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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- Take Jeremys total utility information in Exercise 6.1, and use the marginal utility approach to confirm the choice of phone minutes and round trips that maximize Jeremys utility.Would you expect total utility to rise or fall with additional consumption of a good? Why?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?
- please only do: if you can teach explain each partc: what does it mean? can you show graphs: For these to be optimal choices with such preferences, the indifference curve through a must lie entirely on or above the budget line associated with (p, w), and simi- larly for r' for the budget line associated with (p', w'). how do you know this:Because each of these bundles lies below the other budget line, this implies that the indifference curves must cross, which is impossible. can you show graphs: note that (3,1) is a conver combination of x and x', so for conver preferences must be weakly preferred to x (the less preferred bundle between a and a'). But then the bundle (3,5/3) must be strictly preferred z, contradicting that is optimal given the initial budget setWhat do we mean by well-behaved preferences? How do the indifference curves look like for suchpreferences? Provide an example, in terms of a utility function, where preferences are not well-behavedand illustrate. Provide a figure with indifference curves and a budget line where there are exactly twosolutions to the utility maximization problem.Draw a well-labeled graph that shows the substitution effect (SE), incomeeffect (IE), and total effect of good 1 and is consistent with the following: The consumerreceives $m per month and has well-behaved preferences with strictly convex indifferencecurves; the price of good 1 increases; the original utility-maximizing point is labeled at A; thenew utility-maximizing point is labeled C; the compensated budget’s utility maximizing point islabeled B; good 1 is inferior but not Giffen. Make sure to clearly state and graphically showwhether the SE, IE, and total effect of good 1 are each positive or negative. Also state if the SEor IE is higher in magnitude if possible. Good 1 needs to be on the horizontal axis.
- Assume that an individual has convex indifference curves (i.e. diminishing MRS). Suppose the individual has $3 to spend on good #1 and good #2. In addition, suppose we know that at the bundle where q1=1 and q2=1, the marginal utility of good #1 is 2 utils and the marginal utility of good #2 is 1 util. Given this information, which set of prices would this individual prefer to face? A. p1=1 and p2=2 B. p1=2 and p2=1 C. p1=2 and p2=2Question 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.Hella the Greek's preferences can be described by the utility function U(x, y) = (x^1/2 + 3^1//2)^2. (a) What is the indifference curve for a utility of 49? (b) By how much does utility increase when Hella increases consumption of good y by one (small) unit, when initially U = 49 and x = 1? (c) Holding utility constant at 49, if initially x = 1, how many additional (small) units of y does Hella have to consume if her consumption of x drops by 6 (small) units?
- 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.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?Draw some hypothetical indifference curves for John Q.Public on a diagram identical to the one you constructedfor Test Yourself Question 1.a. Approximately how much gasoline and how manyhot dogs will Mr. Public buy?b. How will these choices change if his income increasesto $140? Is either good an inferior good?c. How will these choices change if gasoline price risesto $3.00 per gallon? Test Yourself Question 1: John Q. Public spends all of his income on gasoline andhot dogs. Draw his budget line under several conditions:a. His income is $100, and one gallon of gasoline andone hot dog each cost $2.b. His income is $150, and the two prices remain thesame.c. His income is $100, hot dogs cost $2 each, andgasoline costs $2.50 per gallon. (See photo of answers for question #1)