
6. (10 points) Wendy's utility is given by u(x1, x2) = VX1 + 1X2 + 4....
(10 points) Wendy's utility over consumption bundles (x1, x2) is given by u(x1,x2) = VX1 + 21X2. If the price of good 1 is $2/unit, the price of good 2 is $1/unit and income is $120, what is Wendy's optimal consumption of Good 2? (You can use the 5 step method to solve this problem). (10 points) When u(x1, x2) = min ), at prices and income P1, P2, and I, demand for good 1 is given by xi (P1,...
1. (20 points) Mac has utility over x; and x2 given by u(x1, x2) = min . If P. = $1. P. = $1. and I = $100. find the value of xı* (Hint: This is Leontief utility, the kind with right-angled indifference curves) 2. (10 points) If P, = $4, P2 = $2, and I = $20, and my utility is given by u(x1, x2) = 4x1 + 3x2, find x* (Note: I'm asking for optimal consumption of Good...
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...
Christine has utility given by u(x1, x2) = 1X1 + 4/X2. If P, = $10, P, = $20, and 1 = $180, find Christine's optimal consumption of good 1. (Hint: You'll need to use the 5 step method to answer this question). Using the information from question 7, find Christine's optimal consumption of good 2
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)....
What are the marginal utilities of x1 and x2 given the following utility functions, then find the MRS: U(x1, x2) = 4 x1 + 8 x2 U(x1, x2) = (x1 + 2)(x2 + 1) Example. To find the marginal utility for x1, think about how a 1 unit increase in x1, keeping all else constant, will change the amount of utility U. Once you have the marginal utilities for both, you can calculate the MRS.
Problem 1 Suppose that a person has a utility U = 3x1 + 9x2, where x1 is the quantity of good 1 consumed, and x2 is the quantity of good 2 consumed. Answer the following questions, and write your answers in the Answer Sheet. Find the equation representing the person’s indifference curve for a level of utility represented by the constant K. (Hint: Isolate x1 on one side.) Find the person’s marginal utility with respect to good 1 (MUx1 )....
Robin has the utility function U ( x1 , x2)= 1/ 5 ln ( x1 )+ 4 /5 ln ( x2 ) . a) Set up the Lagrangian and derive an expression for the marginal rate of substitution and calculate the Marshallian demand for both goods. b) What will happen to Robin’s share of expenditures on good x1 if the price of good one, p1 , increases. Verify your conclusion formally!
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...
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....