econ 302 homework 1

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Econ 302 Exam 1 McLeodNAME ______________________________________________PSU ID #______________________________________________PLEASE ANSWER ALL QUESTIONS IN THE SPACE PROVIDED.1. (12 total points) Suppose a consumer’s utility function is given by U(X,Y) = MIN(2X,Y). The consumer has $60 to spend (M = $60) and the price of Y is PY = 1. a) (8 points) Draw the Price Consumption Curve for the following values of PX: PX = 1; PX = 2; PX = 3. Be sure to label your graph carefully and accurately. You do not need to draw the indifference curves that run through each of the consumer’s optimal bundles, but your graph should include accurately drawn budget constraints associated with each level of income, and show the consumer’s optimal bundle for each budget constraint.When PX = $1, the budget constraint will have a vertical intercept (Y-axis) of 60 and a horizontal intercept (X-axis) of 60. The bundle chosen is (X = 20, Y = 40). When M = $2, the budget constraint will have a vertical intercept (Y-axis) of 60 and a horizontal intercept (X-axis) of 30. The bundle chosen is (X = 15, Y = 30). When M = $3, the budget constraint will have a vertical intercept (Y-axis) of 60 and a horizontal intercept (X-axis) of 20. The bundle chosen is (X = 12, Y = 24). PXX Y1 20 402 15 303 12 24- Each Budget Constraint: 1 point (both intercepts must be correct) (3 total points)- Each Bundle: 1 point (both X and Y values must be correct) (3 total points)- Labeling Each Axis: 1 point each (2 total points)b) (4 points) Sketch the graph of the consumer’s Engel curve for good X.The Demand Curve is the graph of the first two columns above. PX is on the vertical axis, and X is on the horizontal axis. - Each combination of PX and X: 1 point (3 points total)- Labeling the graph: 1 point- NOTE: IF THE GRAPH IS NOT LABELED CORRECTLY, IT IS NOT A Demand CURVE, SO 0 POINTS.2. (8 total points) Suppose there are two consumers, A and B. There are two goods, X and Y. There is a TOTAL of 8 units of X and a TOTAL of 8 units of Y. The consumers’ utility functions are given by:UA(X,Y) = 3X + YUB(X,Y) = X*YFor each of the following allocations, answer True if the allocation is Pareto Efficient, and FALSE if the allocation is not Pareto Efficient. i) Consumer A gets 6 units of X and 2 units of Y, and Consumer B gets 2 units of X and 6 units of Y.TRUEii) Consumer A gets 4 units of X and 6 units of Y, and Consumer B gets 4 units of X and 2 units of Y.FALSEiii) Consumer A gets 7 units of X and 0 units of Y, and Consumer B gets 1 units of X and 8 units of Y.FALSEiv) Consumer A gets 4 units of X and 0 units of Y, and Consumer B gets 4 units of X and 8 units of Y. TRUE3. (12 total points) Suppose there are two consumers, A and B, and 2 goods, X and Y. The utility functions of each consumer are given by:UA(X,Y) = 2X+YUB(X,Y) = MIN(4X,Y)The initial endowments are: A: X = 7; Y = 4B: X = 1; Y = 4a) (8 points) Using an Edgeworth Box, illustrate the initial endowments. Also, for each consumer, draw the indifference curve that runs through their bundle. Be sure to label your graph carefully and accurately. In Classb) (4 points) Is the initial allocation Pareto Efficient?YES4. (24 total points) Suppose there are two consumers, A and B, and two goods, X and Y. Consumer A is given an initial endowment of 3 units of good X and 8 units of good Y. Consumer B is given an initial endowment of 3 units of good X and 4 units of good Y. Consumer A’s utility function is given by:UA(X,Y) = X4*Y,And consumer B’s utility function is given byUB(X,Y) = X*Y.Therefore, consumer A’s marginal utilities for each good are given by:MUX = 4X3YMUY = X4Also, consumer B’s marginal utilities for each good are given by:MUX = YMUY = Xa) (8 points) Suppose the price of good Y is equal to one. Calculate the price of good X that will lead to acompetitive equilibrium.PX = 4b) (4 points) How much of each good does each consumer demand in equilibrium?Consumer A’s Demand for X: 4Consumer A’s Demand for Y: 4Consumer B’s demand for X: 2Consumer B’s demand for Y: 8c) (2 points) What is the marginal rate of substitution for consumer A at the competitive equilibrium?MRSA = -4d) (10 points) Illustrate the situation in an Edgeworth Box. Be sure to label your box carefully and accurately. Identify the initial endowment and label it W. Identify the competitive equilibrium and label it D. Draw the budget constraint that each consumer faces and identify the values where it intercepts the perimeter of the Edgeworth Box (there are two different intercepts to identify). The Edgeworth Box should have the following dimensions:X-dimension = 6; Y-dimension = 12. I will illustrate this in class. The Budget constraint should intercept B’s X-axis at 4 . It should also intercept A’s X-axis at 5.Dimensions: 2 pointsW: 2 pointsD: 2 pointsBudget constraint intercepts: 2 points (1 point each)Labeling: 2 points (1 point for labeling the x and y axes; 1 point for labeling the graph with A and B)5. (8 points) Suppose a consumer’s utility function is given by U(X,Y) = 3X +Y. The consumer has $48 to spend (M = $30). The price of the goods are PX = 8 and PY = 3. Draw the consumer’s budget constraint and identify the optimal bundle that the consumer should choose in order to maximize her utility. Also, draw the indifference curve that runs through this bundle. Your graph should be labeled carefully and accurately.- The Budget Constraint has Y-Intercept = 16 and X-Intercept = 6. - The Optimal Bundle is X* = 6; Y* = 0.- The Indifference Curve has Y-Intercept = 18 and X-Intercept = 6- Budget Constraint: 2 points (both intercepts must be correct). - Optimal Bundle: 2 Points (both X and Y values must be correct). - Indifference Curve: 2 points (both intercepts must be correct). - Labeling Graph: 2 points (1 point for each axis).6. (20 total points) Suppose a consumer’s utility function is given by U(X,Y) = X*Y. Also, the consumerhas $64 to spend, and the price of X, PX = 16, and the price of Y, PY = 1.a) (4 points) How much X and Y should the consumer purchase in order to maximize her utility?X* = 2; Y* = 32b) (4 points) How much total utility does the consumer receive?U = 64 (Okay if consistent with a)) c) (4 points) Now suppose PX decreases to 1. What is the new bundle of X and Y that the consumer will demand?X** = 32; Y** = 32d) (4 points) How much money would the consumer need in

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