A decision maker allocates an endowment of W > 0 dollars across two periodst = 1, 2. He discounts the future by β ∈ (0, 1) while facing a gross interest rateof R > 1. His utility is the same as studied in class. Solve for the intertemporalchoice problem. Show that the optimal consumption is decreasing over time ifβR < 1, constant over time if βR = 1, and increasing over time if βR > 1.

A decision maker allocates an endowment of W > 0 dollars across two periodst = 1, 2. He discounts the future by β ∈ (0, 1) while facing a gross interest rateof R > 1. His utility is the same as studied in class. Solve for the intertemporalchoice problem. Show that the optimal consumption is decreasing over time ifβR < 1, constant over time if βR = 1, and increasing over time if βR > 1.

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

Complete utility maxamization problem using lagrangian method, ignore other question parts.
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),…
Suppose that consumer uses 2 units of X and 5 units of Y always in fixed proportion. Suppose also that Px = 1. Py respectively? = 2 and I = 120. What would be the optimal consumption of X and Y at the equilibrium, 20, 50 40, 40 24. 60 50. 35
The consumer choice is not restricted to the choice of consumptiongoods. In fact, it can apply to all our decisions that involve trade-offs. Suppose Mary has awage per hour of 10 euros. With her earned income she consumes. That isC=wH per day.She also decides how many hours to work of take leisure time each day.H=24-N, whereHis work and N is leisure. Her utility is given by （picture） Solve for the optimal decision of labor/leisure. Plot the budget constraint and the indif-ferent curve. What is the labor supply function?
Gina is at a toy store and is buying toy T-Rex's (x), which cost på, and toy yaks (y), which cost py. Her income is I. She likes 3 T-Rex's as much as she likes 4 yaks. These toys are perfect substitutes for her.
can you please provide a explanation with any mathematical working out
Consider the two period consumption savings problem faced by an individual whose utility is defined on period consumption. This utility function u(c) has the properties that it is strictly increasing and concave, u'(c) > 0, u"(c) < 0 (where u'(c) denotes the first derivative while u"(c) represents the second derivative) and satisfies the Inada condition lim.-→0 u'(c) approaches zero). The individual's lifetime utility is give by u(cı) + Bu(c2). In the first period of life, the individual has y1 units of income that can be either consumed or saved. In order to save, the individual must purchase bonds at a price of q units of the consumption good per bond. Each of these bonds returns a single unit of the consumption good in period 2. Total savings through bond purchases is s1 so that total expenditures on purchasing bonds is qs1. Let c1 denote the amount of consumption in period 1 chosen by the individual. In the second period of life, consumption in the amount c2 is financed out of the…
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.
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
An agent lives for 2 periods and gains utility only by consuming. Future consumption is discounted at rate θ where 0<θ<1. Agent consumes c, saves s at interest rate r in first period of life from income y. In second period agent consumes from savings plus interest earned but must pay a flat fixed tax. Find the Euler equation for this agent and what it shows.
image attached