Ask Question, Ask an Expert


Ask Microeconomics Expert

1. (a) Derive the Marshalian demand functions and the indirect utility function for the following utility function:

u(x1,x2,x3) x11/6 x21/6 x31/6  x1 ≥ 0x2 ≥ 0x3 ≥ 0

(b) Using the indirect utility function which you obtained in part (a), derive an expenditure function and from it, derive Hicksian demand function for good 1.

(c) Jack and his grandfather are sitting at the dinner table, discussing their lives. Both share the same utility function as given in part (a). Jack is boasting about his $5000 a month salary, with per-unit prices of x1,x2 and x3 being $4, $4 and $16 respectively. Jack’s grandfather claims that the old days were much better because although his salary was $500 a month, the per-unit prices of x1, x2 and x3 were all only $1. Do you agree with his grandfather?
2. (a) Derive the Marshalian demand functions for the following utility function:

u(x1,x2,x3) = x1 + δ ln(x2), x1 ≥ 0, x2 ≥ 0

Does one need to consider the issue of “corner solutions” here?

(b) Derive the Hicksian demand functions and the expenditure function for the following utility function:

u(x1,x2,x3) =min{√x1, 2√x2, 4√x3},x1 ≥ 0, x2 ≥ 0, x3 ≥ 0

Using the expenditure function and the Hicksian demand functions that you obtained, derive the indirect utility function and the Marshalian demand function for good 1.

[Utility theory is a powerful tool, and has been used to study a wide range of issues. The next two problems will expose you to just a few of the many applications of this theory; you may see more applications in other economics courses.]

3. Consider a person’s decision problem in trying to decide how many children to have. Although she cares about children and will like to have as many as possible, she knows that children are “costly” in the sense that there are costs to their upbringing as well as the time that she would have to take off from work in order to have children. Her utility function over her own consumption (x), her own leisure (l) and the number of children (n) is given by the following utility function:
u(x, l,n) = x1/6l 1/6 n 1/6

For tractability (and to be able to use calculus), we will assume that the number of children, n, is a continuous variable (i.e. it could take any nonnegative value, including decimal values like 2.15 etc.).

This individual is endowed with a total of T units of time in her life, which she can divide between working, leisure and having children. For having each child, she will have to take time t off from work, during which she will not earn anything. In addition this, there is a per child cost of Ε for upbringing expenses.

Her wage rate is w; she uses her total income to purchase good x for her own consumption, as well as to provide for the upbringing expenses of her children. Suppose that good x is priced at p per unit.

(a) prepare consumer’s optimization problem with suitable resource constraint, and derive her Marshalian demand for children n.

(b) Assume the government introduces child benefits such as for every child she has, the government provides her an amounts. How would this affect her decision on how many children to have i.e. is dn/ds greater or less than 0?

4. Assume an individual lives for two periods, t = 1, 2. He consumes only one good,X The price of this good is p in period t = 1 and is p(1 + i) in period t = 2. Thus i is the inflation rate.

His income at period t = 1 is I, but he has no income in period t= 2 and should depend on his savings from the first period. Savings earn an interest rate of r from the bank.

The individual’s life-time utility is given by:

u(x1, x2) = x1 + δ ln(x2)
where xt is his consumption of the single good in period t.
(a) What is the individual’s optimal savings decision?

(b) What is the effect of inflation on the individual’s savings decision i.e. does it increase or decrease in i? What is the intuition for your result?

(c) Assume the government introduces a pension plan in which the individual’s income in period t = 1 is taxed at the rate τ, but he would be given an amount B in period t = 2. What is the individual’s savings decision now? Can it occur now that he may not save at all?

Microeconomics, Economics

  • Category:- Microeconomics
  • Reference No.:- M91672

Have any Question? 

Related Questions in Microeconomics

Question 1 a scatter diagram is useful to determine if a

Question 1. A scatter diagram is useful to determine if a relationship exists between two variables. True False Question 2. Consider the following gasoline data: Quarter 1, Year 1, Year 2 1, 150, 156 2, 140, 148 3, 185, ...

Assignment production cost analysis and estimation applied

Assignment: Production Cost Analysis and Estimation Applied Problems Please complete the following two applied problems: Problem 1: William is the owner of a small pizza shop and is thinking of increasing products and lo ...

Assignmentin this assignment you will discuss the role of

Assignment In this assignment, you will discuss the role of entrepreneurship in improving the economic condition of countries and individuals and understand the manner in which this perception has spread around the world ...

1 please prove that two indifferent curve cannot cross each

1. Please prove that two indifferent curve cannot cross each other. 2. Please solve the following maximization problem u = √x 1 + x 2 max√x 1 + x 2 , st, p 1 x 1 + p 2 x 2 ≤ m 3. a. When prices are (p 1 , p 2 ) = (1, 2) ...

Great depression economy paperwritten assignmentplease

Great depression , economy paper Written Assignment Please provide a comprehensive answer to the following two questions: 1) Which were the main causes of the Great Depression? 2) Why did the Great Depression last so lon ...

Assignmentin the article at the beginning of the readings

Assignment In the article at the beginning of the readings book, Aronson talks about Social Psychology as a leap of faith, and about the imperfect nature of social psychological experiments (which is true of science in a ...

Q1 in quantity theory of money model mv py assume that v

Q1. In quantity theory of money model, MV = PY, assume that V is constant, M is growing at 6% per year, Y is growing at 3%. a. If r = 2, what is i? b. If the Fed reduces the money growth rate by 2% points per year, what ...

Assignmentthe paper is on googles business ethics in the

Assignment The paper is on Google's Business Ethics in the area of Sustainability. How does Google contribute or detract from various aspects of sustainability? Sustainable businesses make products and services which fil ...

Microeconomicsdiscussion forumnote the video has closed

Microeconomics DISCUSSION Forum Note: The video has Closed Captioning. To activate it, start the video, mouse over the bottom of the video and click on the CC icon, then select from the menu. Note: The video has Closed C ...

Suppose the economy was at equilibrium before the start of

Suppose the economy was at equilibrium before the start of the recession. Show this using the IS-LM, Keynesian cross, AD-SRAS-LRAS and money market spaces. Following the start of the recession, what happened to aggregate ...

  • 4,153,160 Questions Asked
  • 13,132 Experts
  • 2,558,936 Questions Answered

Ask Experts for help!!

Looking for Assignment Help?

Start excelling in your Courses, Get help with Assignment

Write us your full requirement for evaluation and you will receive response within 20 minutes turnaround time.

Ask Now Help with Problems, Get a Best Answer

Section onea in an atwood machine suppose two objects of

SECTION ONE (a) In an Atwood Machine, suppose two objects of unequal mass are hung vertically over a frictionless

Part 1you work in hr for a company that operates a factory

Part 1: You work in HR for a company that operates a factory manufacturing fiberglass. There are several hundred empl

Details on advanced accounting paperthis paper is intended

DETAILS ON ADVANCED ACCOUNTING PAPER This paper is intended for students to apply the theoretical knowledge around ac

Create a provider database and related reports and queries

Create a provider database and related reports and queries to capture contact information for potential PC component pro

Describe what you learned about the impact of economic

Describe what you learned about the impact of economic, social, and demographic trends affecting the US labor environmen