ZuoTi.Pro
Question

Robin has the utility function U ( x1 , x2)= 1/ 5 ln ( x1 )+...

Robin has the utility function U ( x1 , x2)= 1/ 5 ln ( x1 )+ 4 /5 ln ( x2 ) .

a) Set up the Lagrangian and derive an expression for the marginal rate of substitution and calculate the Marshallian demand for both goods.

b) What will happen to Robin’s share of expenditures on good x1 if the price of good one, p1 , increases. Verify your conclusion formally!

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

Homework Answers

Answer #1

0 0
Add a comment
Know the answer?
Add Answer to:
Robin has the utility function U ( x1 , x2)= 1/ 5 ln ( x1 )+...
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

  • An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3....

    An individual has the utility function: U(x1,x2,x3) = ln x1 + ln x2 + 0.5ln x3. The price of good x1 is p1, the price of good x2 is p2 = 1 and the price of good x3 is p3. The individual’s income is I. Derive the Marshallian demand functions (x1* , x2*, x3* ).

  • Question 1 1 4 5 .5 U (x1,x2)=xix2 Kim has the utility function a) Set up...

    Question 1 1 4 5 .5 U (x1,x2)=xix2 Kim has the utility function a) Set up the Lagrangian and derive an expression for the marginal rate of substitution and calculate the Marshallian demand for both goods. (9p) b) Are both goods normal goods to Kim? (4p) c) Calculate the price elasticity of demand for both goods at prices p 2 , p2=4 and income m=150 . Do you expect the elasticity to change with different prices and income? Explain why....

  • The utility function is u = x1½ + x2, and the budget constraint is m =...

    The utility function is u = x1½ + x2, and the budget constraint is m = p1x1 + p2x2. Derive the optimal demand curve for good 1, x1(p1, p2), and good 2, x2(m, p1, p2). Looking at the cross price effects (∂x1/∂p2 and ∂x2/∂p1) are goods x1 and x2 substitutes or complements? Looking at income effects (∂x1/∂m and ∂x2/∂m) are goods x1 and x2 inferior, normal or neither? Assume m=100, p1=0.5 and p2=1. Using the demand function you derived in...

  • Q1. Sam consumes two goods x1 and x2. Her utility function can be written as U(x1,x2)=x...

    Q1. Sam consumes two goods x1 and x2. Her utility function can be written as U(x1,x2)=x 1raised to 2/3 and x 2 raised to 1/5 ⁄. Suppose the price of good x1 is P1, and the price of good x2 is P2. Sam’s income is m. [20 marks] a) [10 marks] Derive Sam’s Marshallian demand for each good. b) [5 marks] Derive her expenditure function using indirect utility function. c) [5 marks] Use part c) to calculate Hicksian demand function...

  •    1) Optimization problem 1 Max U(x, y) = x1^0.5 + x2^0.5 s.t. x1 + x2...

       1) Optimization problem 1 Max U(x, y) = x1^0.5 + x2^0.5 s.t. x1 + x2 =16 Find the optimum bundle; check if there is a minimum or a maximum. 2) Give the interpretation of the expenditure function, explain and show its properties. Draw the diagram of the expenditure function. Derive the compensated demand function for x1 and x2 E( p, u) = p(p1. p2)^0,5 and the uncompensated demand function. 3) Derive the expenditure function when the direct utility function...

  • Consider the utility function u(x) = ​√x1 + √x2 ; and a standard budget constraint: p1x1+p2x2=I

     1. (Consumer theory) Consider the utility function u(x) = √x1 + √x2 ; and a standard budget constraint: p1x1+p2x2=I. a. Are the preferences convex? (1 pt) b. Are the preferences represented by this function homothetic? (1 pt) c. Formally write the utility maximization problem, derive the first order conditions and find the Marshallian demand function. (2 pt) d. Verify that the demand function is homogeneous of degree 0 in prices and income. (1 pt) e. Find the indirect utility function. (1 pt) f.  Find the expenditure function by...

  • Consider two goods, good 1 and good 2. The consumer’s utility function is given by U(x1,x2)=V(x1)+x2....

    Consider two goods, good 1 and good 2. The consumer’s utility function is given by U(x1,x2)=V(x1)+x2. Derive the ordinary demand function of good 1. When the market price of good 1 is given P1=P1' , derive the consumer’s surplus. If the price is changed to P1=P1", prove that the change measured by consumer’s surplus is the same as the Compensating variation. Also prove that it is the same as Equivalent variation.

  • 6. Modou has a utility function U(X1,X2) = 2X1 + X2 The prices of X1 &...

    6. Modou has a utility function U(X1,X2) = 2X1 + X2 The prices of X1 & X2 are $1 each and Modou has an income of $20 budgeted for this two goods. a. Draw the demand curve for X1 as a function of p1.: b. At a price of p1 = $1, how much X1 and X2 does Modou consume?: c. A per unit tax of $0.60 is placed on X1. How much of good X1 will he consume now?:...

  • What is the MRS for the following utility function U(x1, x2) = ln(x1) + ln(x1 +...

    What is the MRS for the following utility function U(x1, x2) = ln(x1) + ln(x1 + x2) (show all the work). Does it satisfy the law of diminishing MRS?

  • 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?

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