2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose...
Suppose a consumer’s preferences are represented by the utility function U(X,Y) = X2*Y. Therefore, MUx = 2XY • MUy = X2 Also, suppose the consumer has $32 to spend (M = $32), PY = 1, and that they spend all of their money on goods X and Y. Also, assume the consumer maximizes their utility subject to their budget constraint. Complete the following table: Px Quantity Demanded of X $1 $2 $3
4. Andy's utility is represented by the function U(X,Y) - XY. His marginal utility of X is MUx = Y. His marginal utility of Y is MUY = . He has income $12. When the prices are Px - 1 and Py -1, Andy's optimal consumption bundle is X* -6 and Y' = 6. When the prices are Px = 1 and P, = 4, Andy's optimal consumption bundle is X** = 6 and Y* 1.5. Suppose the price of...
1. (24 total points) Suppose a consumer’s utility function is given by U(X,Y) = X1/2*Y1/2. Also, the consumer has $72 to spend, and the price of Good X, PX = $4. Let Good Y be a composite good whose price is PY = $1. So on the Y-axis, we are graphing the amount of money that the consumer has available to spend on all other goods for any given value of X. a) (2 points) How much X and Y...
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.
Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumer has $180 to spend, and the price of X, PX = 4.50, and the price of Y, PY = 2 a. How much X and Y should the consumer purchase in order to maximize her utility? b. How much total utility does the consumer receive? c. Now suppose PX decreases to 2. What is the new bundle of X and Y that the consumer will demand?...
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...
Suppose an individual’s utility function for two goods X and Y is givenby U(X,Y) = X^(3/4)Y^(1/4) Denote the price of good X by Px, price of good Y by Py and the income of the consumer by I. a) (2 points) Write down the budget constraint for the individual. b) (4 points) Derive the marginal utilities of X and Y. c) (3 points) Derive the expression for the marginal rate of substitution of X for Y. Write down the tangency...
Suppose a consumer views two goods, X and Y, as perfect complements. Her utility function is given by U = MIN [2X, Y]. Sketch the graph of the consumers indifference curve that goes through the bundle X = 7 and Y = 8. Put the amount of Y on the vertical axis, and the amount of X on the horizontal axis. Which of the three assumptions that we made about consumer preferences is violated in this case?
1. Consider an agent with preferences represented by the utility function: u(x,y) = xy (a) For each pair of bundles, indicate which is preferred or if they are indifferent between the two. Show your work. (4 points) A (3,9) B(2,8) ------------ C(4,7) D(8,8) E (5,20) F(10,10) G(5,9) H(12,4) (b) Using the bundles in (a), make a list that orders the bundles according to the agent's preferences. Start the descending list with the most preferred bundle and end with the least...
2. (20 points) Suppose there are two consumers, A and B The utility functions of each consumer are given by: UA(X,Y) XY UB(X,Y) Min(X,Y) The initial endowments are: A: X 1; Y 1 B: X 5; Y 5 Illustrate the initial endowments in and Edgeworth Box. Be sure to label the Edgeworth Box carefully and accurately, and make sure the dimensions of the box are correct. Also, draw each consumer's indifference curve that runs through the initial endowments. Is this...