Your friend tells you that although she has a largeamount of M&Ms and just a few Skittles, she wouldstill be willing to give up the rest of her Skittles, just toget one last M&M. What characteristic of indifferencecurves is your friend going against?
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Your friend tells you that although she has a large
amount of M&Ms and just a few Skittles, she would
still be willing to give up the rest of her Skittles, just to
get one last M&M. What characteristic of indifference
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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?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?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=2
- Consider preferences for cookies (on the x-axis) and ice cream bars (on the y-axis) fordifferent people. Draw an indifference curve map with 3 indifference curves on each (labelthem) for each scenario below. The consumera. views 2 cookies and an ice cream bar as perfect substitutesb. always eats 2 cookies with one ice cream barc. likes ice cream bars but doesn’t care about cookies (is neutral)d. loves ice cream but hates cookies (hint: cookies are a “bad”).What 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.Roxanne is considering chipping in to pay for some tree trimming in her neighborhood. If the trees are trimmed, everyone's view improves by the same amount. Roxanne's utility function is given by u(x,t)=3x+1200t, where x is the amount of money she has to spend and t is a variable that equals 1 if the trees are trimmed and 0 if they are not. 1st attempt See Hint Suppose Roxanne starts with $8000. Her utility of that amount of money without the trees being trimmed is 24000 (that is, u(8000,0)=24000). Calculate her reservation price for contributing to the tree-trimming project. $
- Suppose that one of your friends does not care if she consumes spaghetti (S) or noodle (N). She wants toconsume either two-dish spaghetti or two-dish noodle or any combination of both which adds up to twodishes.(i) Write the utility function of your friend to represent his preferences.(ii) Draw couple of indifference curves of your friend on graph with appropriate labels.(iii) Denote prices as Pn, Ps; income as M. If Pn < Ps, then determine the demand function of your friend foreach product as a function of prices and income.Paul derives utility from cups of coffee (C) and donuts, which he eats a dozen at a time (D). His utility function is: U = √C.D d. Show that Paul's income will not permit him to reach the =20 indifference curve. e. If Paul buys five dozen donuts, how many cups of coffee can he buy and what is his utility? f. Use a carefully drawn graph to show that the utility calculated in part e is the highest Paul can achieve with his $200.With a high stress job that oversees the public health of a nation, Tony loves to eatpomegranate (qm) and spinach (qs), both rich in anti-oxidants, to keep him healthy.Suppose his preferences for the two goods can be captured by the utility functionU(qm, qs) = (qm)^1/3(qs)^2/33 . Explain whether each of the following statements is true orfalse.(a) Tony weakly prefers (27, 1) to (3, 3).(b) Tony likes (27, 1) at least as much as (3, 3).(c) Tony strictly prefers (27, 1) to (3, 3).(d) Tony is indifferent between (27, 1) and (3, 3).(e) Tony weakly prefers (9, 1) to (3, 3).(f) Tony weakly prefers (3, 3) to (9, 1).
- Provide the critic of the cardinal utility and justify how the ordinal or indifference theory is superior to the cardinal utility.We claimed in the text that if preferences were monotonic, then a diagonal line through the origin would intersect each indifference curve exactlyonce. Can you prove this rigorously? (Hint: what would happen if itintersected some indifference curve twice?)lets us assume ,aleeza consumption basket consist os two goods ,X1 and X2.three preferences statements from a-c are given below .develope MRS and graph the indifference curves that matches the given information; a) aleeza consider X1 and X2 as perfect substitutes with one unit of X1 equivalent to four un its of X2. b) aleeza consume three units of x2 with every unit of X1 c) aleeza likes good X1 ands neither likes nor dislikes good X2.
