Question

The utility function is given by u (x1,x2) = x1^0.5 + x2^0.5 1) Find the marginal...

The utility function is given by u (x1,x2) = x1^0.5 + x2^0.5

1) Find the marginal rate of substitution (MRSx1,x2 )

2) Derive the demand functions x1(p1,p2,m) and x2(p1, p2,m) by using the method of Lagrange.

Homework Answers

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
The utility function is given by u (x1, x2) = x1^0.5+x2^0.5 1) Find the marginal rate...
The utility function is given by u (x1, x2) = x1^0.5+x2^0.5 1) Find the marginal rate of substitution (MRSx1,x2 ) 2) Derive the demand functions x1(p1, p2, m) and x2(p1,p2, m) by using the method of Lagrange.
1. Using the following utility function, U(x1,x2) = x1x2+x1+2x2+2 Find the demand functions for both x1...
1. Using the following utility function, U(x1,x2) = x1x2+x1+2x2+2 Find the demand functions for both x1 and x2 (as functions of p1, p2, and m). Thank you!
2. A consumer has the utility function U ( X1, X2 ) = X1 + X2...
2. A consumer has the utility function U ( X1, X2 ) = X1 + X2 + X1X2 and the budget constraint P1X1 + P2X2 = M , where M is income, and P1 and P2 are the prices of the two goods. . a. Find the consumer’s marginal rate of substitution (MRS) between the two goods. b. Use the condition (MRS = price ratio) and the budget constraint to find the demand functions for the two goods. c. Are...
Qin has the utility function U(x1, x2) = x1 + x1x2, where x1 is her consumption...
Qin has the utility function U(x1, x2) = x1 + x1x2, where x1 is her consumption of good 1 and x2 is her consumption of good 2. The price of good 1 is p1, the price of good 2 is p2, and her income is M. Setting the marginal rate of substitution equal to the price ratio yields this equation: p1/p2 = (1+x2)/(A+x1) where A is a number. What is A? Suppose p1 = 11, p2 = 3 and M...
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
1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10, P2=$20, and I = $150, find Liz’s...
1.) Liz has utility given by u(x2,x1)=x1^7x2^8. If P1=$10, P2=$20, and I = $150, find Liz’s optimal consumption of good 1. (Hint: you can use the 5 step method or one of the demand functions derived in class to find the answer). 2.) Using the information from question 1, find Liz’s optimal consumption of good 2 3.) Lyndsay has utility given by u(x2,x1)=min{x1/3,x2/7}. If P1=$1, P2=$1, and I=$10, find Lyndsay’s optimal consumption of good 1. (Hint: this is Leontief utility)....
Consider utility function u(x1,x2) =1/4x12 +1/9x22. Suppose the prices of good 1 and good 2 are...
Consider utility function u(x1,x2) =1/4x12 +1/9x22. Suppose the prices of good 1 and good 2 are p1 andp2, and income is m. Do bundles (2, 9) and (4, radical54) lie on the same indifference curve? Evaluate the marginal rate of substitution at (x1,x2) = (8, 9). Does this utility function represent convexpreferences? Would bundle (x1,x2) satisfying (1) MU1/MU2 =p1/p2 and (2) p1x1 + p2x2 =m be an optimal choice? (hint: what does an indifference curve look like?)
Given a utility function for perfect complements: U(x1,x2) = min{x1,βx2}, where β is a positive num-...
Given a utility function for perfect complements: U(x1,x2) = min{x1,βx2}, where β is a positive num- ber, and a budget constraint: p1x1 + p2x2 = Y , where p1 and p2 are prices of good 1 and good 2 respectively, Y is the budget for the complements. Find the demand functions for good 1 and good 2.
1. Al Einstein has a utility function that we can describe by u(x1, x2) = x21...
1. Al Einstein has a utility function that we can describe by u(x1, x2) = x21 + 2x1x2 + x22 . Al’s wife, El Einstein, has a utility function v(x1, x2) = x2 + x1. (a) Calculate Al’s marginal rate of substitution between x1 and x2. (b) What is El’s marginal rate of substitution between x1 and x2? (c) Do Al’s and El’s utility functions u(x1, x2) and v(x1, x2) represent the same preferences? (d) Is El’s utility function a...
A consumer has utility function U(x1,x2)= x1x2 / (x1 + x2) (a) Solve the utility maximization...
A consumer has utility function U(x1,x2)= x1x2 / (x1 + x2) (a) Solve the utility maximization problem. Construct the Marshallian demand function D(p,I) and show that the indirect utility function is V (p, I) = I / (p1+ 2 * sqrt (p1*p2) + p2) (b) Find the corresponding expenditure function e(p; u). HINT: Holding p fixed, V and e are inverses. So you can find the expenditure function by working with the answer to part (a). (c) Construct the Hicksian...