Homework Answers
The Marginal Rate of Substitution represents the rate of exchange between good X and good Y. It shows the amount of Y which the person is willing to trade to get an additional unit of good X. The answer to the above question is option a which can be answered in the following manner:
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4. An individual has preferences represented by the utility function U(x,y)=(x12+yızg Which of the following statements...
3. Originally, the price of X is $150 and the price of Y is S50. If the price of X increases by $20 and the price o...
3. Originally, the price of X is $150 and the price of Y is S50. If the price of X increases by $20 and the price of Y increases by S10, the new budget line will a. move outward and be parallel to the old budget line b. move outward and become steeper c. move inward and become steeper d. move outward and become flatter e. move inward and become flatter x"2 + 1n0) 4. An individual's preferences are represented...
2. An individual's preferences over food (F) and clothing (C) are represented by the utility function...
2. An individual's preferences over food (F) and clothing (C) are represented by the utility function U(F, C)FiC. She currently has 9 units of food and 8 units of clothing According to her MRS, she would be willing to give up a maximum of 4/3 units of food to obtain one more piece of clothing. a. True b. False
7. An individual's preferences are represented by the utility function Ua, y) 4xy x. Which of...
7. An individual's preferences are represented by the utility function Ua, y) 4xy x. Which of the following statements is false? a. The marginal utility of x increases as x increases, holding y constant. b. Preferences are monotonic in both goods. c. The indifference curves slope downward at a decreasing rate. d. The marginal rate of substitution ofx for y increases as y increases, holding x constarnt e. The consumer is willing to give up decreasing amounts of good y...
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)=...
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)= min[3x,2y]. Furthermore, suppose that she faces a standard linear budget constraint, with income denoted by m and prices denoted by px and p,, respectively. a) Derive the demand functions for x and y. b) How does demand for the two goods depend on the prices, p, and p, ? Explain.
Suppose utility is given by the following function: u(x, y) = xy3 Use this utility function...
Suppose utility is given by the following function: u(x, y) = xy3 Use this utility function to answer the following questions: (d) What is the marginal rate of substitution implied by this utility function? What does this mean in words? (e) How much of each good would this individual need to have to be willing to trade 1 unit of good x for 1 unit of good y (i.e. for the MRS to be equal to 1)? (f) Suppose we...
5. Assume an individual has preferences represented by the utility function U(x, y) = x1/2y1/3 Which...
5. Assume an individual has preferences represented by the utility function U(x, y) = x1/2y1/3 Which of the following statements is necessarily TRUE? Assume prices and income are positive. a. The price consumption curve as the price of x changes) slopes downward. b. The income consumption curve slopes downward. c. Cross-price elasticity of demand for good x with respect to the price of y is negative. d. Price elasticity of demand for good y is negative. (See Besanko 5.6 and...
Sally the Sleek’s preferences can be described by the utility function U(x, y) = x^2y^3/1000. Prices...
Sally the Sleek’s preferences can be described by the utility function U(x, y) = x^2y^3/1000. Prices are px = 4 and py = 3; she has an income of $80 to spend. (a) If Sally initially consumed 5 units of x and 20 units of y, how much additional utility does she get from spending one (small fraction of a) dollar more on good x? How much additional utility does she get from spending one (small fraction of a) dollar...
8. An individual's preferences are represented by the utility function Ulx, y) . Which of the...
8. An individual's preferences are represented by the utility function Ulx, y) . Which of the following statements is true? a. The marginal utility of x decreases as x increases, holding y constant. b. The marginal rate of substitution of x for y increases as the consumer substitutes x for y (i.e. more x and less y) along an indifference curve. c. The consumer needs to be compensated with (i.e. gain) increasing amounts of good x in order to be...
4. An individual has preferences over two goods (x and y) that are represented by function...
4. An individual has preferences over two goods (x and y) that are represented by function U = min{x,y}. The individual has income $60, the price of x is $4 and the price of good y is $2. (a) What kind of goods are these to the individual? (i.e. what "special case” is this?) (b) What is this individual's budget constraint? (c) What is this individual's optimal bundle of x and y? [HINT: You can't take the derivative of this...
ots) Mark has preferences that can be represented by the following utility function: U(x,y)= (18+x)(+1). Sarah's...
ots) Mark has preferences that can be represented by the following utility function: U(x,y)= (18+x)(+1). Sarah's utility function is v) 6x +60 y - 4x + 2xy - 24 y +29: Do Mark and Sarah have the same preferences? You must prove your answer. U (x, y) = 6x+60 y - 4x + 2
3. Originally, the price of X is $150 and the price of Y is S50. If the price of X increases by $20 and the price of Y increases by S10, the new budget line will a. move outward and be parallel to the old budget line b. move outward and become steeper c. move inward and become steeper d. move outward and become flatter e. move inward and become flatter x"2 + 1n0) 4. An individual's preferences are represented...
2. An individual's preferences over food (F) and clothing (C) are represented by the utility function U(F, C)FiC. She currently has 9 units of food and 8 units of clothing According to her MRS, she would be willing to give up a maximum of 4/3 units of food to obtain one more piece of clothing. a. True b. False
7. An individual's preferences are represented by the utility function Ua, y) 4xy x. Which of the following statements is false? a. The marginal utility of x increases as x increases, holding y constant. b. Preferences are monotonic in both goods. c. The indifference curves slope downward at a decreasing rate. d. The marginal rate of substitution ofx for y increases as y increases, holding x constarnt e. The consumer is willing to give up decreasing amounts of good y...
3. Suppose an individual has perfect-complements preferences that can be represented by the utility function U(x,y)= min[3x,2y]. Furthermore, suppose that she faces a standard linear budget constraint, with income denoted by m and prices denoted by px and p,, respectively. a) Derive the demand functions for x and y. b) How does demand for the two goods depend on the prices, p, and p, ? Explain.
5. Assume an individual has preferences represented by the utility function U(x, y) = x1/2y1/3 Which of the following statements is necessarily TRUE? Assume prices and income are positive. a. The price consumption curve as the price of x changes) slopes downward. b. The income consumption curve slopes downward. c. Cross-price elasticity of demand for good x with respect to the price of y is negative. d. Price elasticity of demand for good y is negative. (See Besanko 5.6 and...
8. An individual's preferences are represented by the utility function Ulx, y) . Which of the following statements is true? a. The marginal utility of x decreases as x increases, holding y constant. b. The marginal rate of substitution of x for y increases as the consumer substitutes x for y (i.e. more x and less y) along an indifference curve. c. The consumer needs to be compensated with (i.e. gain) increasing amounts of good x in order to be...
4. An individual has preferences over two goods (x and y) that are represented by function U = min{x,y}. The individual has income $60, the price of x is $4 and the price of good y is $2. (a) What kind of goods are these to the individual? (i.e. what "special case” is this?) (b) What is this individual's budget constraint? (c) What is this individual's optimal bundle of x and y? [HINT: You can't take the derivative of this...
ots) Mark has preferences that can be represented by the following utility function: U(x,y)= (18+x)(+1). Sarah's utility function is v) 6x +60 y - 4x + 2xy - 24 y +29: Do Mark and Sarah have the same preferences? You must prove your answer. U (x, y) = 6x+60 y - 4x + 2
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