🏷️ LIMITED TIME OFFER: GET 20% OFF GRADE+ YEARLY SUBSCRIPTION →
Log in
Economics
3
answers
0
watching
135
views

Hi, my question is about Pareto optimal.

There are 2 consumers and 2 commodities. Consumer A's initial endowment is 4 units of good x and 1 unit of y, and the utility function is U=x*y. Consumer B's initial endowment is 0 unit of x and 7 units of B, and the utility function is U=min{x,y}.

Question: 1) show the locus of Pareto optimal allocations.

2) let good x be the numeraire (price=1) and p denote the price of goody. Write the expression for the amount of goody that consumer B will demand at these prices.

Please show all work and thank you in advance for your help!

Watch
3
answers
0
watching
135
views

For unlimited access to Homework Help, a Homework+ subscription is required.

Unlock all answers

Get 1 free homework help answer.
Already have an account? Log in
Share
Already have an account? Log in
Share
Chika Ilonah
Chika IlonahLv10
28 Sep 2019
Already have an account? Log in
Share

Related textbook solutions

Principles of Economics
2nd Edition, 2017
Openstax
ISBN: 9781947172364
Principles of Macroeconomics
2 Edition,
Openstax
ISBN: 9781947172388
Principles of Microeconomics
2 Edition,
Openstax
ISBN: 9781947172340

Related questions

In another economy consumer 1 has no x and 8 units of y and the utility fucntion U(x,y) = x - (1/4)y2. Consumer 2 has 16 units of x and 8 units of y and the utility function U(x,y) = x +2y(1/2). Describe the set of pareto optimal allocations for this economy. Math not required; just intution. If possible, include the Edgeworth box.

Suppose that there are two goods (X and Y). The price of X is $2 per unitu, and the price of Y is $1 per unit. There are two consumers ( A and B). The utility functions for the consumers are: for consumer A: U (X,Y)= X^.5Y^.5 and for consumer B: U(X,Y)=X^.8Y^.2

Consumer A has an income of $100, and Consumer B has an income of $300.

1. Derive the marginal utlities of goods X and Y for consumer A


2. Derive the marginal utilities of goods X and Y for consumer B


3. Set consumer A's MRS equal to the price ratio. Then use the budget constraint to solve for her optimal bundle


4. Set consumer B's MRS equal to the price ratio. Then use the budget contraint to solve for his optimal consumption bundle.


5. Calculate the MRS for each consumer at their optimal consumption bundles.


6. Suppose that there is another conusmer (let's call her C). You don't know anything about her utility function or her income. All you know is that she consumes both goods. What do you know about C's MRS at her optimal consumption bundle? Why?


Please explain the steps to get to the answers. I already have just the answers.

Adam and Eve are consumers in a 2-consumer, 2-good exchange economy. The price of X is Px, and the price of Y is $1. Each one has an initial endowment of (X=6, Y=6); therefore, each one has a "budget line" of X*Px+ Y*Py = 6*Px + 6. Adam's utility function is U = XY. The expression for Adam's marginal rate of substitution (i.e.   ) is Y/X, which at his initial endowment of (6, 6) has the value of 1. Adam's demand for X as a function of the price of X is X = 3 + 3/PX.

If Eve's utility function is,  

find: (i) the expression for Eve's marginal rate of substitution.

(ii) the value of Eve's marginal rate of substitution at her initial endowment.

(iii) Eve's demand for X as a function of the price of X.

(iv) What is the price of X in equilibrium?

Weekly leaderboard

Home
Homework Help 3,900,000
Economics 400,000
Start filling in the gaps now
Log in