This problem set is partitioned into two sections. Section I require the application of consumer theory to analyze consumer choice. Section II requires the use of consumer theory to derive the consumers Marshallian demand curve.

Section I: Consumer Choice (50 points)A. The federal government is interested in purchasing two types of antipollution equipment. After extensive tests, government officials are convinced that three units of type-I equipment are as effective as one unit of type-II equipment. Assuming that the officials want to reduce pollution (i.e. government official derive satisfaction from reducing pollution), draw their indifference curves for the two types of equipment. For ease of graphic presentation limit the quantity of both goods in the range from zero to 30 units. Hint, the indifference curve is NOT convex to the origin. (25 points)B. Now assume the government has $30 million to spend on either type-I equipment, type-II equipment, or a combination of both. On the same figure you drew for part A, draw the relevant budget line and indicate the optimal choice of type of equipment if a unit of type-I equipment cost $1 million and a unit of type-II equipment costs $6 million. (25 points)

Section II: Application of consumer utility (50 points)Tom Bradys utility function is as follows:U= 10X2Y2Where, X, is the quantity of good X consumed, Y, is the quantity of good Y consumed and, U, is Toms utility function.A. If Tom spends all of his income, B, on goods X and Y what is the general form of his budget constraint? (Hint: the budget constraint should be specified such that budget is the sum of the expenditures on good X and Y.) Also note that you should use notation such that, PX, is the unit price of good X, and PY, is the unit price of good Y. (5 points) B. What is Toms marginal rate of substitution? Note his respective marginal utilities are MUX =20XY2 and MUY = 20X2Y. Please show all of your work to receive full credit. (10 points)C. Now suppose that Toms income is $500, and that the price of good X is 1 and the price of good Y is 2 what is the optimal amount of good X and good Y that he should purchase? Use the information from above to help answer this question. Please show all of your work to receive full credit. (10 points)D. Suppose the price of good X has increased to 2 and Toms income and the price of good Y has remained the same. Now, what is the optimal amount of good X and good Y that he should purchase? Please show all of your work to receive full credit. (10 points)E. Plot Toms demand curve for good X using your answers from questions 1D and 1E. Feel free to use EXCEL to construct your graph (10 points).F. Given the results you found for questions 1D and 1E, are goods Y and X complements, substitutes or neither? Please explain(5 points).