Econ 302 Homework 2 -Suppose a consumer’s utility function

Econ 302 Homework #2Due in class Wednesday, February 15th, 2017.Name ______________________________________________________ID # ________________________________________________________HOMEWORK!! 1. (10 total points) Suppose a consumer’s utility function is given by U(X,Y) = X 1/2*Y1/2. Also, theconsumer has $576 to spend, and the price of X, PX = 16, and the price of Y, PY = 4.a) (2 points) How much X and Y should the consumer purchase in order to maximize her utility? b) (2 points) How much total utility does the consumer receive? c) (2 points) Now suppose PX decreases to 9. What is the new bundle of X and Y that the consumer willdemand? d) (2 points) How much money would the consumer need in order to have the same utility level after theprice change as before the price change? e) (2 points) Of the total change in the quantity demanded of X, how much is due to the substitution effectand how much is due to the income effect? 2. (16 total points) Suppose there are two consumers, A and B.The utility functions of each consumer are given by:UA(X,Y) = X1/2*Y1/2UB(X,Y) = 2X + YThe initial endowments are:A: X = 4; Y = 4B: X = 4; Y = 12a) (10 points) Using an Edgeworth Box, graph the initial allocation and draw the indifference curve foreach consumer that runs through the initial allocation. Be sure to label your graph carefully andaccurately. b) (2 points) What is the marginal rate of substitution for consumer A at the initial allocation? c) (2 points) What is the marginal rate of substitution for consumer B at the initial allocation? d) (2 points) Is the initial allocation Pareto Efficient? 3. (24 total points) Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A isgiven an initial endowment of 6 units of good X and 1 units of good Y. Consumer B is given an initialendowment of 2 units of good X and 7 units of good Y. Consumer A’s utility function is given by:UA(X,Y) = X1/2*Y1/2,And consumer B’s utility function is given byUB(X,Y) = X1/4*Y3/4.Therefore, consumer A’s marginal utilities for each good are given by:MUX = (1/2)X-1/2Y1/2MUY = (1/2)X1/2Y-1/2Also, consumer B’s marginal utilities for each good are given by:MUX = (1/4)X-3/4Y3/4MUY = (3/4)X1/4Y-1/4a) (8 points) Suppose the price of good Y is equal to one. Calculate the price of good X that will lead to acompetitive equilibrium. b) (4 points) How much of each good does each consumer demand in equilibrium?Consumer A’s Demand for X:Consumer A’s Demand for Y:Consumer B’s demand for X:Consumer B’s demand for Y: c) (2 points) What is the marginal rate of substitution for consumer A at the competitive equilibrium? d) (10 points) Illustrate the situation in an Edgeworth Box. Be sure to label your box carefully andaccurately. Identify the initial endowment and label it W. Identify the competitive equilibrium and labelit D. Draw the budget constraint that each consumer faces and identify the values where it intercepts theperimeter of the Edgeworth Box (there are two different intercepts to identify).