Question

Consider Sarah’s utility function: ?(?, ?) = ? + ?^1/2 a. Write down the lagrangian for...

Consider Sarah’s utility function: ?(?, ?) = ? + ?^1/2

a. Write down the lagrangian for Sarah’s utility maximization problem. Use the usual budget constraint. ii. What are the three first order conditions from the maximization problem? iii. Solve for the Marshallian demand functions of X and Y.

b. Suppose that Sarah’s income is $10 and Px=2 and Py=1. She learns about a new store in town in which she pays a fee of $2 but then she can buy all the X she wants at a price of just $1. Would Sarah be willing to pay the fee to shop at the new store?

c. Write down Sarah’s cost minimization problem. ii. What are the first order conditions for this problem? iii. Solve for the Hicksian demand functions. iv. What is the expenditure function?

Business   Economics   
0 0
Add a commentTranscribed image text
Next >

Homework Answers

Answer #1

0 0
Know the answer?
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
Similar Questions
2. For the production function ?(?, ?) = 10 ?^(1/3) ?^(1/ 3) A)Write down the Lagrangian...
2. For the production function ?(?, ?) = 10 ?^(1/3) ?^(1/ 3) A)Write down the Lagrangian for the cost minimization problem B)Find the first-order conditions for the cost minimization problem and e what they mean (economic terms, not math). C). Find the contingent input demand functions. Give an intuitive explain what they are. D). Find the firm supply function for a firm that is a price taker. Give an intuitive explanation of what it is. d. Find the firm supply...
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...
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...
A consumer's preferences are given by the utility function u=(107)^2+2(x-5)y and the restrictions x>5 and y>0...
A consumer's preferences are given by the utility function u=(107)^2+2(x-5)y and the restrictions x>5 and y>0 are imposed. 1. Write out the Lagrangian function to solve the consumer's choice problem. Use the Lagrangian to derive the first order conditions for the consumer's utility maximizing choice problem. Consider only interior solutions. Show your work. 2. Derive the Optimal consumption bundles x*(px,py,w) and y*(px,py,w) 3. Use the first order condition from 1 to calculate the consumer's marginal utility of income when w=200,...
(A). Find the maximum of the following utility function with respect to x; U= x^2 *...
(A). Find the maximum of the following utility function with respect to x; U= x^2 * (120-4x). The utility function is U(x,y)= sqrt(x) + sqrt(y) . The price of good x is Px and the price of good y is Py. We denote income by M with M > 0. This function is well-defined for x>0 and y>0. (B). Compute (aU/aX) and (a^2u/ax^2). Is the utility function increasing in x? Is the utility function concave in x? (C). Write down...
2. For Each of the following situations, i) Write the Indirect Utility Function ii) Write the...
2. For Each of the following situations, i) Write the Indirect Utility Function ii) Write the Expenditure Function iii) Calculate the Compensating Variation iv) Calculate the Equivalent Variation a) U(X,Y) = X^1/2 x Y^1/2. M = $288. Initially, PX= 16 and PY = 1. Then the Price of X changes to PX= 9. i) Indirect Utility Function: __________________________ ii) Expenditure Function: ____________________________ iii) CV = ________________ iv) EV = ________________ b) U(X,Y) = MIN (X, 3Y). M = $40. Initially,...
1. Consider the general form of the utility for goods that are perfect complements. a) Why...
1. Consider the general form of the utility for goods that are perfect complements. a) Why won’t our equations for finding an interior solution to the consumer’s problem work for this kind of utility? Draw(but do not submit) a picture and explain why (4, 16) is the utility maximizing point if the utility is U(x, y) = min(2x, y/2), the income is $52, the price of x is $5 and the price of y is $2. From this picture and...
Let income be I = $90, Px = $2, Py = $1, and utility U =...
Let income be I = $90, Px = $2, Py = $1, and utility U = 4X½Y. a.[12] Write down and simplify the two conditions required for utility maximization. b.[6] Compute the optimal consumption bundle for the consumer. What is the level of utility at the optimum?
2. Firm Fiat Lux, a light bulb company, has the production function q = 2L 0.5K...
2. Firm Fiat Lux, a light bulb company, has the production function q = 2L 0.5K 0.5. If it has to make 800 light bulbs, and the price of one unit of capital is 40 and the price of one unit of labor is 25, use the Lagrangian method to find the marginal cost of production. 3. Jack’s preferences are represented by the utility function U = X0.4Y0.6. PX = 2, PY = 3 and his budget is $120. Setting...
Set up the Lagrangean function and take the first order conditions for the following utility function:...
Set up the Lagrangean function and take the first order conditions for the following utility function: U (x1, x2 ) = x1a +x2a     The budget constraint is: p1 x1 + p2 x2 = y Then solve for your Marshallian demand functions: xi* (p1, p2, y) for i = 1,2. Verify that the second-order conditions hold for the consumption bundles solved for above. What conditions are required on the second derivatives of the utility function to ensure that the second order...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT