Exercise 1. Suppose that there are two goods X and Y. Consider three bundles created of these goods: A = (2, 3) (2 units of good X and 3 units of good Y), B = (3, 2) and C = (3, 3). Which of the three properties of consumer preferences (completeness, transitivity or more is better) if any are violated in each of the following cases. Please Explain:
a) consumer strictly prefers A to B, strictly prefers A to C and strictly prefers B to C;
b) consumer strictly prefers A to B, strictly prefers C to A and strictly prefers B to C;
c) consumer strictly prefers A to B, is indifferent between A and C and strictly prefers C to B;
d) consumer strictly prefers B to A, strictly prefers C to A and does not know how to compare B and C;
e) consumer strictly prefers B to A, strictly prefers C to A and strictly prefers C to B.
Exercise 2. Please label your graphs carefully and accurately. Use a different graph for each change of the budget constraint.
a) Graph the budget constraint for a consumer who can buy either of two goods, X and Y . The price of good X is $4 per unit, and the price of good Y is $5 per unit, and the consumer has income M =$20 to spend. (Put good X on the horizontal axis and good Y on the vertical axis).
b) What is the slope of the budget constraint?
c) Suppose that the price of good Y decreases to $4. Use a graph to show how the budget constraint changes. What is the slope of a new budget line?
d) Suppose the price of good Y is $5, and the price of good X increases to $5. Repeat part c) of the problem.
e) Now suppose the prices return to their original value, but the consumer has only M = $10 to spend. Use a graph to show how the budget constraint changes. Explain why the slope of budget constraint is the same as in part b).
f) Now suppose that prices and income M all doubled comparably to ones in part a). Explain how these changes a↵ect the budget constraint.
Exercise 3. For each of the fol lowing three situations (a - c), use a graph to indicate the reference bundle and accurately draw the indi↵erence curve that goes through that bundle. Be sure to label you graph carefully and accurately. In all cases put the amount of good X on the horizontal axis, and the amount of good Y on the vertical axis.
a) The consumer’s utility function is given by U(X, Y )= X * Y2, and thereference bundle is X = 4 and Y = 4.
b) Suppose that consumer is making barstools. Let X be the number of legs and Y be the number of seats. Each stool must have 3 Legs and one Seat. Consumer gains utility only from the number of barstools that he(she) makes. Any leftover Legs or Seats give him no extra utility. The reference bundle is X = 3and Y = 4 and utility at this bundle is U =3.
c) Suppose that products X and Y are perfect substitutes. More precisely, each unit of good X can be substituted by 3 units of good Y without change of the consumer’s utility. Reference bundle is X = 2and Y = 3. Utility at this bundle is U‾ =11.
d) For part b) and c) specify the functional form of the corresponding utility functions.
Exercise 4. For each of the following situations, ?nd the consumer’s optimal bundle. Also, for each case, draw the consumer’s budget constraint, indicate the optimal bundle on the graph, and accurately draw the indifference curve that runs through the consumer’s optimal bundle. Be sure to show your work.
a) U(X, Y )= X2*Y .The consumer has $12 to spend and the prices of the goods are PX =$2 and PY = $4. Note that the MUX =2XY and the MUY = X2.
b) U(X, Y )= MIN{2X, Y}. The consumer has $42 to spend and the prices of the goods are PX =$2 and PY =$2.
c) U(X, Y )=2 * X + Y .The consumer has $40 to spend and the prices of the goods are PX = $5 and PY =$1.