Utility is a type of function that occurs in economics. When a consumer receives x units of a certain product, a certain amount of pleasure, or utility U, is derived. The graph represents a typical utility function. a) Find the average rate of change of U as x changes from 0 to 1; from 1 to 2; from 2 to 3; from 3 to 4. b) Why do the average rates of change decrease as x increases? a) The average rate of change of U as x changes from 0 to 1 is (Type an integer or a decimal.) Utility (pleasure uni AU 200- 150- 100- 50- 0 (2,106) (1.67) I (3,134) (4,156) 2 Number of units of product 4 X G

Utility is a type of function that occurs in economics. When a consumer receives x units of a certain product, a certain amount of pleasure, or utility U, is derived. The graph represents a typical utility function. a) Find the average rate of change of U as x changes from 0 to 1; from 1 to 2; from 2 to 3; from 3 to 4. b) Why do the average rates of change decrease as x increases? a) The average rate of change of U as x changes from 0 to 1 is (Type an integer or a decimal.) Utility (pleasure uni AU 200- 150- 100- 50- 0 (2,106) (1.67) I (3,134) (4,156) 2 Number of units of product 4 X G

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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draw the graph as well.
Questions 1. Will's utility from vacations (91) and meals (92) is given by the function U(V, M) = 91 x 92. Last year, the price of vacations was $200 and the price of meals was $50. This year, the price of meals rose to $75, while the price of vacations remained the same. Both years, Will had an income of $1500. (a) What is the compensating variation for the price change in meals? (b) What is the equivalent variation for the price change in meals?
U(x, y) = xayb A consumer maximises utility subject to a budget constraint M = Pxx+Pyy Where px is the price of good x, py is the price of good y and M is the budget available. a. Derive an expression for the marginal utility of x. Under what condition is the marginal utility diminishing. b. Derive an expression for the marginal utility of y. Under what condition is the marginal utility diminishing.
The law of diminishing marginal utility allows us to conclude that A) demand curves slope downward to the right. B) total utility will increase by an increasing amount as consumption increases. C) supply curves slope upward. D) a consumer will buy positive amounts of all goods.
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Apples (pounds per week) 0 A> B B> D b d Butter (pounds per week) he graph above indicates that a consumer's preference combination. Which one of the following is correct based on the graph? C> B C E>F E F B
Suppose we are able to model the total utility function for the consumption of two goods, good x and good z. The utility function is structured as U(x, z) = 3x2 + z2 - 2xz. The consumer is faced with the prices of goods x and z. The price for each unit of good x and z is $1 each. The consumer has an income $1 (in thousands). How many units of each good should the consumer consume so as to maximize his/her utility?
A consumer has an income of $400 and is deciding between two products: X and Y. Assume that the X product is the horizontal axis product. The price of X is $10 and the price of Y is $2. Assume the consumer currently wants to consume 50 units of product Y to maximize his utility. a) Write out the equation to this consumers budget line. What is the slope to this budget constraint? b) How much of X and Y will the consumer consume to maximize his utility subject to his budget constraint. C) Now assume the price of X changes to $5 and price of Y and Income stays the same. At the new price, the consumer wants to buy 60 units of product X to maximize her utility given her budget. How much X and Y will the consumer consume to maximize utility. g in the before and after the change of the budget constraint and indifference graph on the same graph space. Show all necessary points. Label clearly. ead oubstitutiofs. Draw d) Write out the expression of the utiiity maximizing ruie here.?
Tony is throwing a party at his Fraternity and is trying to choose what booze to buy. A bottle of vodka has three times the alcohol as a six-pack of beer. Assume that Tony only cares about the total amount of alcohol in his basket. (use vodka on the X-axis and beer measured in six-pack on the Y-axis) a) Devise a utility function to represent these preferences. b) Suppose a bottle of vodka costs $40, a six-pack of beer costs $10, and the budget is $200. Write the budget constraint. c) Solve Tony’s utility maximization problem and find the optimal combination. d) Suppose that a bottle of vodka cost has increased to $50. What will be his new optimal combination.
2. Vibha consumes three goods X, (shirts), X, (food in pounds), and X, (shelter in square feet). Vibha's utility function is given by: U (X,, X, X,) = 5ln Xt 3ln X + 2ln X, where In (x) or log. (x) is the natural logarithm. Vibha's weekly income is $100. Let the price of X, = P, = $10, the price of X, = P, = $2, and the price of X, = P; = $4. What is the equation for Vibha's budget constraint? а. b. |How many shirts, pounds of food, and square feet of shelter, will Vibha consume, as a rational consumer?
The utility function of a consumer is u = √x + 2y. (a) Calculate how much MRS of that consumer when x = 4. (b) If the consumer currently consumes 4 units of goods x and the price ratio of Px / Py = 1/4, then the consumer should increase or decrease the consumption of goods x?
A student has a lunch utility function U(S, P) 8S + 3P, where S is number of salads per month and P is number of pizzas per month. The price of a salad is $5, the price of a pizza is 8, and his monthly income for lunch is $80. a) Derive the equation representing the consumer's demand for Salad. Represent the demand for Salad graphically. b) The price of Salad goes up to $25 and the price of Pizza does not change. Compute and represent graphically the new equilibrium of the student. What can you tell about the substitution effect on Salad and pizza