2 decimal places.)Consider an economy where individuals live for two periods only. Their utility function over consumption in periods 1 and 2 is given by U = 2 log(C1) + 2 log(C2), where C1 and C2 are period 1 and period 2 consumption levels respectively. They have labor income of $100 in period 1 and labor income of $50 in period 2. They can save as much of their income in period 1 as they like in bank accounts, earning interest rate of 5 percent per period. They have no bequest motive, so they spend all their income before the end of period 2. a. What is each individual’s lifetime budget constraint? If they choose consumption in each period so as to maximize their lifetime utility subject to their lifetime budget constraint, what is the optimal consumption in each period? How much do the consumers save in the first period? b. Suppose that the government introduces a social security system that will take $10 from each individual in period 1, put it in a bank account, and transfer it back to…
- Assume an intertemporal budget constraint that shows how consumption can be traded off between two periods, t and t+1. Assume the consumer can save and borrow at the same interest rate of 10%. Assume the consumer collects income of $100 in each period. To gain an extra $10 dollars in period t+1, what must the consumer give up in period t?What is meant by “excess sensitivity” of consumption? Is this view of consumption consistent with the permanent-income hypothesis? Explain. How does the stock market affect consumption according to the permanent-income hypothesis? Is this prediction in line with the empirical evidence? Explain.Discuss the lifecycle income hypothesis theory of consumption and explain its applicability in the Kenyan context.
- Assume a consumer has current-period income y = 200, future-period income y′ = 150, current and future taxes t = 40 and t′ = 50, respectively, and faces a market real interest rate of r = 0.05, or 5% per period. The consumer would like to consume according to the following utility function: U (c, c′ ) = ln(c) + ln(c′ ). Show mathematically the lifetime budget constraint for this consumer. Find the optimal consumption in the current and future periods and optimal saving. Suppose that instead of r = 0.05 the interest rate is r = 0.1. Repeat parts (a) and (b). Does the substitution effect or the income effect dominate?Consider an individual who lives for two periods and has utility of lifetime consumption U = log(C1) + 1/1+δ log(C2), where C1 and C2 are the consumption levels in the first and second period respectively, and δ, 0 1 > 0 in the first period and no income in the second period, so Y2 = 0. He can transfer some income to the second period at a before-tax rate of return of r, so saving $S in the first period gives $[1 + r]S in the second period. The government levies a capital tax at rate τ on capital income received in the second period. The tax proceeds are paid as a lump-sum transfer to the following generation. The present generation does not care about the next one. a. What is the lifetime consumption profile of this individual? What is his lifetime indirect utility function expressed as a function of Y1 and b. Evaluate the change in initial income Y1 that is required to compensate the individual for the welfare loss due to the capital income tax τ. c. What is…According to the basic discounting principle, individuals value current consumption (i.e. consumption now) more than future consumption (i.e. consumption tomorrow). A) True B) False
- Section 1. Multiple Choice WITH Explanation. Choose the one alternative that best completes the statement or answers the question and EXPLAIN your reasoning. Do not forget to include equations, graphs, or any other material you believe is needed to understand your choice. To answer this problem assume a two-period economy with the following logarithmic utility function: U(C1,C2)=[ln(C1)+ln(C2)] where C1 and C2 are the consumption in the first and second periods, respectively. Households are endowed with Q1 and Q2 units of consumption goods in periods 1 and 2 and can borrow or lend at the world interest rate, r1=r*. Every household starts period 1 with B∗0≠ 0. Households can purchase bonds, B∗1, which pay the interest rate r1. The terms of trade in periods 1 and 2 are TT1 and TT2 , respectively. Then in this economy, the country adjust to____________________changes in the terms of trade by mostly changing____________________and the country adjusts to____________________changes in…In the intertemporal choice model (C0 and C1 ) an individual is endowed with only future goods and no current goods. A drop in the real interest rate would cause the budget line to ______and move______. a. steepen, downward b. steepen, upward c. flatten, downward d. flatten, upward e. keep a constant slope, upward Note : I know the correct answer is D) but PLEASE DRAW A PICTURE TO HELP EXPLAIN THE ANSWER TO THIS QUESTION!!!!In the discussion of the life-cycle hypothesis, income is assumed to be constant during the period before retirement. For most people, however, income grows over their lifetimes. How does this growth in income influence the lifetime pattern of consumption and wealth accumulation shown in Figure 17-12 under the following conditions? Consumers can borrow, so their wealth can be negative. Consumers face borrowing constraints that prevent their wealth from falling below zero. Do you consider case (a) or case (b) to be more realistic? Why?