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- Naomi has the following utility function, U(x, y) = x + 3y. Suppose that py > 4pr. What are the hicksian demands of x and y? (a) (hr, hy) = (U, 0) (b) (h, hy) = (0, U/3) (c) (ha, hy) = (U, U/3) (d) (ha, hy) = (In (U), In (U/3))Ken has a utility function for tennis rackets (X) and tennis balls (Y) of the form U(X,Y)=min(4X,2Y). His Hicksian demand for X is given by :Joan has the following utility function: u(x, y) (a) Find Jane's marshallian demands. 5x + 3y.
- For the utility function U = Qx0.15Qy(1-0.15) find the trade-off rate between good X and good Y at Qx= 4 and Qy=19Suppose there are two agents Ahmet and Berk in an economy, and both consume two goods X and Y. Also assume that price of X is 2 YTL and Y is the numeraire good, thus price of Y is 1 YTL. Ahmet and Berk has the following utility functions:UAhmet (XA,YA)= 5ln(XA)+ln(YA)UBerk (XB,YB)= XB0,5 YB0,5a. Now assume that both X and Y are private goods. Write down the optimality condition for both agents. Then, write down the optimal level of X as a function of Y for both agents.b. Now assume that X is a public good, but Y is a private good. Write down the optimality condition for good X. Then, write down the optimal level of X as a function of Y for both agents.c. Now compare the consumption levels for X in parts a and b.James works for a delivery company in College Station where he consumes bundles of two commodities x and y. Prices in College Station are px=1 and py=5. He is offered a transfer to Dallas where prices are px=2 and py=5; James is guaranteed a salary in Dallas with which he would be able to buy exactly what he buys in College Station. James’s utility function is U(x,y)=x1/3y2/3 and his income in College Station is $2500. What happens to James’ utility if he accepts the transfer (James’ utility maximization is always characterized by the tangency rule)?
- For the utility function U = Qx0.31Qy(1-0.31) find the trade-off rate between good X and good Y at Qx= 7 and Qy=17 Please enter your response as a positive number with 1 decimal and 5/4 rounding (e.g. 1.15 = 1.2, 1.14 = 1.1).Suppose that you want to derive and draw the demand function for Mr. Seong (also known as Player 456). Mr. Seong likes to eat Dalgona Candy (D) and drink Soju (S). Suppose Mr. Seong's preferences can be expressed as U(D,S) = (D)º.² · (S)0.8. Suppose further the price of a Dalgona Candy is 2 (pº = 2) and the price of Soju is 4 (ps = 4). Mr. Seong has a budget of 100 to spend on the two goods. A. Use the substitution method to find Mr. Seong's optimal choice of Dalgona Candy and Soju. B. Use any method to find Mr. Seong's optimal choice of Dalgona Candy and Soju if the price of Soju was 5 (instead of 4). Feel free to use the Cobb-Douglas short-cut method if you want. C. Use your answers to A and B to derive the demand for Soju in the two diagrams below. That is, draw the change in the top diagram and then use your result to derive the demand curve in the bottom diagram. Several hints have been drawn in the diagram below. D 50 10 ps 5 4 20 20 25 S FYI: The Cobb-Douglas short-cut can be…uestion1:Donna and Jim are two consumers purchasing strawberries and chocolates. Jim’s utility function is U (x, y) = xy and Donna’s utility function is U (x, y) = x2y where x denotes strawberries and y denoteschocolates. Jim’s marginal utility functions are MUX=y and MUy=x while Donna’s are MUX=2xy and MUy=x2. Jim’s income is $100, and Donna’s income is $150. What is the optimal bundle for Donna if the price of strawberries is $2 and the price of chocolate is $4? What is the optimal bundle for Jim, and for Donna, when the price of strawberries rises to $3?Question2:Consider a one-period eco
- Sarah has the following utility function: u(x, y) = 10x + 12y.For the utility function U = Qx^0.84Qy^(1-0.84) rate between good X and good Y at Qx= 7 and Qy=19 find the trade-offRoger's utility function is Cobb-Douglas, U=B^0.80 Z^0.20 Y the price of B is P_B and the price of Z is P_z. Derive his demand curves. B= and Z=