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(c₂,c₂) = C₁³ +(1+p)¹ C₂5, where is the subjective discount rate, and C₁,C₂ 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 /">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.

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(c₂,c₂) = C₁³ +(1+p)¹ C₂5, where is the subjective discount rate, and C₁,C₂ 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 /">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.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

Felix chooses between clothing, 9₁, and food, 92. His initial income is $4,000 a month, p₁ = 400, and p₂ = 40. At his initial bundle, he consumes q₁ = 2 and q₂ = 80. Later, his income rises to $4,800 and the price of clothing rises to p₁ = $600, but the price of food does not change (p2 = 40). As a result, he reduces his consumption of clothing to q₁ =1. Using a revealed preference reasoning (that is, knowing nothing about his indifference curves), can you determine how he ranks the two bundles? O A. Felix may prefer his initial bundle or he may be indifferent between them. B. Felix is indifferent between his initial bundle and his new bundle. O C. Felix prefers his new bundle. D. Felix prefers his initial bundle. O E. Insufficient information exists to determine which bundle Felix prefers.
Emma has a utility functionU(x1, x2, x3) = logx1+ 0.8 logx2+ 0.72 logx3over her incomes x1, x2, x3 in the next three years. This is an example of(A) expected value;(B) quasi-hyperbolic utility function;(C) standard discounted utility;(D) none of the above. Emma’s preferences can exhibit which of the following behavioral patterns?(A) preference for flexibility;(B) context effects;(C) time inconsistency;(D) intransitivity.
Please solve the last 3 parts
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?
Economics u (x₁, x₂) = x²x² If the price of good 1 is $6/unit, the price of good 2 is $8/unit, and income = $118... What is this person's optimal consumption level for good 1?
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…
The utility derived by a consumer from the consumption of two commodities is given by the function U (A, B) = 0.5In (A) + 0.5 In (B) where A are the number of units of the first commodity consumed and B are the number of units of the second commodity consumed each month. A unit of the first commodity costs $8 and a unit of the second commodity costs $ 4 using the Lagrange multiplier method determine the optimal quantity of each of the commodities consumed each month given that consumer has $32 to spend on both commodities each month
I have uploaded the question and my answer can you check if it's correct?
Suppose an individual makes consumption and savings decisions in two time periods (1 and 2). Its utility function is given by: U = In addition, the prices and income of said individual and the interest rate he faces are known: P1 = 1, P2=3; M1 = 100, M2 = 200 r=0.23 Determine: a) The budget constraint and plot b) Optimal demand functions c) The savings supply function d) In equilibrium, will the individual be a lender or a borrower?
Suppose a utility function is given by u(x1, x2) = x12 + x2. Graph the indif- ference curve for utility level 100 and 400. What is wrong about the shape of the indifference curves? Does the utility function describe reasonable preferences? Now suppose prices are p1 = 2, p2 = 1 and I = 10. Determine the optimal consumption graphically.
Merge the two budget constraints into a single lifetime budget constraint by eliminating savings from the system of two constraints.
Thank you for your solutions of questions 1-3. Please answer questions 4-5.