5.3 What is the slope (value) of Mrs. Bain budget line? 5.4 In theory, what is the slope (value) of the indifference curve at Mrs. Bain's utility maximization point? Justify your answer. W 7 Ms. Bain maximizes 6. utility (given her budget constraint) at point X, skiing 2 days and spending 3 days horseback riding. 5 4 S Budget liņe 3 Curve B X 2 Y Curve A 1 Curve C V 1 2 3 4 5 6 . 7 Days of horseback riding per semester Part II Graph Days of skiing per semester
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- If Utility=.5lnX+3Z+10+4VW then Marginal utility from X is...... and the Mu of Z is...... Select an answer and submit. For keyboard navigation, use the up/down arrow keys to select an answer. a b с 10; 3 3,4 5/X; 3 d 2/VW; 36. Indifference curves and utility maximization Giberto plays the violin as part of a string trio and advertises booking opportunities using brochures he distributes in bars around the oity. Making one graysale brochure costs$0.02, but adding color increases the cost to$0.08per brochure. Gilberto sets aside a monthly budget of$14,00for creating brochures. The following graph shows three of Gaberto's indifference curves for the number of grayscale and color brochures that he makes. Use the green line (triangle symbol) to plot Giberto's budget constraint. Then, place the black point (alus symbol) on the graph to indicate Giberto's optimal consumption choice given that budget constraint. optimal consumption choice given that budget constraint.(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…
- A consumer is making purchases of products Alpha and Beta such that the marginal utility of product Alpha is 63 and the marginal utility of product Beta is 40. The price of product Alpha is $9, and the price of product Beta is $5. The utility-maximizing rule suggests that, to stay within a given budget constraint, this consumer should Multiple Choice O O O increase consumption of product Beta and increase consumption of product Alpha. make no change in the consumption of Alpha or Beta. increase consumption of product Beta and decrease consumption of product Alpha. increase consumption of product Alpha and decrease consumption of product Beta.Mylie’s total utility from singing the same song over and over is 50 utils after one repetition, 90 utils after two repetitions, 120 utils after three repetitions, 80 utils after four repetitions, 20 utils after five repetitions, and -60 utils after six repetitions, as shown in the table below. a. Write down her marginal utility for each repetition. Instructions: Enter your answers as a whole number. If you are entering any negative numbers be sure to include a negative sign (-) in front of those numbers. Repetitions Total Utility Marginal Utility 0 0 — 1 50 2 90 3 120 4 80 5 20 6 -60ceriuppose 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
- 7. Bob receives utility from days spent traveling on vacation domestically (D) and daysspent traveling in a foreign country (F) as given by the utilityU(D; F) = DFThe price of a day spent traveling domestically is 160 pounds and in a foreigncountry 200 pounds. Bobís annual budget for traveling is 8000 pounds. (a) Find Bobís utility maximising choice of days traveling domestically and of daystravelling in a foreign country. Find also his utility level from consuming thatbundle. Suppose that the price of domestic traveling increases to 250 pounds per day.Denoting his budget for traveling x, (suppose by now that it is unknown) findthe demand for D and F under the new prices as a function of x.NIVERSITY DURAI Consider the following data describing the change in Nora's utility when she consumes various levels of Nuts and chocolate per week, the price per portion for the considered goods are respectively AED 20 and AED10. Nora has a budget equal to 160 per day to spend on her snack. Q Nuts Total UtilityQ Chocolate Total Utility ChocolateMU Nuts MU ChocolateMU/ AEDMU/AED MRS Chocolate Nuts Nuts 40 1 28 72 52 100 3. 72 4 124 88 144 5. 102 160 6. 114 7 172 122 1. Complete the table above by calculating the marginal utility, the marginal utility per dollar spent and marginal rate of substitution for each good. 2. Identify the potential set of equilibrium points Where MUI/P1=MU2/P2 Nuts Chocolate Income 2. 2. 6.Currently, Paula is maximizing utility by purchasing five TV dinners (T) and four LeanCuisine Meals (L) each week. Suppose both T and L cost $5 each.a. Graph Paula’s initial utility-maximizing choice.b. Suppose the price of T falls by $1 and the price of L rises by $1.25. Can Paula stillafford to buy her initial consumption choices? What do you know about her new budgetconstraint?c. Make a new graph to show why Paula will choose to consume more T and less Lgiven her new budget constraint to maximize utility. Is her utility increased, decreased,or unchanged given the price change? [Hint: try to make the graph as big as possible tosee how the utility is tangent/intersects with the lines more easily] d. In part (b), suppose another scenario where the price of T rises by $1 and the priceof L falls by $1.25. Is Paula’s utility increased, decreased, or unchanged given the pricechange?
- 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?Praxilla, who lived in ancient Greece, derivesutility from reading poems and from eating cucumbers.Praxilla gets 30 units of marginal utility from her firstpoem, 27 units of marginal utility from her secondpoem, 24 units of marginal utility from her third poem,and so on, with marginal utility declining by three unitsfor each additional poem. Praxilla gets six units ofmarginal utility for each of her first three cucumbersconsumed, five units of marginal utility for each of hernext three cucumbers consumed, four units of marginalutility for each of the following three cucumbersconsumed, and so on, with marginal utility declining byone for every three cucumbers consumed. A poem coststhree bronze coins but a cucumber costs only one bronzecoin. Praxilla has 18 bronze coins. Sketch Praxilla’sbudget set between poems and cucumbers, placingpoems on the vertical axis and cucumbers on thehorizontal axis. Start off with the choice of zero poemsand 18 cucumbers, and calculate the changes in…. Answer all parts (a) (c) of this question. (a) Consider an agent whose preferences over any couple (x1, x2), where 2₁ ER+ and x2 € R+, e.g., apples and oranges, is such that she prefers the bundle that is closest to having the same number of apples and oranges. Write a utility function u: R² → R+ which represent these preferences. A politician remarks "Our recent increases in the wage rates of teachers has been a total suc- cess! The shortage of teachers has been reduced drastically. Another, similar wage increase should eliminate this shortage entirely" (b) Explain and illustrate in a diagram what is meant by "income effects" and "substitution effects" of a wage rate change. (c) Explain and illustrate how you would model the labour supply decision of a potential teacher. Do you agree that the wage increase will increase the labour supply in this case? Carefully outline the assumptions underlying your argument.