Question 2 9 pts Suppose a consumer has $800 to spend on two goods, Good X and Good Y. The price of Good X is given by Py = $16. The price of Good Y is given by Py = $10. a) Consider the consumer's budget constraint. If Good X is on the horizontal axis and Good Y is on the vertical axis, where will the budget constraint intersect each axis? Put your answers in the blanks below. The budget constraint will intersect the horizontal axis at and the vertical axis at b) Calculate the Marginal Rate of Transformation (MRT) and put your answer in the blank below. MRT = Question 3 5 pts Using the budget and prices from the previous guestion, write the equation for the consumer's budget constraint. Then sketch a graph of this budget constraint, putting the quantity of Good X on the horizontal axis, and the quantity of Good Y on the vertical axis. Be sure to label your graph carefully and accurately. Note: You will upload your equation and graph, along with your work for all other questions in this exam, in a single pdf file at the end of the exam. Enter the word "Finished" into the text box below when you have written out the budget constraint equation and drawn the graph. Edit View Insert Format Tools Table B = @ N 12pt Paragraph B I U A+ v Tv @v EHv G By &~ p | owords | Question 4 8 pts Suppose a consumer's preferences are represented by the utility function U(KY) = X2Y. Therefore, MUy = 2XY - MUy = X2 Also, suppose the consumer has $120 to spend (M = $120), the price of Good X is Py = 2, and the price of Good Y is Py = 4. If the consumer maximizes utility subject to their budget constraint, how much of Good X and how much of Good Y will the consumer purchase? Put your answers in the blanks below. The consumer will purchase units of Good X. The consumer will purchase units of Good Y. Note: To earn the full 8 points for this question, you must enter the correct numbers in the blanks above AND upload your work, showing how you arrived at your answer. You will upload this work, along with your work for all the other exam questions, as a single pdf at the end of the exam. Question 5 8 pts Suppose a consumer's preferences are represented by the utility function UIX.Y) = MIN(3X, Y). Also, suppose the consumer has $240 to spend (M = $240), the price of Good X is Py = 2, and the price of Good Y is Py = 2. If the consumer maximizes utility subject to their budget constraint, how much of Good X and how much of Good Y will the consumer purchase? Put your answers in the blanks below. The consumer will purchase units of Good X. The consumer will purchase units of Good Y. Note: To earn the full 8 points for this question, you must enter the correct numbers in the blanks above AND upload your work, showing how you arrived at your answer. You will upload this work, along with your work for all the other exam questions, as a single pdf at the end of the exam. Question 6 22 pts Suppose a consumer's utility function is given by U(X, Y) = X*Y. Therefore: MUy = Y MUy = X Also, the consumer has $900 to spend, and the price of X, Py = 25, and the price of Y, Py = 9. a) How much X and Y should the consumer purchase in order to maximize their utility? b) How much total utility does the consumer receive? Utility = c) Now suppose Py decreases to 9. What is the new bundle of X and Y that the consumer will demand? At the new bundle, X = and Y = d) How much money would the consumer need in order to have the same utility level after the price change as before the price change? The consumer would need $ to maintain the same utility after the price change. ) Of the total change in the quantity demanded of X, how much is due to the substitution effect and how much is due to the income effect? The consumer's quantity demanded changes by units due to the substitution effect. The consumer's quantity demanded changes by units due to the income effect. Note: To earn the full 22 points for this question, you must enter the correct numbers in the blanks above AND upload your work, showing how you arrived at your answers. You will upload this work, along with your work for all the other exam questions, as a single pdf at the end of the exam. Question 7 15 pts Suppose a consumer's preferences are given by U(X.Y) = MIN (2X, 3Y), the price of good X (Py) is $2, and the price of good Y (Py) is $1. Consider the budget constraints that a consumer would face at these prices at the following levels of income (M): - M=$32 M=$64 - M=$96 If good X is on the horizontal axis and good Y is on the vertical axis, where will the budget constraints intersect the horizontal and vertical axes for each value of M above? Indicate this information in the blanks below: At M = $32, the budget constraint will intersect the horizontal axis at and the vertical axis at At M = $64, the budget constraint will intersect the horizontal axis at and the vertical axis at At M = $96, the budget constraint will intersect the horizontal axis at and the vertical axis at Next, solve for the consumer's optimal bundle at each value of income (M) above. In the blanks below, indicate the optimal amount of X and Y that the consumer will purchase. At M = $32, the consumer will purchase units of X and units of Y. At M = $64, the consumer will purchase units of X and units of Y. At M = $96, the consumer will purchase units of X and units of Y. Finally, sketch the income-consumption curve (ICC) for the values of M given above. To do this, carefully draw the budget constraints associated with each of the income levels, and indicate on your graph the bundle that the consumer chooses in each case. Put good X on the horizontal axis and good Y on the vertical axis. Be sure to label your graph accurately. Note: The 12 fill-in-the-blank responses above are worth 1.25 points each, for a total of 15 points. Your graph of the ICC is worth 7 points and will be scored separately as part of the next "question." You will upload your graph of the ICC, along with your work for all the other exam questions, as a single pdf at the end of the exam. Question 8 7 pts The graph you were asked to draw in the previous question will be scored here out of 7 points. (It will be evaluated for accuracy and clear labels.) As noted before, you will upload your graph, along with your work for all other questions in this exam, in a single pdf file at the end of the exam. Enter the word "Finished" into the text box below when you have finished sketching your curve with each budget constraint and optimal consumption bundle clearly labeled. Edit View Insert Format Tools Table 120t v Pargraphv | B ] U A v v Tiv F v v v B> it Question 9 5 pts Suppose a consumer has preferences represented by the utility function U(X,Y) = MIN (X,2Y). The price of good X is Py = 3, and the price of good Y is Py = 2. What is the slope of the Engel curve for good X? You will be asked to sketch a graph of this Engel curve in the next question, but for this question, just indicate the slope of the Engel curve for good X below. (Think carefully about which variable is on the horizontal axis and which variable is on the vertical axis for an Engel curve.) The slope of the Engel curve for good X is: Question 10 5pts Based on the consumer's utility function and the prices of good X and Y from the previous question, sketch the graph of the consumer's Engel curve for good X. Be sure to label your graph carefully, and include at least three points on the Engel curve. ished" into the text box below when you have drawn and labeled your graph Note: You will upload your sketch of the Engel curve, along with your work for all other questions in this exam, in a single pdf file at the end of the exam. Enter the word "Fi and identified at least three points on the curve. Edit View Insert Format Tools Table l2pt~ Pargaphv B T U A~ Z v Tv P EY G B Fv = p @ | owords | > [/ Question 11 8 pts Suppose a consumer considers good X and good Y to be perfect substitutes. They are willing to trade 6 units of good Y for 1 unit of good X. The price of good X is $5 and the price of good Y is $1. Also, assume the consumer has $50 to spend on X and Y. If the consumer maximizes utility subject to their budget constraint, how much of good X and how much of good Y will they purchase? (Hint: Consider how the MRS compares to the MRT.) The consumer will purchase units of good X. The consumer will purchase units of good Y. Note: To earn the full 8 points for this question, you must enter the correct numbers in the blanks above AND upload your work, showing how you arrived at your answers. You will upload this work, along with your work for all the other exam questions, as a single pdf at the end of the exam