19. Suppose you find that MU1( x1,x2)=2x2 and MU2( x1,x2)=2x1. What is the rate at which...

19. Suppose you find that MU1( x1,x2)=2x2 and MU2( x1,x2)=2x1. What is the rate at which the consumer is willing to trade good 2 for good 1 at bundle (2,4)? (Note: enter a positive number, i.e. enter the quantity of good 2 that the consumer is willing to give up for an additional—marginal—unit of good 1.)
20. Suppose you find that the expressions of the marginal utilities for a consumer are given by MU1( x1,x2)=1 and MU2( x1,x 2)=3. Then you can conclude that:
a. This consumer has Cobb-Douglas tastes
b. For this consumer good 1 and good 2 are perfect complements
c. For this consumer good 1 and good 2 are perfect substitutes
d. None of the above
21. Suppose a consumer is always willing to give up 5 units of good 2 for an additional unit of good 1. For this consumer:
a. Good 1 and good 2 are perfect complements
b. Good 1 and good 2 are perfect substitutes
c. Good 1 and good 2 are both essential goods
d. None of the above
22. Suppose a consumer is always willing to give up 4 units of good 2 for an additional unit of good 1. Which of the following utility functions represents the tastes of this consumer?

a. u(x1,x2)=min{4x1,x2}
b. u(x1,x2)=min{x1,4x2}
c. u(x1,x2)= x1+4x2
d. u(x1,x2)=4x1+x2
e. None of the above

25. Consider the following utility functions: u1(x1,x2)=x1+x2 ans u2(x1,x2)=3x1+3x2 Do they represent the same tastes?
a. Yes
b. No
c. There is not enough information to answer

Expert Solution

19. MU1(x1,x2) = 2x2 MU2(x1,x2) = 2x1

To know the rate we need to know the MRS (Marginal rate of substitution) = MU1/ MU2 = 2x2/ 2x1 = x2/ x1

This is the MRS of well behaved preferenes. At bundle (2,4) MRS = 4/2 = 2/1.

At bundle (2,4) a consumer is willing to give up 2 units of good2 for having an additional unit of good1.

20. c) For this consumer good1 and good2 are perfect substitutes.

Since perfect substitutes are of the form: U = ax+ by where a and b are constants.

To find the MRS = -MUx/ MUy = -a/b. Here also in the question, MRS = -1/3 .

21) b) Both good1 and good2 are perfect substitutes as their rate of substitution is always same.

22) d) u(x1,x2)=4x1+x2 . Here MRS =dux1/ dux2 = 4/1 which implies a consumer is always willing to give up 4 units of good 2 for an additional unit of good 1.

23) a) Yes because second one is just the monotonic transformation of the first one. u1(x1,x2)=x1+x2 and u2(x1,x2)=3(x1+x2) = 3 (u1)

Rahul Sunny answered 7 months ago

Find dual from primal conversion MIN Z = x1 - 2x2 subject to 4x1 - x2 >= 8 2x1 + x2 >= 10 -x1 + x2 <= 7 and x1,x2 >= 0

Find dual from primal conversion MIN Z = x1 - 2x2 subject to 4x1 - x2 >= 8 2x1 + x2 >= 10 -x1 + x2 = 0

4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0...

4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0 Solve the problem by using the M-technique.

Find a basis and the dimension of the subspace: V = {(x1, x2, x3, x4)| 2x1...

Find a basis and the dimension of the subspace: V = {(x1, x2, x3, x4)| 2x1 = x2 + x3, x2 − 2x4 = 0}

For the system 2x1 − 4x2 + x3 + x4 = 0, x1 − 2x2 +...

For the system 2x1 − 4x2 + x3 + x4 = 0, x1 − 2x2 + 5x4 = 0, find some vectors v1, . . . , vk such that the solution set to this system equals span(v1, . . . , vk).

Given the utility function U(x1, x2)= -2x1 + x2^2, (a)Find the marginal utility of both the...

Given the utility function U(x1, x2)= -2x1 + x2^2, (a)Find the marginal utility of both the goods. Explain whether preferences satisfy monotonicity in both goods. (b)Using the graph with a reference bundle A, draw the indifference curve and shade the quadrants that make the consumer worse off and better off for the given preferences.

U= x (x1, x2) = x1+ 2x2 Suppose that a recent scandal has resulted in bad...

U= x (x1, x2) = x1+ 2x2 Suppose that a recent scandal has resulted in bad publicity for Uber. The scandal has not affected your preferences. However, in response to the bad publicity, Uber has reduced their price to $0.40 per mile. You have a budget of $10, and riding with Lyft costs $1 per mile. What is the substitution effect (SE) for Lyft rides following the price change?

If there are 3 known functions, namely: X1 + 2X2 + 3X3 = 6 2X1 -...

If there are 3 known functions, namely: X1 + 2X2 + 3X3 = 6 2X1 - 2X2 + 5X3 = 5 4X1 - X2 - 3X3 = 0 Use the Jacobian determinant to see whether there is a functional freedom function for each pair. Determine the values of X1, X2 and X3 in the above equation?

Find the general solution to the coupled system dx1 /dt = 2x1 +x2 dx2/dt = x1...

Find the general solution to the coupled system dx1 /dt = 2x1 +x2 dx2/dt = x1 + 2x2 Sketch the phase portrait for the system and classify the origin as a node, a saddle, a center, or a spiral. Is the origin unstable, asymptotically stable, or stable? Explain and show as much work as needed

Exercise Solve the following linear programs graphically. Maximize Z = X1 + 2X2 Subject to 2X1...

Exercise Solve the following linear programs graphically. Maximize Z = X1 + 2X2 Subject to 2X1 + X2 ≥ 12 X1 + X2 ≥ 5 -X1 + 3X2 ≤ 3 6X1 – X2 ≥ 12 X1, X2 ≥ 0

Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}. (a) Prove...

Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}. (a) Prove that U is a subspace of F4. (b) Find a basis for U and prove that dimU = 2. (c) Complete the basis for U in (b) to a basis of F4. (d) Find an explicit isomorphism T : U →F2. (e) Let T as in part (d). Find a linear map S: F4 →F2 such that S(u) = T(u) for all u ∈...

Question