Answer : The answer is option b.
The given utility function is :
u = q1 + 2q2
Here q2 is the double than the q1.
The utility function of option b is :
u = 4q1 + 8q2
Here also q2 is double than the q1.
This means that the utility function of option b and given utility function both of them shows the same preferences. Therefore, option b is correct.
1. Suppose that preferences are represented by u q1 2q2. Which of the following utility functions...
4. Suppose preferences are represented by the Cobb-Douglas utility function, u(x1x2) = xx-. a) Show that marginal utility is decreasing in X and X2. What is the interpretation of this property? b) Calculate the marginal rate of substitution c) Assuming an interior solution, solve for the Marshallian demand functions.
Suppose Bill has preferences over chocolate,x, and ice cream,y, that are represented by the Cobb-Douglas utility function u(x, y) =x^2 y. 1. Write down two other Cobb-Douglas utility functions, besides the one above, that represent Bill’s preferences. 2. Write down two more Cobb-Douglas utility functions that do NOT represent Bill’s prefer- ences. 3. Draw 3 indifference curves that represents Bill’s preferences at 3 different levels of satsifaction. 4. What is Bill’s marginal rate of substitution between chocolate and ice cream?...
For each of the following 5 utility functions assume that α>0 and β>0 U^A (x_1,x_2 )=x_1^α x_2^β U^B (x_1,x_2 )=αx_1+βx_2 U^C (x_1,x_2 )=αx_1+βlnx_2 U^D (x_1,x_2 )=(α/β)lnx_1+lnx_2 U^E (x_1,x_2 )= -αlnx_1-βlnx_2 Calculate the MRS for each utility function Which utility function represent a preference with linear indifference curves? Which of these utility functions represent the same underlying tastes? Which of these utility functions does not satisfy the monotonicity assumption? Which of these utility functions represent...
Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function are MU1 = x23 and MU2 = 3x1x22. (a) Show that Alex’s utility function belongs to a class of functions that are known to be well-behaved and strictly convex. (b) Find the MRS. [Note: find the MRS for the original utility function, not some monotonic transformation of it.] (c) Write down the tangency condition needed to find an optimal consumption bundle for well-behaved preferences....
Suppose a consumer’s preferences over goods 1 and 2 are represented by the utility function U(x1, x2) = (x1 + x2) 3 . Draw an indifference curve for this consumer and indicate its slope.
2. (25%) Consider a consumer with preferences represented by the utility function: u(x1, x2) = min {axı, bx2} If the income of the consumer is w > 0 and the prices are p1 > 0 and P2 > 0. (a) Derive the Marshallian demands. Be sure to show all your work. (b) Derive the indirect utility function. (c) Does the utility function: û(x1, x2) = axı + bx2 represent the same preferences?
Cobb-Douglas Preferences: Cobb-Douglas preferences on the consump- tion set R2+ can be represented by a utility function of the form U (q1,q2) = Aq1αq2β, where A > 0, α ∈ (0,1), and β ∈ (0,1) are fixed parameters. 1. If we assume that preferences are ordinal, explain why these precise preferences are also represented by the utility function U(q ,q )=qγq1−γ, 1212 whereγ= α .Isγ∈(0,1)? (α+β) 2. If we assume that preferences are ordinal and restrict attention to the consumption...
Do the following utility functions represent the same
preferences? Please provide your reasoning
(a) u(X1; XY) = X1 X2, V(X; X2) = 3(x] X2)2 +6 (b) u(x]; X») = X1X2, V(X]; X2) =-3(x1x2)2 +6 (c) u(x1,x2)=X]X2,v(x1,x2)=lnx1 +lnx2 (d) u(x]; X) = X1 X2, V(X1; X2) = x1 + x2
Suppose the preferences of an individual are represented by a quasilinear utility function: U (x, y) = ln(x) + y (a)Suppose px =1, py =5 and I = 20. The price of x increases to 2 (px = 2). Calculate the changes in the demand for x. What can you say about the substitution and income effects for small changes in the price of x? What happens to the demand for y? Is y a gross substitute? (b)Now suppose px...
ots) Mark has preferences that can be represented by the following utility function: U(x,y)= (18+x)(+1). Sarah's utility function is v) 6x +60 y - 4x + 2xy - 24 y +29: Do Mark and Sarah have the same preferences? You must prove your answer. U (x, y) = 6x+60 y - 4x + 2