Consider a household with the following utility function representing their preferences over consumption: with U=u(C)+Bu(C₁+1) u(C)-exp(-aC), 8€ (0,1), a>0 where Ct and Ct+1 represent consumption in the current and future periods, respectively. The household faces a two-period decision problem. They receive endowments of Yt and Yt+1 in the current and future periods, respectively. The real interest rate is denoted by rt. Notice: The utility function u(C) takes on negative values for all positive consumption levels. However, in economic models, the absolute value of utility is less important than how utility changes with consumption. A higher level of utility represents a more preferred outcome for the household. Solving for Current Consumption Demand Function Solve for the household's demand function for current consumption (Ct). Express Ct as a function of Yt, Yt+1, rt, and the parameters ẞ and a. Discuss what happens to Ct when Yt and Yt+1, increase and decrease.

Consider a household with the following utility function representing their preferences over consumption: with U=u(C)+Bu(C₁+1) u(C)-exp(-aC), 8€ (0,1), a>0 where Ct and Ct+1 represent consumption in the current and future periods, respectively. The household faces a two-period decision problem. They receive endowments of Yt and Yt+1 in the current and future periods, respectively. The real interest rate is denoted by rt. Notice: The utility function u(C) takes on negative values for all positive consumption levels. However, in economic models, the absolute value of utility is less important than how utility changes with consumption. A higher level of utility represents a more preferred outcome for the household. Solving for Current Consumption Demand Function Solve for the household's demand function for current consumption (Ct). Express Ct as a function of Yt, Yt+1, rt, and the parameters ẞ and a. Discuss what happens to Ct when Yt and Yt+1, increase and decrease.

Microeconomic Theory

12th Edition

ISBN:9781337517942

Author:NICHOLSON

Publisher:NICHOLSON

Chapter7: Uncertainty

Section: Chapter Questions

Problem 7.8P

See similar textbooks

Similar questions

main features of calssical economics
Clare is contemplating her possible consumption patter for this year and next. She know that she will have income of $50,000 this year and $55,000 next yea. Her plan is to consume $40,000 this year (t=0). She is also going to invest 30,000. This investment has a positive NPV of $450. She decides to take the investment; in addition, the return on the investment is 9.62%. What consumption she can expect at t=1? (show a detailed procedure)
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?
An estate agent advertises its houses in two media; Daily Graphic and Ghanaian Times. The agent believes that there is a relationship between the sales S and the amounts spent on the two advertising media. The relationship is given by; where, d is the amount spent in Daily Graphic and g is the amount spent in Ghanaian Times. The estate’s agent fee is 12½% and this includes the cost of adverting. If the agent has planned to spend only 200 thousand Ghana Cedis on advertisement, show how it should be allocated between the two media in order to maximize net profit.
Show solutiion
6. If intertemporal preferences are consistent and the lifetime utility function is additive, then the discount function 8(t) must be (a) bounded (b) exponential (c) hyperbolic (d) linear (e) logarithmic
(ii) For what values of x is ()Px increasing?(iii) For what values of x is ()Pxdecreasing?
Suppose a consumer has $1500 in the current time period and $1100 in the future time period.Suppose also that the consumer can borrow and lend freely and, unless otherwise specified, borrowing and lending interest rates are the same. (a) If the interest rate between time periods is 50%, what is the budget constraint between consumption in the present and consumption in the future? (B) If the interest rate at which the consumer can borrow is 75% but the rate at which she can lend is25%, what is the budget constraint? (C) Suppose the interest rate is 50%. If the consumer has to pay a fee of 10% of the loan amount in order to borrow money, what is the budget constraint?
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…
Upgrading an Organization’s ComputersYour organization earns $50 million in annual sales, has 500 employees, andplans to acquire 250 new mobile computers this year along with another 250next year. The goal is to issue every employee a company-owned computer,which they can use at work and at home. The computers will be loaded withantivirus software and productivity software to meet each employee’s business needs. Your organization has decided it will purchase the computersfrom the same manufacturer to obtain a quantity purchase discount. To theextent possible, the goal is to have the same hardware and software foreveryone to simplify the troubleshooting and support of the computers. Thechief financial officer has asked you to lead a project team to define users’computer hardware needs and recommend the most cost-effective solutionfor meeting those needs. Critical Thinking Questions1. Who else (role, department) and how many people would you select to bea member of the team? How would…
DEFINE Limit of consumption options
When AP L is positive but declining, the MP L could be (i) declining (ii) zero (iii) negative or (iv) any of them. Which one is the correct alternatives? Explain with diagram.