Question

(Use this information to answer a, b, c below) Suppose Mary’s utility function for two goods...

(Use this information to answer a, b, c below) Suppose Mary’s utility function for two goods X and Y is given by:

U(X,Y) = 3X1/2Y1/2 . Suppose consumption bundle A consists of 10 units of X and 30 units of Y, and consumption bundle B consists of 40 units of X and 20 units of Y.

a. Consumption bundle A lies on a higher/lower/same indifference curve than consumption bundle B. Show computations.

b. Compute Mary’s MRSxy at consumption bundle A. What does this number tell you?

c. If Mary chose consumption bundle B, her MRSxy would be a higher or lower compared to MRSxy at A? Please explain why.

d. Mary’s preference is transitive. Could two of Mary’s IC’s intersect? Please explain using a graph below.

e. State the equi-marginal principle. Suppose Jane is consuming a bundle of X and Y where MUx = 3,  MUy = 4, Px = $1, Py = $2. To maximize utility, Jane should increase the consumption of good ___ and decrease the consumption of good ____. Explain your answer by using the equi-marginalprinciple.

f. True or False and briefly explain: If at any consumption bundle, MRSxy <Px/Py, a consumer can enjoy a higher level of utility by increasing the consumption of X and decreasing the consumption of Y.




2. (12*3 = 36 pts) Suppose Mary’s utility function for two goods X and Y is given by: U(X,Y) = 6X1/3Y2/3

  1. If Px = $3, Py = $5, and Income I = $600, compute Mary’s utility maximizing consumption bundle. Show the utility maximizing consumption bundle on a graph. Show computations using the calculus approach.









b. Suppose Px and Py are the same as in part (a), but Mary’s income falls to $300. Construct Mary’s Income Consumption Curve, and Mary’s Engel Curve for Good Y. Is good Y a normal good? Briefly explain (Can use either calculus or solver to do computations.)

c. Define Price Consumption Curve. Suppose Px and Income are the same as in part (a), but Py falls to $2. On a graph, construct Mary’s demand curve for good Y. ((Can use either calculus or solver to do computations.)

0 0
Add a comment Improve this question Transcribed image text
Answer #1

A)At budle A ,

U=3*√10*√30=51.96

At bundle B

U=3*√40*√20=84.85

So lower utility shows consumption bundle A is lies on lower indifference curve than consumption bundle B.

B)MRSxy=MUx/MUy

MUx=1.5√y/(√x)

MUy=1.5√x/(√y)

MRS=MUx/MUy=y/x

MRS at bundle A,

MRS=30/10=3

This tells CONSUMER is willing to trade 3 units of y foe one unit of x.

C)MRS at bundle B,

MRSxy=y/x=40/2=20

MRS at bundle be is 2 ,which tells CONSUMER is willing to trade 2 y for 1 x.

So MRS at bundle B is lower than bundle A

D)NO,

IC curve shows different combination of two goods athat gives same utility.if curves intersect means at some point different IC curve shows same utility.

Which also suggest that with same number of X , increasing y has has no effect on utility ,which is not possible.

So it can't be true.

Add a comment
Know the answer?
Add Answer to:
(Use this information to answer a, b, c below) Suppose Mary’s utility function for two goods...
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. Our experts will answer your question WITHIN MINUTES for Free.
Similar Homework Help Questions
  • PLEASE ANSWER QUESTIONS (E) and (F).  I already got the answer for the other questions but the...

    PLEASE ANSWER QUESTIONS (E) and (F).  I already got the answer for the other questions but the expert did not answer questions E and F. Thank you! (Use this information to answer a, b, c below) Suppose Mary’s utility function for two goods X and Y is given by: U(X,Y) = 3X1/2Y1/2 . Suppose consumption bundle A consists of 10 units of X and 30 units of Y, and consumption bundle B consists of 40 units of X and 20 units...

  • 4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X...

    4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andy's optimal consumption bundle is X* -6 and Y' = 6. When the prices are Px = 1 and P, = 4, Andy's optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of...

  • Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4)...

    Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4) Denote the price of good X by Px, price of good Y by Py and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency...

  • 2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose...

    2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose Py, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values Px-1, Px 2, and Px- 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference curve that goes through...

  • A consumer buys two goods, good X and a composite good Y. The utility function is...

    A consumer buys two goods, good X and a composite good Y. The utility function is given as U(X,Y) = In3XY. The price of X is Py, the price of Y is Py and Income is I. 1) Derive the demand equation for good X. ( 5 marks) 2) Are the two goods X and Y complements or substitutes? Why? ( 5 marks) 3) Suppose that I=$10 and suppose that initially the Px = $1 and subsequently Px falls and...

  • Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r...

    Sally consumes two goods, X and Y. Her preferences over consumption bundles are repre- sented by the utility function r, y)- .5,2 where denotes the quantity of good X and y denotes the quantity of good Y. The current market price for X is px 10 while the market price for Y is Pr = $5. Sally's current income is $500. (a) Write the expression for Sally's budget constraint. (1 point) (b) Find the optimal consumption bundle that Sally will...

  • A consumer buys two goods, good X and a composite good Y. The utility function is...

    A consumer buys two goods, good X and a composite good Y. The utility function is given as U(X, Y) = 2X1/2+Y. The demand function for good X is X = (Py/Px)2. (Edit: The price of X is Px, the price of Y is Py.) Suppose that initially Px=$0.5 and then it falls and becomes Px=$0.2 Calculate the substitution effect, income effect, and the price effect and show the answer graphically.

  • Consider the following utility function of 3 goods, x, y and z: U(x,y,z)=ax+by+cz; x,y,z≥0 and a,...

    Consider the following utility function of 3 goods, x, y and z: U(x,y,z)=ax+by+cz; x,y,z≥0 and a, b, c are constants. The prices of good x and y is denoted by pX and pY respectively. The income is denoted by m. Good z is provided by the government free of cost but the quantity of good z provided by the government depends on the consumption of good x and y chosen by the consumer. For example, if in equilibrium, the consumer...

  • 2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer   Utility Function C1...

    2. Consider the following four consumers (C1,C2,C3,C4) with the following utility functions: Consumer   Utility Function C1                 u(x,y) = 2x+2y C2                 u(x,y) = x^3/4y^1/4 C3                u(x,y) = min(x,y) C4                u(x,y) = min(4x,3y) On the appropriate graph, draw each consumer’s indifference curves through the following points: (2,2), (4,4), (6,6) and (8,8), AND label the utility level of each curve. Hint: Each grid should have 4 curves on it representing the same preferences but with different utility levels. 3. In the following parts,...

  • Suppose a consumer had a utlity function given by U- X04Y02. If the price of Good...

    Suppose a consumer had a utlity function given by U- X04Y02. If the price of Good X (Px) is $8 and the price of Good Y is $16 then what is the utility maximizing quantity of Good X the consumer will purchase with a budget of $84? Round to the nearest decimal place if necessary) Answer Suppose an individual had a utility function given by U XY? Suppose that Bundle A contains 5 units of Good X and 5 units...

ADVERTISEMENT
Free Homework Help App
Download From Google Play
Scan Your Homework
to Get Instant Free Answers
Need Online Homework Help?
Ask a Question
Get Answers For Free
Most questions answered within 3 hours.
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT