ECON 323 - HW2
Suppose you can only consume nonnegative units of Good X and Good Y. Your utility function is U(x, y) = ln(xy) where ln() is the natural logarithm operator. Which of the following statement is NOT true? (a) The marginal utility of Good X may be positive or negative (depending on the sign of x and y). (b) The marginal utility of Good Y cannot be negative. (c) The marginal utility of Good X does not depend on the quantity of Y consumed. (d) The marginal utility of Good Y does not depend on the quantity of X consumed.
A
Envision a graph with meat on the horizontal axis and vegetables on the vertical axis. A strict vegetarian would have indifference curves that are: (a) vertical lines. (b) horizontal lines. (c) right angles. (d) upward sloping.
B
Pencils sell for 10 cents and pens sell for 50 cents. Suppose your preferences satisfy all the basic assumptions. Suppose that your budget allows you to buy 5 pens and one pencil each semester. With this consumption bundle, your MRS of pencils for pens is 3. Which of the following is true? (a) You could increase your utility by buying more pens and fewer pencils. (b) You could increase your utility by buying more pencils and fewer pens. (c) You could increase your utility by buying fewer pencils and fewer pens. (d) All the above statements can happen
B
Suppose Andy has a utility function of U(x, y) = x + y. The price of Good X is 2 and the price of Good Y is 1. Which of the following statement is optimal? (a) Andy will spend all the wealth on the consumption of Good X. (b) Andy will spend all the wealth on the consumption of Good Y. (c) There are multiple optimal solutions. (d) All above statements are incorrect.
B
Andy uses his entire budget to purchase Goods X and Y. Now he spends all his wealth on Good Y. The price of Good X is 1 and that of Good Y is 2. His marginal utility from Good X is 2 and that of Good Y is 6. Is his current consumption decision optimal? (a) No, he should increase Good X consumption and reduce Good Y consumption. (b) No, he should increase Good Y consumption and reduce Good X consumption. (c) Yes, the corner solution is best. (d) We do not have enough information to answer this question.
C
Suppose Andy has a utility function of U(x, y) = 2x + y and a wealth level of 12. The price of Good X is 2 and the price of Good Y is 1. Which of the following statement is optimal? (a) Andy will spend all the wealth on the consumption of Good X. (b) Andy will spend all the wealth on the consumption of Good Y. (c) There are multiple optimal consumption bundles. (d) All above statements are incorrect.
C
Suppose a consumer has a utility function of U(x, y) = x 2 + y 2 for x, y ≥ 0. Which of the following statements is the most likely to be true about a consumer's optimal decision? (a) Both goods are consumed. (b) No goods are consumed. (c) Only one of the goods is consumed. (d) It occurs where the indifference curve is tangent with the budget line.
C
Suppose in a two-good society with Good X and Good Y, a consumer has a utility function of U(x, y) = min{2x, y}, where x is the number of Good X the consumer consumes and y is that of Good Y. The consumer has a wealth level of 12. The price of Good X is 2 and the price of Good Y is 1. What is the consumer's utility maximization consumption bundle? (a) 4 units of Good X and 4 units of Good Y. (b) 4.8 units of Good X and 2.4 units of Good Y. (c) 3 units of Good X and 6 units of Good Y. (d) 4 units of Good X and 8 units of Good Y.
C
11. Suppose you live in a two-good society with Good X and Good Y. The fact that you spend no money on Good X: (a) implies that you do not derive any satisfaction from Good X. (b) implies that you are at a corner solution. (c) implies that MRS does not equal the price ratio. (d) Any of the above are possible.
D
5. Suppose a consumer has a utility function of U(x, y) = x 2 +y 2 . Which of the following basic assumption on preferences is violated? (a) Completeness. (b) Transitivity. (c) More is better than less. (d) Diminishing marginal rate of substitution
D
Consider the following three market baskets: Basket A: 6 units of food and 3 units of clothing, Basket B: 8 units of food and 5 units of clothing, Basket C: 5 units of food and 8 units of clothing. If preferences satisfy all four of the basic assumptions, which of the following statement is optimal? (a) A is on the same indifference curve as B. (b) B is on the same indifference curve as C. (c) A is preferred to C. (d) B is preferred to A.
D
If prices and income in a two-good society double, what will happen to the budget line? (a) The intercepts of the budget line will increase. (b) The intercepts of the budget line will decrease. (c) The slope of the budget line may either increase or decrease. (d) There will be no effect on the budget line
D
When you maximize utility, you find that your MRS of Good X for Good Y is greater than PX/PY . It is mostly likely that (a) your preferences are incomplete. (b) your preferences do not satisfy transitivity. (c) you are not consuming Good X. (d) you are not consuming Good Y.
D
Which of the following statement is NOT true? (a) If Good X and Good Y are perfect substitutes and the slope of indifference curves is always -1, then you will only consume the good with the lowest price. (b) If Good X and Good Y are perfect substitutes and the slope of indifference curves is always -1, then you will only consume some quantity of both goods if the prices of them are equal. (c) If Good X and Good Y are perfect complements and the kinks of your indifference curves follow the 45-degree line. As long as your income and the prices are positive, you will choose a consumption bundle at a kink. (d) If Good X and Good Y are perfect complements and the kinks of your indifference curves follow the 45-degree line. You will consume Good X and Good Y at some point along the 45-degree line where the MRS equals the price ratio.
D
