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3. Sam's preferences are represented by the following utility function: U(x, y)-min(4x, 2y a. Are any...
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.
Assume that an individual’s preferences is represented by the following utility function: ?(?, ?) = (?^1/3)*(y^2/3) a. What could you tell about the type of x and y? (“good” , “bad” or a “neuter”) b. Derive the equation for his/her indifference curve for utility level of 100? c. Derive marginal utility of x and marginal utility of y as a function of x,y. d. Does goods x and y exhibit diminishing marginal utility, constant marginal utility, or increasing marginal utility?...
3. Suppose the utility function for two goods, x and y, is: U = U(x,y) = xłyż. a. Graph the indifference curve for U = 10. b. If x = 5, what must y equal to be on the U = 10 indifference curve? What is the MRS at this point? c. Derive a general expression for the MRS for this utility function. Show how it can be interpreted as the ratio of the marginal utilities. d. Does this individual...
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
Suppose a consumer’s preferences over goods 1 and 2 are represented by the utility function U(x1, x2) = (x1 + x2) 3 . Draw an indifference curve for this consumer and indicate its slope.
Molly consumes two goods, good x and good y and her preferences are represented by the utility function U (x, y) = 1/2x^2 + 4y. 1. Draw (sketch) Molly’s indifference curves for U(x,y) = 10, U(x,y) = 16, U(x,y) = 24 and for U(x,y) = 32.5. 2. Do Molly’s preferences satisfy strict monotonicity? Explain briefly 3. Do the indifference curves you’ve drawn reflect preferences that are convex? Explain briefly
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...
2. (24 points) Suppose a consumer has preferences represented by the utility function U(X,Y)- X2Y Suppose Py, and the consumer has $300 to spend. Draw the Price-Consumption Curve for this consumer for income values Px-1, Px 2, and Px- 5. Your graph should accurately draw the budget constraints for each income level and specifically label the bundles that the consumer chooses for each income level. Also, for each bundle that the consumer chooses, draw the indifference curve that goes through...
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...
Consider an individual making choices over two goods, x and y with initial prices px=5 and py= 2, with income I= 100: a) If the individual's preferences can be represented by the utility function u = 4x+ 2y; find the income, substitution and total effects of a decrease in the price of x to px= 3. b) If the individual's preferences can be represented by the utility function u = min(4x,2y); find the income, substitution and total effects of a...