Question

In a two goods (x and y) world, two districts (A and B) are identical, except...

In a two goods (x and y) world, two districts (A and B) are identical, except the prices of good x (Px) and good y (Py) are higher and lower in district A, respectively. Suppose two identical individuals (i.e. same preferences and income) live in the two districts separately and their optimal choices are interior solutions. Evaluate the following statement: ‘The MRS at the optimal choices of two individuals are the same’. True, false, or uncertain? Explain your answer intuitively and graphically. (draw indifference curves and budget constraints)

Homework Answers

Answer #1

Sol;

Let us asume following

PXA = 4 , PYA = 2 , PXB = 2 , PYB = 4, IA = IB = 100

Budget constraint of A is

4X + 2Y = 100

slope of budget line = 4/2 = 2

Budget constraint of B is

2X + 4Y = 100

slope of budget line = 2/4 = 1/2

Since slopes of the budget constraints of the two individuals are different , MRS at optimal choice will not be same.

It is because at optimal choice MRS equals slope of budget constraint.

Under our assumptions AB is budget line of A and CD is budget line of B . Assumede preference for both is

U = XY

EA is equilibrium point of A and EB is equilibrium point for B.

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In a two goods (x and y) world, two districts (A and B) are identical, except...
In a two goods (x and y) world, two districts (A and B) are identical, except the price of good x (Px) is higher in district A. Suppose two identical individuals (i.e. same preferences and income) live in the two districts separately and their optimal choices are interior solutions. Evaluate the following statement: ‘The MRS at the optimal choices of two individuals can be the same’. True, false, or uncertain? Explain your answer intuitively and graphically.
Tom spends all his $100 weekly income on two goods, X and Y. His utility function...
Tom spends all his $100 weekly income on two goods, X and Y. His utility function is given by U(X,Y) =XY. If Px=4 and Py=10 a) how much of each good should the buy? Please show graphically (specify clearly x-axis and y-axis and intercepts of each axis) b) Same as Problem 1, except now Tom’s utility function is given by U(X,Y) = X^1/2 Y^1/2 c) Find the MRS at the tangent points (optimal point) in a and b. Can you...
Dan’s preferences are such that left shoes (good x) and right shoes (good y) are perfect...
Dan’s preferences are such that left shoes (good x) and right shoes (good y) are perfect complements. Specifically, his preferences are represented by the utility function U (x, y) = minimum{x, y}. (a) Draw several of Dan’s indifference curves. Which bundles are at the “kink- points” of these curves? (b) Assume that Dan’s budget for shoes is M = 10 and that the price of a right shoe is py = 2. Find and draw Dan’s demand curve for left...
A consumer's preferences are given by the utility function u=(107)^2+2(x-5)y and the restrictions x>5 and y>0...
A consumer's preferences are given by the utility function u=(107)^2+2(x-5)y and the restrictions x>5 and y>0 are imposed. 1. Write out the Lagrangian function to solve the consumer's choice problem. Use the Lagrangian to derive the first order conditions for the consumer's utility maximizing choice problem. Consider only interior solutions. Show your work. 2. Derive the Optimal consumption bundles x*(px,py,w) and y*(px,py,w) 3. Use the first order condition from 1 to calculate the consumer's marginal utility of income when w=200,...
1. Suppose utility for a consumer over food(x) and clothing(y) is represented by u(x,y) = 915xy....
1. Suppose utility for a consumer over food(x) and clothing(y) is represented by u(x,y) = 915xy. Find the optimal values of x and y as a function of the prices px and py with an income level m. px and py are the prices of good x and y respectively. 2. Consider a utility function that represents preferences: u(x,y) = min{80x,40y} Find the optimal values of x and y as a function of the prices px and py with an...
Sam's is interested in two goods, X and Y. His indirect utility function is U* =...
Sam's is interested in two goods, X and Y. His indirect utility function is U* = M px-.6 py-4.    ( same as U* = M /(px.6 py0.4 ) ) where M is Sam's income, and px   and py denote respectively the price of good X and the price of good Y.   Sam's market demand functions are X*=0.6M/px and Y* = 0.4M/py . Find the absolute value of the change in Sam's consumers surplus if the price of good X...
Jasina has preferences for two goods  x, y and her marginal rate of substitution (MRS) between x...
Jasina has preferences for two goods  x, y and her marginal rate of substitution (MRS) between x and  y  is given by  3y/x. Her budget constraint takes the form  m ≥ pxx + pyy,   where  m is income and  px, py   are the prices of  x,  y respectively. (a) Someone says that Jasina’s expenditure on y  (i.e., pyy) is always one third of her expenditure on  x  (i.e., pxx).   Is this correct? Are x  and  y normal goods? (b) Jason has different preferences to Jasina: his marginal rate of substitution (MRS) between  x and  y is...
Consider a student who purchases education (x) and other goods (y). The student has preferences over...
Consider a student who purchases education (x) and other goods (y). The student has preferences over these goods given by u(x,y) = ln(x) + 3ln(y). The prices of education and other goods are, respectively, px = 10 and py = 5, and the student’s income is I = 20. 1. What do limMUx(x,y) and limMUy(x,y) tell you about the optimal consumption x→0 y→0 bundle? (2 points) 2. Find an expression for the slope of the indifference curve through the point...
Question 1 The following are key characteristics of Indifference Curves, EXCEPT: A. Each indifference curve identifies...
Question 1 The following are key characteristics of Indifference Curves, EXCEPT: A. Each indifference curve identifies the combinations of X and Y where the consumer is equaly happy. B. Indifference curves are convex to the origin because X and Y are assumed to be close substitutes. C. For any combination of X and Y there is one and only one Indifference Curve. D. Indifference curves cannot logically cross between them if preferences are well defined. Question 2 The following are...
1. Emily has preferences for two goods x, y while her marginal rate of substitution (MRS)...
1. Emily has preferences for two goods x, y while her marginal rate of substitution (MRS) between x and y is given by 3y/x. Her budget constraint is m ≥ pxx + pyy, where m = income and px, py are prices of x, y respectively. (a) Emily's expenditure on y (i.e., pyy) is 1/3 of her expenditure on x (i.e., pxx). Is this true Are x and y normal goods? (b) Andrew has different preferences: his marginal rate of...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT