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.
(d) Write down Alex’s budget constraint.
(e) Using the equations you wrote in (c) and (d), find Alex’s
ordinary demand functions for goods 1 and 2 (in other words, find
out how much Alex will consume of good 1 as a function of p1, p2,
and m, and how much Alex will consume of good 2 as a function of
p1, p2, and m).
(f) Suppose that m = 100, p1 = 2 and p2 = 3. How much of good 1
will Alex choose to consume? How much of good 2 will Alex choose to
consume?
Suppose Alex’s preferences are represented by u(x1,x2) = x1x32. The marginal utilities for this utility function...
Suppose a consumer has quasi-linear utility: u(x1, x2) = 3.01 + x2. The marginal utilities are MU(X) = 2x7"! and MU2:) = 1. Throughout this problem, assume P2 = 1. (a) Sketch an indifference curve for these preferences (label axes and intercepts). (b) Compute the marginal rate of substitution. (c) Assume w> . Find the optimal bundle (this will be a function of pı and w). Why do we need the assumption w> (d) Sketch the demand function for good...
how did they get MRS= -x2/x1? Consider the utility function u ( 2 2) = Inc. +Inc. Suppose that the initial situation s given by Pi = 1, P2 = 2 and m = 100. Note that MU = 1 and MU2 = a) Find the consumer's optimal consumption bundle (0,2) and his utility at this consumption bundle. Solution: The budget line is 2.02 = 100 - 21 (1) Since the optimal bundle is an interior point, the tangency condition...
A consumer has preferences represented by the utility function: u(21,12)=x2? Market prices are p1 = 2 and P2 = 5. The consumer has an income m = 13. Find an expression for the consumer's demand for good 1,21 (P1). 39p1
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?
Luke's choice behavior can be represented by the utility function u(x1,x2)= x1 + x2.The prices of x1 and x2 are denoted as p1 and p2, and his income is m. 1. Draw at least three indifference curves and find its slope (i.e. MRS). Is the MRS changing depending on the points of (x1, x2) at which it is evaluated, or constant? 2. Draw a budget constraint assuming that p1 < P2. Find the optimal bundle (x1*,x2*) as a function of income and prices. 3....
The utility function of the consumer is u(x1, x2) = VX1 + X2. a) Let P1 = 2,P2 = 20 and m = 24. Calculate the optimal quantity demanded of good 1 and 2. (7 points) b) Let p. = 1,P2 = 4 and m = 100. Calculate the optimal quantity demanded of good 1 and 2. (6 points) c) Let P1 = 1,P2 = 4 and m = 4. Compared to point b), by how much would the consumer...
QUESTION 11 Suppose there are two goods, X1 and x2, and your preferences are represented by the following utility function: , u(x1,x2) = x1/4xz.! The price, P1, for good x1, is 2.5 and the price, P2, for good x2, is 3.5. You have units of money (M) of 60. Compute the consumer's optimal consumption of x1and x2 Enter x1 only here:
6. Modou has a utility function U(X1,X2) = 2X1 + X2 The prices of X1 & X2 are $1 each and Modou has an income of $20 budgeted for this two goods. a. Draw the demand curve for X1 as a function of p1.: b. At a price of p1 = $1, how much X1 and X2 does Modou consume?: c. A per unit tax of $0.60 is placed on X1. How much of good X1 will he consume now?:...
1 pts Question 2 A consumer has preferences represented by the utility function: u(x1, x2)= x x Market prices are pi = 3 and P2 = 4. The consumer has an income m 30. Find an expression for the consumer's Engel curve for good 1. x1(m). ооо D Question 3 1 pts
Question 1 (20 points). The utility function of the consumer is u(x1, x2) = x1 + x2. a) Let pı = 2 ,P2 = 20 and m = 24. Calculate the optimal quantity demanded of good 1 and 2. (7 points) b) Let p1 = 1,P2 = 4 and m = 100. Calculate the optimal quantity demanded of good 1 and 2. (6 points) c) Let P1 = 1, p2 = 4 and m = 4. Compared to point b),...