Question

1.54 The n-good Cobb-Douglas utility function is u(x) = A n i=1 x αi i ,...

1.54 The n-good Cobb-Douglas utility function is u(x) = A n i=1 x αi i , where A > 0 and n i=1 αi = 1. (a) Derive the Marshallian demand functions. (b) Derive the indirect utility function. (c) Compute the expenditure function. (d) Compute the Hicksian demands.

Homework Answers

Answer #1

Please ask your query if any in comment.

PLEASE RATE THUMBS UP ??

THANKYOU

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
Consider the Cobb-Douglas utility function u(x1,x2)=x1^(a)x2^(1-a). a. Find the Hicksian demand correspondence h(p, u) and the...
Consider the Cobb-Douglas utility function u(x1,x2)=x1^(a)x2^(1-a). a. Find the Hicksian demand correspondence h(p, u) and the expenditure function e(p,u) using the optimality conditions for the EMP. b. Derive the indirect utility function from the expenditure function using the relationship e(p,v(p,w)) =w. c. Derive the Walrasian demand correspondence from the Hicksian demand correspondence and the indirect utility function using the relationship x(p,w)=h(p,v(p,w)). d. vertify roy's identity. e. find the substitution matrix and the slutsky matrix, and vertify the slutsky equation. f....
The utility function U(X,Y)=XaY1-a where 0≤a≤1 is called the Cobb-Douglas utility function. MUx=aXa-1Y1-a MUy=(1-a)XaY-a (note for...
The utility function U(X,Y)=XaY1-a where 0≤a≤1 is called the Cobb-Douglas utility function. MUx=aXa-1Y1-a MUy=(1-a)XaY-a (note for those who know calculus MUx=∂U∂x and MUy=∂U∂y) Derive the demand functions for X and Y Are X and Y normal goods? If the quantity of the good increases with income a good is a normal good. If the quantity decreases with income the good is an inferior good. Describe in words the preferences corresponding to a=0, a=1, a=.5
Assume that we have following utility maximization problem with quasilinear utility function: U=2√ x + Y...
Assume that we have following utility maximization problem with quasilinear utility function: U=2√ x + Y s.t. pxX+pyY=I (a)derive Marshallian demand and show if x is a normal good, or inferior good, or neither (b)assume that px=0.5, py=1, and I =10. Then the price x declined to 0.2. Use Hicksian demand function and expenditure function to calculate compensating variation. (c)use hicksian demand function and expenditure function to calculate equivalent variation (e) briefly explain why compensating variation and equivalent variation are...
Jane’s utility function has the following form: U(x,y)=x^2 +2xy The prices of x and y are...
Jane’s utility function has the following form: U(x,y)=x^2 +2xy The prices of x and y are px and py respectively. Jane’s income is I. (a) Find the Marshallian demands for x and y and the indirect utility function. (b) Without solving the cost minimization problem, recover the Hicksian demands for x and y and the expenditure function from the Marshallian demands and the indirect utility function. (c) Write down the Slutsky equation determining the effect of a change in px...
Suppose that a consumer has the utility function given by: U(x,y)= (x^a)*(y^b) With prices p^x, p^y...
Suppose that a consumer has the utility function given by: U(x,y)= (x^a)*(y^b) With prices p^x, p^y and the income M, and where a>0, b>0. a) Maximize this consumer's utility. Derive Marshallian demand for both goods. b) Show that at the optimum, the share of income spent on each good does not depend on prices or income. c) Show that the elasticity of Marshallian demand for x is constant. d) For good x, use your answers to b) the elasticities of...
Suppose the utility function for goods ?? and ?? is given by: u(x, y) = x0.5...
Suppose the utility function for goods ?? and ?? is given by: u(x, y) = x0.5 y0.5 a) Explain the difference between compensated (Hicksian) and uncompensated (Marshallian) demand functions. b) Calculate the uncompensated (Marshallian) demand function for ??, and describe how the demand curve for ?? is shifted by changes in income , and by changes in the price of the other good. c) Calculate the total expenditure function for ??.
Consider the following Constant Elasticity of Substitution utility function U(x1,x2) = x1^p+x2^p)^1/p                         &nbs
Consider the following Constant Elasticity of Substitution utility function U(x1,x2) = x1^p+x2^p)^1/p                                                                                                                                           a. Show that the above utility function corresponds to (hint:use the MRS between good 1 and good 2. The ->refers to the concept of limits.                  1. The perfect substitute utility function at p=1 2. The Cobb-Douglas utility function as p -->0 3. The Leontiff (of min(x1,x2) as p--> -infinity b. For infinity<p<1, a given level of income I and prices p1 and p2. 1. Find the marshallian...
May I get any assistance with these following questions please? U(x,y)=min(4x,2y) Prices: px,py Incme : I...
May I get any assistance with these following questions please? U(x,y)=min(4x,2y) Prices: px,py Incme : I 1)Find Marshallian demand. 2) Find Hicksian demand, indirect utility function and expenditure function.
Consider the utility function: u( x1 , x2 ) = 2√ x1 + 2√x2 a) Find...
Consider the utility function: u( x1 , x2 ) = 2√ x1 + 2√x2 a) Find the Marshallian demand function. Use ( p1 , p2 ) to denote the exogenous prices of x1 and x2 respectively. Use y to denote the consumer's disposable income. b) Find the indirect utility function and verify Roy's identity c) Find the expenditure function d) Find the Hicksian demand function
Consider a consumer with Cobb-Douglas preferences over two goods, x and y described by the utility...
Consider a consumer with Cobb-Douglas preferences over two goods, x and y described by the utility function u(x, y) = 1/3ln(x) + 2/3n(y) 1. Assume the prices of the two goods are initially both $10, and her income is $1000. Obtain the consumer’s demands for x and y. 2. If the price of good x increases to $20, what is the impact on her demand for good x? 3. Decompose this change into the substitution effect, and the income effect....