Consider a two-period consumption saving model and let ci and c2 denote the first and secondperiod consumption, respectively. Assume that the interest rate at which the consumer may lend or borrowis 10%. Suppose that a consumer's utility function is u (C1, c2) = c1 + 20 c2. The consumer first periodincome is I1 = $100 and the present value of her income stream is $330.(a) What is the optimal consumption stream (consumption bundle) of this consumer?(b) Is this consumer borrower or lender? How much does she borrow or lend?(c) What is the effect of a reduction of the interest rate to 5% on the consumer's optimal first-periodsaving? (Make sure to take into account the effect of the decline in the interest rate on the present value ofthe consumer's income stream.)

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Answered: Consider a two-period consumption…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Consider the household model that you have seen in class but now assume that the goal of the household is to consume twice as much in period 2 as in period 1. She earns $100 in the first period and $150 in the second period. The interest rate is 5%. What is her optimal saving in the first period? Note: Type in your answer approximated to two decimal points, i.e., your answer must be of the form "999.99". I will not be able to fix correct answers that were entered incorrectly, such as "999.999" or "999,99" or "999". In case the last digit in the correct answer is zero, e.g., "999.90" or "999.00", Blackboard will automatically delete it and you should not do anything about it.
Problem 4 - Costless Magical MacGuffin Consider a consumer that lives only for two periods. He works in period 1 (and gets income ₁) and moves up the corporate ladder in period 2 (and gets income ₁ 0 in the first period, and is expected to trade at P₂ in the second period. 3. Write down the new budget constraint. 4. Under what conditions on P₂ would a consumer borrow and then sell a MacGuffin? Would they be better off with this option?
Consider an economy with two periods (interpreted as “when young” and “when old” periods)and two consumers, Gillian Davis and Joana Wolinsky. Gillian is a star ballet dancer with a lifetime income given by ωG= (400,0). Joana is an Econ Ph.D. student with incomeωJ= (0,400). Gillian and Joana have identical utility functions given by Ui(x1,x2) = 6 lnx1+ 3 lnx2 for i=G, J a) Plot an Edgeworth box and mark the initial endowment point. b) Write the general definition of Pareto efficient allocation (one sentence) and give the equivalent condition in terms of MRS (give formula). Check if this condition is satisfied for initial endowments. c) Derive the contract curve (write down the appropriate conditions and solve for the curve) and depict it in the Edgeworth box. d) Suppose Gillian and Joana can “trade” consumption in both periods at pricesp1,p2. Find the competitive equilibrium (6 numbers) and depict the equilibrium allocation in the Edgeworth box. e) Using the MRS condition from part b),…
How does savings change with changes in y2? Provide some intuition behind this result.
Q3. Consider a utility function with one consumption good q1 and one type of leisure q2 c) Show mathematically and diagrammatically the decomposition of totaleffect.
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Consider the model where an individual has wealth k which they can either save or consume. If they save it, they receive a fixed and exogenous return r. The instantaneous utility function is given by: u(c, k) = c + a(k) where c is consumption, k is wealth, and a(k) is a function that defines the utility that an individual gets from holding wealth. The growth in wealth is given as the returns on wealth rk, plus income from working z(t), minus consumption c(t). a. Write out the differential equation for wealth. b. For an infinite time model, set up the optimal control problem with discounting at a rate 8. c. Write the current-valued Hamiltonian of this problem. d. Derive the steady-state level of consumption.
Suppose you have a monthly income of $1000, $850 in monthly expenses, and you can put money in a savings account that yields a monthly interest rate of 4%. Create a budget constraint showing the trade-off between present consumption (horizontal axis) and future consumption (vertical axis). How much will you have in the future if you choose to consume $850 now? Show this point on your budget constraint.
2. Suppose Jill derives utility from not only consuming goods, but also from enjoying leisure time. Let her utility function be defined as follows: U=C.25.R.75 where C is a consumption good that can be bought at a price of $1 and R is hours of leisure (relaxation) consumed per day. There are 24 hours in a day and leisure is defined as time spent not working. Jill has a job that pays $w per hour, a trust fund that pays her $M per day, and she can work any number of hours per day, L, she desires. C, consumption good; R, Leisure (relaxation); L, labor M, non-wage income; w, wage rate. a. Derive her labor supply function? b. Assume M = $100, at what wage is her quantity supplied of hours = 0?
Consider a consumer who can borrow or lend freely at an interest rate of 100% per period of time (think of the period as being, say, 30 years, a bit like with a mortgage). So r = 1.0, or 100%. The consumer's two-period utility function is: U = In(ct) + (1/2)In(Ct+1) The consumer earn Y=100 each period, so Y₁=100 and Yt+1 also equals 100. If this consumer is behaving optimally, trying to maximize her lifetime utility subject to the IBC, what's her consumption in period t?
Consider a model in which individuals live for two periods and have utility functions of the form U = In(C1) + In(C2). They earn income of $100 in the first period and save S to finance consumption in the second period. The interest rate, r, is 10%. 1. Set up the individual's lifetime utility maximization problem. Solve for the optimal C1, C2, and S. (Hint: Rewrite C2 in terms of income, C1, and r.) Draw a graph showing the opportunity set. (5 marks) 2. The government imposes a 20% tax on labor income. Solve for the new optimal levels of C1, C2, and S. Explain any differences between the new level of savings and the level in part (a), paying attention to any income and substitution effects. 3. Instead of the labor income tax, the government imposes a 20% tax on interest income. Solve for the new optimal levels of C1, C2, and S. (Hint: What is the new after tax interest rate?) Explain any differences between the new level of savings and the level in a, paying attention to any income…
Fred is planning his consumption over two time periods. Fred's preferences for consumption in period and two can be represented by the following utility function: U(c,,c,) = C +(1+p) C" , where pis the subjective discount rate, and c;,c, is consumption in the first and second period. Fred's income in the first period is y, and grows by g % from the first period to the second period. Fred has access to perfect financial markets. The rate of interest is r>0. (a) Derive Fred's demand functions for consumption in the two periods as functions of p,r , y and g. (b) Derive Fred's demand for borrowing/saving as a function of p,r, y and g. (c) Give a condition involving the relationship between r and g for when Fred will borrow and when he will save.

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