HomeworkLib
Question

4. Suppose preferences are represented by the Cobb-Douglas utility function, u(x1x2) = xx-. a) Show that marginal utility is
business   economics   
0 0
Add a comment Improve this question Transcribed image text
Next > < Previous
Sort answers by oldest

Homework Answers

Answer #1

a un M2 М Ч, - и a-1 m 2 muz= du = (1-2) u, a na d(my) = a (2-1) n,d - 2 m - Lo because (x-1) Co as & <1 d (muz) – – 2 (1-0)Budget Pin constraint: pn, t2x2 = I + P2 (1-2) P, u = I Pini t (1-4) Pin = I s a - pin & Pin – apin, Med I - & I n = (1-x) I

0 0
Add a comment
Know the answer?
Add Answer to:
4. Suppose preferences are represented by the Cobb-Douglas utility function, u(x1x2) = xx-. a) Show that...
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

  • Suppose Bill has preferences over chocolate,x, and ice cream,y, that are represented by the Cobb-Douglas utility...

    Suppose Bill has preferences over chocolate,x, and ice cream,y, that are represented by the Cobb-Douglas utility function u(x, y) =x^2 y. 1. Write down two other Cobb-Douglas utility functions, besides the one above, that represent Bill’s preferences. 2. Write down two more Cobb-Douglas utility functions that do NOT represent Bill’s prefer- ences. 3. Draw 3 indifference curves that represents Bill’s preferences at 3 different levels of satsifaction. 4. What is Bill’s marginal rate of substitution between chocolate and ice cream?...

  • Cobb-Douglas Preferences: Cobb-Douglas preferences on the consump- tion set R2+ can be represented by a utility...

    Cobb-Douglas Preferences: Cobb-Douglas preferences on the consump- tion set R2+ can be represented by a utility function of the form U (q1,q2) = Aq1αq2β, where A > 0, α ∈ (0,1), and β ∈ (0,1) are fixed parameters. 1. If we assume that preferences are ordinal, explain why these precise preferences are also represented by the utility function U(q ,q )=qγq1−γ, 1212 whereγ= α .Isγ∈(0,1)? (α+β) 2. If we assume that preferences are ordinal and restrict attention to the consumption...

  • 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 the preferences of an individual are represented by a quasilinear utility function: U (x, y)...

    Suppose the preferences of an individual are represented by a quasilinear utility function: U (x, y) = ln(x) + y (a)Suppose px =1, py =5 and I = 20. The price of x increases to 2 (px = 2). Calculate the changes in the demand for x. What can you say about the substitution and income effects for small changes in the price of x? What happens to the demand for y? Is y a gross substitute? (b)Now suppose px...

  • Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7...

    Problem 1 (10 marks) Answer the following questions regarding a Cobb-Douglas utility function U(X,Y)= X0.3 0.7 (a) Does this utility function exhibit diminishing marginal utility in X? Show why or why not. (b) Does this utility function exhibit diminishing marginal rate of substitution? Mathematically show and verbally explain why it has (or doesn't have) such property. Problem 2 (10 marks) Consider the following utility function U(X,Y)= X14734 Suppose that prices and income are given as following Px= 1 Py =...

  • 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?

  • 5. Suppose that each consumer has the Cobb-Douglas utility function u:(X1i, X2i) X11 X21-4. In addition...

    5. Suppose that each consumer has the Cobb-Douglas utility function u:(X1i, X2i) X11 X21-4. In addition the endowments are wi=(1,2) and w2=(2,1). What should be the vector of prices (pı", p2') in order to achieve equilibrium (supply-demand). [Note use an increasing transformation of the utility functions given by a In Xii+(1-a) In X2i] . . following utility functions:

  • Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function...

    Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function are MU1 = x23 and MU2 = 3x1x22. (a) Show that Alex’s utility function belongs to a class of functions that are known to be well-behaved and strictly convex. (b) Find the MRS. [Note: find the MRS for the original utility function, not some monotonic transformation of it.] (c) Write down the tangency condition needed to find an optimal consumption bundle for well-behaved preferences....

  • 4. Suppose you have the following Cobb-Douglas Utility Function: And $200 to spend. a. Use the...

    4. Suppose you have the following Cobb-Douglas Utility Function: And $200 to spend. a. Use the method of Lagrangian Multipliers, to maximize this consumer's utility and derive demand equations for both goods. Sketch their respective demand curves. Show all work. (5 pts) b. If Px = Py = $1, how much utility will the consumer enjoy? Show work/explain. (2.5 pts) c. Does this allocation satisfy the rule of equal marginal utility per dollar spent? Explain/show work. (2.5 pts)

  • An individual has a utility function given by U = x1x2 Marginal Rate of Substitution is...

    An individual has a utility function given by U = x1x2 Marginal Rate of Substitution is –x2/(x1) and therefore the Demand function for good 1 is x1= m/(2P1) Assume m=$42, P1=$1, P2=$1 (m=income, P1 is the price of good 1 , P2 is the price of good 2) Calculate the quantity of good one in the optimal choice bundle (x1A)

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