ENGR.ECONOMIC ANALYSIS
14th Edition
ISBN: 9780190931919
Author: NEWNAN
Publisher: Oxford University Press
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- The utility possibility frontier is defined as the set of maximum utility levels for all consumers that is feasible in the economy, given resource constraints and preferences. For a two-consumer economy, it is defined formally as the solution to: u (ūB) = max u A (xA) subject to ug(xB) > ūg and (xA, XB)feasible. For each of the economies above, find an equation for the utility possibilities frontier, and graph it.arrow_forwardThere are two shows on Netflix that Jeff can watch, Show 1 and Show 2. x₁ measures the number of episodes watched of Show 1 and x₂ measures the number of episodes watched of Show 2. Jeff's preferences can be represented by u(x₁, x₂) = x² + ax². Jeff has 11 hours available for watching Netflix today. Each episode of Show 1 lasts 30 minutes, while each episode of Show 2 lasts one hour. For all question parts, round to three decimal places if necessary. For parts (a) - (f), let a = 1. Draw Jeff's indifference curves for the utility levels u = 4, 9, 16. Draw a straight line between the bundles (x₁, x₂) = (4, 0) and (x₁, x2) = (0, 4). Now, use your picture to determine whether the following two statements are true or false. Answer "1" for true. Answer "0" for false. a) Statement 1: Jeff's preferences are strongly monotone. 1 b) Statement 2: Jeff's preferences are strictly convex. 0 c) Find the bundle at which one of Jeff's indifference curves is tangent to the budget line. (x₁, x^2) = ( d)…arrow_forwardDing Ding is a cat philosopher. He spends his time on two activities. Sleep and thinking. Both activities produce pleasure to Ding Ding. How effective Ding Ding is in each activity varies day by day. But on a given day, if he spend “s” effective hours in sleeping and “t” effective hours in thinking, his utility is u(s,t)=s^2+t. you can assume that time is continuous in answering the following question. (A) Let us first ignore that there are only 24 hours each day. Label “s” on the x-axis and “t” on the y-axis in a diagram. Draw two indifference curves u(s,t)=s^2+t=24^2=576, and u(s,t)= s^2+t=12^2=144. On each indifference curve, you have to mark at least the coordinates of four points to illustrate the shape of it. (B) Describe in words how these two indifference curves in (a) relate to each other.arrow_forward
- Which of the following conditions should hold for an interior optimum? Px MRSXY and PxX + PyY < I Py MUx and MUy should be maximized and Px X + PyY = I Px MRSXY and PxX + PyY = 1 Py MRSXY should be maximized and PxX + PyY = Iarrow_forwardExplain why the lifetime budget constraint must be satisfied as a strict equalityarrow_forwardimage attachedarrow_forward
- Please help me to solve questions (a) (b) (e). (especially question e). thank you!arrow_forwardAnswer please with added diagrams b) Assume that your optimal choice of consumption and leisure is to work 8 hours per day. Illustrate this choice diagrammatically using the feasible set and indifference curves. c) Use indifference curves and the feasible set to show why, given the properties of the optimal choice in part b it is not optimal to work, say, 10, or 6 hours per day.arrow_forwardReese thinks peanut butter and chocolate are great when separate, but when they combine they are even more epic. In other words, Reese likes to eat either peanut butter or chocolate, but when he eats them together, he gets additional satisfaction from the combination. His preference over peanut butter (x) and chocolate (y) is represented by the utility function: u(x, y) = xy + x + y Which of the following is NOT true about Reese’s preference? (a) The MRS decreases when x increases.(b) The preferences are homothetic.(c) The marginal utility of y is higher when x = 10 than when x = 5.(d) For any a > 0, Reese prefers the bundle (x =a/2 , y = a/2 ) over either the bundle (x = a, y = 0) or (x = 0, y = a).arrow_forward
- A consumer has preferences over two goods, carrots and turnips, each measured in kilograms. For each of the following scenarios, identify which, if any, of the standard assumptions of preferences are violated. (a) The consumer will never eat more than ten kilograms of carrots per day. (b) The consumer cares only about the total weight of the two vegetables consumed, and always prefers more to less. (c) The consumer cares only about the product of the respective weights of the two vegetables consumed, and always prefers a greater product to a lesser one.arrow_forwardGinny likes to eat Bertie Bott’s Every Flavour Beans (b), and Chocolate Frogs (f). Herpreferences over these lollies are Cobb-Douglas, and can be presented by the utility functionu(b, f) = 1/5(b − 2)(f + 3). Each Every Flavour Bean costs 25 Knuts and each Chocolate Frogcosts 12 Knuts. Ginny has 314 Knuts to spend. Assume that beans and frogs are both perfectlydivisible goods.(a) Find Ginny’s optimal bundle.(b) Suppose that Ginny is mugged by Draco on her way to the lolly cart, so that by the timeshe is there, she is left only with 75 Knuts. What is her optimal bundle now?(c) Now, consider the general case, where Ginny’s income is m, the price of Every FlavourBeans is pb, and the price of Chocolate Frogs is given by pf . In other words, treat ChocolateFrogs as the numeraire. Find Ginny’s demand for each good in terms of m, pb and pf .(d) Find the good on which Ginny will always spend more than half of her income.(e) Find the own-price, cross-price, and income elasticities of good 2…arrow_forward
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