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26 Feb 2018

1. Consider utility function U(x₁, x₂)=a(x₁)^c/c+ b(x₂)^c/c, where a, b, and c are parameters.

a. Is it homothetic? I.e., does MRS stay constant along a ray from the origin?

b. Does it have a diminishing rate of marginal substitution for some values of the parameters?

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mauveporpoise966Lv1

2 Jun 2021

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Related questions

1. Problem associated with first video: Increasing transformation Consider the following utility function u(x1, x2) = x1x2.
(a) Calculate the MRS for this utility function.
(b) Compute and compare the MRS for the bundles (x1, x2) = (1, 2) and (x1, x2) = (2, 1). What does this comparison tell us about the preferences of the person with this utility function?
(c) Consider the bundles (x1, x2) = (4, 4) and (x1, x2) = (1, 9). Which bundle is the most preferred (i.e. yield the highest utility)?
(d) Consider the following function f(x) = âx and then define a new utility function v(x1, x2) = f (u(x1, x2)).
i. Show that v(x1, x2) is an increasing transformation of u(x1, x2).

ii. Answer, without calculating, which of the bundles in question c) above will be the
most preferred according to v(x1, x2).

iii. Calculate the MRS for v(x1,x2). How it compares with the MRS for u(x1,x2). Why?

indigohornet395

1. Suppose the price of x₁ is $20 and the price of x₂ is $4. If good x₁ is on the horizontal axis, what is the slope of the consumer's budget constraint?

a. -0.20

b. -0.25

c. -5.0

d. -0.2

e. -4.0

f. -20.0

2. Suppose the price of x1 is $5 and the price of x2 is $1 and Toni's income is $20. Suppose Toni gets a $5 gift card that can only be used for the purchase of x1 and there is no resale value of the gift card. With the gift card, the commodity bundle (1,20) is on Toni's budget constraint.

True

False

3. Tiffany's utility function is given by the formula U(x1, x2) = min{20x1, 10x2}. If x1 = x2, which commodity will have a greater marginal utility?

A. Both x1 and x2 have the same marginal utility

B. It is not possible to determine which commodity has higher marginal utility

C. x2

D. x1

4. For U(x₁,x₂) = 6x₁^1/3 + x₂, preferences are

a. consistent with diminishing marginal rate of substitution.

b. consistent with constant marginal rate of substitution.

c. consistent with increasing marginal rate of substitution.

d. not consistent with a utility function.

5. For a utility function of the form U(x₁,x₂)=min{5x₁,10x_2}, the individual will have excess x₂ for commodity bundles where

a. x2>2x1 b. x2>5x₁

c. x₂>0.5x₁ d. x2>10x₁

6. Matt enjoys Fuji and Gala apples and finds 1 Fuji apple to be just as good as 4 Gala apples.

a. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=0.25F+G

b. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=F+4G

c. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=4F+.25G

d. Matt's preferences over Fuji (F) and Gala (G) apples can be represented by the utility function U(F,G)=4F+G

e. Both A and B

f. Both C and D

amaranthelk637

The consumer is choosing between two goods- good1 and good2. Good 1 is priced at $2 and good 2 is priced at $3. The consumer has a total of $600 to spend on both the goods.

1. Let the utility function of the consumer be U (X1, X2) = X1^(1/2)X2^(1/2).

a) Calculate the Marginal rate of substitution.