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

Discussionlong-term investment and cost-benefit analysis

Discussion "Long-Term Investment and Cost-Benefit Analysis" Please respond to the following: • From the scenario for Katrina's Candies, suggest one method in which Herb could use a cost-benefit analysis to argue for or a ...

Topic 1 perfectly competitive market structurea perfectly

Topic 1: Perfectly Competitive Market Structure A perfectly competitive market structure has key features. 1. There are many buyers and sellers so neither side of the market has market power. 2. The product provided to t ...

Economics problem set-question 1 sometimes goods are

Economics Problem Set- QUESTION 1: Sometimes goods are rationed, so people cannot buy as much as they want at the announced price. A good example is Super bowl tickets, which are sold at below market price. Suppose that ...

Short-run economic fluctuationscreate a 3 -slide microsoft

Short-Run Economic Fluctuations Create a 3 -slide Microsoft PowerPoint presentation that will be presented to the organization's Executive Committee. The presentation should cover the following items: • Identify the thre ...

Brainy brian eco discussiondiscussion topic is the lost

Brainy Brian ECO discussion Discussion topic is The Lost Decade: Needs to be 150-250 words and one or two citations. No cover page is needed Aggregate expenditure is the total amount of spending in the economy that deter ...

Question 1 suppose you are given the following information

Question 1: Suppose you are given the following information about an industry: Q D = 8000 - 100p; Q S SR = 20 + 700p; c(q) = 20 + q 2 /20. where q and c (q) stand for a firm's quantity supplied and cost function; Q S SR ...

You have to watch a video in youtube the age of uncertainty

You have to watch a video in youtube :The Age of Uncertainty Episode 1 - The Prophets and Promise of Classical Capitalism link is: and then write a 3pages on answering these fi ...

Microeconomics assignmentshort and long runlets assume that

Microeconomics Assignment Short and Long Run Let's assume that you own a fast food restaurant and you are faced with many customers each day eating in the restaurant without any tables. Describe the difference between th ...

1 explain the difference between explicit and implicit

1) Explain the difference between explicit and implicit costs of production. 2) Explain the reasoning behind the U-shaped, long-run, average cost curve. 3) Explain the law of diminishing marginal returns. 4) Describe eco ...

Research topicthis assignment is the first step towards

Research Topic This assignment is the first step towards completing your research paper. For this submission, you will need to find a topic of interest related to race and ethnicity, social change, or both. You may come ...

  • 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

A cola-dispensing machine is set to dispense 9 ounces of

A cola-dispensing machine is set to dispense 9 ounces of cola per cup, with a standard deviation of 1.0 ounce. The manuf

What is marketingbullwhat is marketing think back to your

What is Marketing? • "What is marketing"? Think back to your impressions before you started this class versus how you

Question -your client david smith runs a small it

QUESTION - Your client, David Smith runs a small IT consulting business specialising in computer software and techno

Inspection of a random sample of 22 aircraft showed that 15

Inspection of a random sample of 22 aircraft showed that 15 needed repairs to fix a wiring problem that might compromise

Effective hrmquestionhow can an effective hrm system help

Effective HRM Question How can an effective HRM system help facilitate the achievement of an organization's strate