HomeworkLib
Question

3) Consider preferences given by the utility function ?(?1, ?2) = ?1^2 + ?2. Derive the...

3) Consider preferences given by the utility function ?(?1, ?2) = ?1^2 + ?2. Derive the MRS and the individual demands for each of the two goods. How an increase in income would affect the demand of each good?

business   economics   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

U = x12 + x2

Budget line: M = p1.x1 + p2.x2

MU1 = U/x1 = 2x1

MU2 = U/x2 = 1

MRS = MU1/MU2 = 2x1/1 = 2x1

Utility is maximized when MRS = p1/p2

2x1 = p1/p2

2p1.x1 = p2

p1.x1 = p2/2

x1 = (p2/2p1)

Substituting in budget line,

M = p1.x1 + p2.x2

M = (p2/2) + p2.x2

2M = p2 + 2p2.x2

2p2.x2 = 2M - p2

x2 = (2M - p2)/2p2

Demand function of x1 is independent of M, so increase in M does not affect demand for x1.

From demand function of x2, s M increases, (2M - p2) increases and so, demand for x2 increases.

0 0
Add a comment
Know the answer?
Add Answer to:
3) Consider preferences given by the utility function ?(?1, ?2) = ?1^2 + ?2. Derive the...
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Log In

Sign Up

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

  • Indifference curves and utility: Consider the utility function ? (?1, ?2) = 6?1^1/2 + ?2 that...

    Indifference curves and utility: Consider the utility function ? (?1, ?2) = 6?1^1/2 + ?2 that describes Moe’spreferences. For the following, think of q1 as the variable you would graph on the horizontal axis. a. Derive an expression for his marginal utility (U1) from a small increase in q1 holding q2 fixed. Also, find U2. b. What is Moe’s marginal rate of substitution (MRS)? Give a brief (2 sentences maximum) intuitive description of what MRS represents. c. Given your answer...

  • QUESTION 5 Reshad's preferences over goods 1 and 2 are given by the following utility function:...

    QUESTION 5 Reshad's preferences over goods 1 and 2 are given by the following utility function: Uq1. 42) Reshad's income is $60 and the prices are given by p1-3 and p2-2. Select all that applies: 1+q1 42 41 a. Marginal rate of substitution for his preferences is given by MRS12 When he consumes zero amount of good 1, his MRS is equal to 1. c. It is optimal for him to consume 20 units of good 1. @dㆎt is optimal...

  • Consider the following utility function over goods 1 and 2, plnx1 +3lnx2: (a) [15 points] Derive...

    Consider the following utility function over goods 1 and 2, plnx1 +3lnx2: (a) [15 points] Derive the Marshallian demand functions and the indirect utility function. (b) [15 points] Using the indirect utility function that you obtained in part (a), derive the expenditure function from it and then derive the Hicksian demand function for good 1. (c) [10 points] Using the functions you have derived in the above, show that i. the indirect utility function is homogeneous of degree zero in...

  • Treat Bob and Joe as the same individual and having the same utility function as provided...

    Treat Bob and Joe as the same individual and having the same utility function as provided at the beginning of the question. Looking for the solutions to part e and f.   Indifference curves and utility: Consider the utility function U (qi,%)-2q1/2 + q2 that describes Joe's preferences. For the following, think of q1 as the variable you would graph on the horizontal axis. 3. a. Derive an expression for his marginal utility (U) from a small increase in qi holding...

  • Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function...

    Income and substitution, Compensating Variation: Show your work in the steps below. Consider the utility function u(x,y)-x"y a. Derive an expression for the Marshallian Demand functions. b. Demonstrate that the income elasticity of demand for either good is unitary 1. Explain how this relates to the fact that individuals with Cobb-Douglas preferences will always spend constant fraction α of their income on good x. Derive the indirect utility function v(pxPod) by substituting the Marshallian demands into the utility function C....

  • 2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min...

    2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min {axı, bx2} If the income of the consumer is w > 0 and the prices are p1 > 0 and P2 > 0. (a) Derive the Marshallian demands. Be sure to show all your work. (b) Derive the indirect utility function. (c) Does the utility function: û(x1, x2) = axı + bx2 represent the same preferences?

  • Suppose a consumer's preferences can be represented by the utility function: U(X,Y)=X3/5Y1/4 a. Derive the function...

    Suppose a consumer's preferences can be represented by the utility function: U(X,Y)=X3/5Y1/4 a. Derive the function for the marginal rate of substitution holding utility constant: U X Y   b. Derive the demand curves for the two goods, X and Y. c. Confirm that both demand curves slope downward. d. Calculate the price elasticity for each of the goods. e. Calculate the income elasticity for each of the goods.

  • Suppose utility is given by the following function: u(x, y) = xy3 Use this utility function...

    Suppose utility is given by the following function: u(x, y) = xy3 Use this utility function to answer the following questions: (d) What is the marginal rate of substitution implied by this utility function? What does this mean in words? (e) How much of each good would this individual need to have to be willing to trade 1 unit of good x for 1 unit of good y (i.e. for the MRS to be equal to 1)? (f) Suppose we...

  • 1. Consider the following utility function over goods 1 and 2, (a) [15 points] Derive the...

    1. Consider the following utility function over goods 1 and 2, (a) [15 points] Derive the Marshallian demand functions and the indirect utility (b) [15 points] Using the indirect utility function that you obtained in part (a), () [10 points] Using the functions you have derived in the above, show that function derive the expenditure function from it and then derive the Hicksian demand function for good 1. iihi İ. the indirect utility function is homogeneous of degree zero in...

  • Treat Bob and Joe as having the same utility function as provided at the beginning of...

    Treat Bob and Joe as having the same utility function as provided at the beginning of the question Indifference curves and utility: Consider the utility function U (qi,%)-2q1/2 + q2 that describes Joe's preferences. For the following, think of q1 as the variable you would graph on the horizontal axis. 3. a. Derive an expression for his marginal utility (U) from a small increase in qi holding q2 fixed. Also, find b. What is Joe's marginal rate of substitution (MRS)?...

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