2. INDIFFERENCE MAPS Sheldo19 For each scenario, GRAPH two indifference curves U1 and U2 (U1 < U2) to represent the following consumers' preferences for goods X and Y. a. Andy insists on consuming exactly two units of X for each unit of Y. Y 2 un its X 2. DIZza b. Billy always gets twice as much satisfaction from an extra unit of Y as he gets from an extra unit of X. Y MRS=½
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- I like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like?Five consumers have the following marginal utility ofapples and pears:Marginal Utilityof ApplesMarginal Utilityof PearsClaire 6 12Phil 6 6Haley 6 3Alex 3 6Luke 3 12The price of an apple is $1, and the price of a pear is$2. Which, if any, of these consumers are optimizingtheir choices of fruit? For those who are not, howshould they change their spending?ceriuppose that Isaiah has a weekly fixed budget and spends it all on haircuts and ice cream. At his current combination arof consumption, the marginal utility of the last dollar spent on haircuts is greater than the marginal utility of the last dollar spent on ice cream. Has Isaiah maximized his utility? A C E Yes, because changing his current consumption combination will reduce his total utility B No, because he can increase his total utility by purchasing more haircuts and D fewer ice creams Yes, because he has purchased 2 goods in proportion so that he can get- the maximum utility from each Yes, because he purchased the maximum possible with a limited budget No, because he can increase his total utility by purchasing fewer haircuts and more ice creams
- Intialy mr. John is at equilibrium such that the last dollar spent on each of several products gives hi identical marginal utility i.e MUorange/porange=MUApple/pApple=...=MUn/pn where Mu orange =aditional utility derived from consuming one more unit of Apple ,pApple=price of a unit of Apple etc Q.how will Mr.Jhon react if the price of orange and other goods remain constant?and how can the equilibrium be restored?A consumer’s preferences between goods x and y are representedby the utility function u(x, y) = 2min{x, y}+10. Suppose this consumer hasincome of $16, the price of good x is $3 and the price of good y is $1. Suppose the price of good x increases to $7 while the price of good y andthe consumer’s income stay constant. Calculate the magnitudes of the compensating and the equivalent variations. Explain what each measures.39. The following chart shows thec total utility-that Ammar receives from çonşuming various amounts-of chocolate.candy bars each day: Number candy, bars consumed për đay Total'utility 1' 40- 2 70 90 100 4. 80 Which of the following statements about Ammar's marginal utility is correct? Hiş marginal utility from the first candy bar is greater-than his marginalutility from the second candy' bar
- 26. Danny has $12 to spend on two goods: pies and soda. The price of a pie is $4, and the price of a can of soda is $2. To maximize his utility, Danny buys A) the combination that gives him equal total utility from pies and soda B) 2 pies and 2 cans of soda C) oniy sodas because they are iess expensive D) the combination that gives him the same marginai utility per doillar spent on pies as on sodaTotal utility is maximized in the consumption oftwo goods by equating thea. prices of both goods for the last dollar spenton each good.b. marginal utilities of both goods for the lastdollar spent on each good.c. ratios of marginal utility to the price of bothgoods for the last dollar spent on each good.d. marginal utility of one good to the price ofthe other good.Question 3Draw indifference curves for the following sets of preferences and indicate the direction inwhich the individuals’ satisfaction (or utility) is increasing. Be specific about slopes when itis necessary. Assume for both parts (a) & (b) that soft drinks are measured on x-axis andhamburgers on the y-axis. (a) Mary always gets twice as much satisfaction from an extra hamburger as she does froman extra soft drink. (b) Bob loves soft drinks but dislikes hamburgers.
- Mylie’s total utility from singing the same song over andover is 50 utils after one repetition, 90 utils after tworepetitions, 70 utils after three repetitions, 20 utils afterfour repetitions, 250 utils after five repetitions, and 2200utils after six repetitions. Write down her marginal utilityfor each repetition. Once Mylie’s total utility beginsto decrease, does each additional singing of the songhurt more than the previous one or less than the previousone?a. A consumer is willing to trade 3 units of x for 1 unitof y when she has 6 units of x and 5 units of y. She isalso willing to trade in 6 units of x for 2 units of y whenshe has 12 units of x and 3 units of y. She is indifferentbetween bundle (6, 5) and bundle (12, 3). What is theutility function for goods x and y? Hint: What is theshape of the indifference curve?b. A consumer is willing to trade 4 units of x for 1 unitof y when she is consuming bundle (8, 1). She is alsowilling to trade in 1 unit of x for 2 units of y when sheis consuming bundle (4, 4). She is indifferent betweenthese two bundles. Assuming that the utility function isCobb–Douglas of the form U (x, y) = xα y β, where α andβ are positive constants, what is the utility function forthis consumer?c. Was there a redundancy of information in part (b)? Ifyes, how much is the minimum amount of informationrequired in that question to derive the utility function?(a) I like to consume two olives with every shot of vodka. If Ihave more olives or more vodka than that ratio, I just toss theextra in the trash (they are perfect complements). What is myutility function? What do my indifference curves look like? (b) I like drinking Smirnoff and Stoli Vodka, but I really only careabout the total amount of alcohol I get out of it. They areperfect substitutes. Smirnoff is sold in liter bottles that are100 proof (that’s 50% alcohol). Stoli is sold in liter bottlesthat are 80 proof (40% alcohol). What is my utility functionfor bundles of these two vodkas? What do my indifferencecurves look like? (c) Antonin notices he is currently spending all of his money ona bundle (x1, x2) where his marginal rate of substitution isgreater than the relative prices (p1/p2). Can Antonin reach abundle on a higher indifference curve with his current income?Explain clearly and provide a graph with your response. * Note that in (a) and (b), there are different utility…