5.6. Bunde's preferences are given by the utility function u(x1, x2) = x1 +X2. For each of the following cases, decompose the price effects into thesubstitution and income effects using either the Hicks-Allen or Slutskydecompositions.-(a) Suppose m = 120, p₁ = 12, and p2P15, keeping p2 and m fixed.(b) Suppose m = 100, P1=20. The price p₁ then falls to= 20, and p2 = 10. The price p₁ then falls to5, keeping p2 and m fixed.

u = x1 + x2 Budget line : m = p1x1 + p2x2 A linear Utility function means that x1 and x2 are…

Answered: 5.6. Bunde's preferences are given by…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

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Utility maximization under constraint, substitution and income effect, CV and EV Josh gets utility (satisfaction) from two goods, A and B, according to the utility function U(A, B) = 4[A-4 + B-4-4 + 40. While Josh would like to consume as much as possible he is limited by his income. a. Maximize Josh's utility subject to the budget constraint using the Lagrangean method b. Suppose PA increases. Show graphically the income, substitution effect and total effect and explain c. Suppose PA increases. Show the graphs for CV and EV and explain. One graph for CV and one graph for EV
1. Suppose a consumer's utility function is: U (x1, x₂) xx. Furthermore, suppose the con- sumer's disposable income is $80, and the prices of the two goods are: x₁ = 4 and 2 2. Obtain the optimal amounts of î₁ and î that the utility maximizing consumer would buy. =
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There are two goods, X and Y, available in arbitrary non-negative quan- tities (so the consumption set is R²). Beenish has preferences over consumption bundles that can be represented by a differentiable, strictly increasing and strictly quasi-concave utility function u R² → R+, given by u(x, y) = xªy¹-a where x is the quantity of good X, y is the quantity of good Y, and a € (0, 1) is a preference parameter. = 1. Suppose Beenish has 80 AED. In a nearby store (called "Store A"), the price of good X is p = 2 AED per unit of good X, and the price of good Y is q 8 AED per unit of good Y. However, Beenish also has a time constraint. At Store A, it takes tx 4 minutes per unit to purchase good X and ty 1 minutes per unit to purchase good Y. That means, purchasing a consumption bundle (x, y) = R² at Store A would take 4x + y minutes. Beenish has only 80 minutes to do her shopping. = (a) In an appropriate diagram, illustrate Beenish's constraint set, given that she has both a monetary…
- Assume an individual has quasilinear preferences of the form U(x1,x2) = 3x1¹2 + 2x2. If the price of Good 1 is $1 and the price of Good 2 is $2, how many additional units will the individual consume of Good 2 if her income increases by $1, assuming we're at an interior optimum? A. B. C. D. The individual's consumption of Good 2 will increase by 1/2 unit. The individual's consumption of Good 2 will increase by 1 unit. The individual's consumption of Good 2 will decrease. The individual's consumption of Good 2 will not change.
12 There are two goods and John's preferences can be represented by u: R²0 R given by u(x) = x₁³x2³. His income and price of the two goods are given by (M, P1, 20 P2) = (12, 1, 2). Which 2 of the following 8 options are false: In John's optimal bundle, he consumes the same amount of good 1 as good 2. If we change John's utility function to u(x) = x + then John's optimal bundle remains unchanged. At John's optimal bundle, the slope of the budget constraint equals the slope of the indifference curve. In John's optimal bundle, he spends the same amount on good 1 as good 2. John's preferences satisfy local non-satiation. At John's optimal bundle, his bang per buck of good 1 equals his bang per buck of good If we change John's utility function to u(x) = In (17 +x₁x₂) then John's optimal bundle remains unchanged. If we change the budget set to (M, P1, P2) = (24, 2, 4) then John's optimal bundle remains unchanged.
4. Assume Megan has preferences represented by utility function U (x₁, x2) = (x₁)¹/4 (x2)³/4 Good 1 is electricity (1) while good 2 is gasoline (x2). Suppose the consumer has an income level of m= 1000 dollars. In addition, the price of good 1 is p₁ = 5 and the price of good 2 is p2 = 5. (a) Compute the Marginal Rate of Substitution (MRS). (b) Find the optimal levels of electricity (x) and gasoline (x2) consumption for Megan. (c) Suppose the government imposes a per-unit tax of t = 5 dollars on gasoline. Find the optimal levels of electricity (x) and gasoline (x2) consumption for Megan with the tax.
Bunde's preferences are given by the utility function u(x1, x2) = x, + x2. For each of the following cases, decompose the price effects into the substitution and income effects using the Hicks-Allen decompositions. (For each part, use the given template to draw the constraints, and then use your completed graph to fill in the description. Enter any points in order from left to right as they would appear on the graph.) 20 15 10 5 10 15 20 (a) Suppose m = 120, P1 = 10, and p2 = 15. The price p1 then falls to 6, keeping p2 and m fixed. Given m = 120 and p, = 15, the budget B° is drawn for p, = 10. The utility-maximizing point on this budget is at A = given the linear preferences yielding utility y° = When p, falls to 6, the new budget is B" and the utility-maximizing point is C = ), yielding utility un = . The movement from A to C is the price effect of units of good 1. Removing income incrementally until Bunde can barely afford the old utility of at the new prices yields the line which…
A consumer has a (direct) utility function over x1 and x2: u(x₁, x2) = x₁x2.5 The price of good 1 is p1=1; the price of good 2 is p2=2; and the consumer has m=24 in income. Indicate which of the following statements is true. Select one: O Demand for good 1 is equal to 24. O Demand for good 2 is equal to 6. O Indirect utility function is equal to 32. O The consumer will demand 0 units of good 2. O None of the statements is correct.

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