Berries2015100 510 15 202530Nuts(f) Now let us explore a case where there is a "boundary solution." Sup-pose that the price of nuts is still 1 and the price of berries is 2, butAmbrose's income is only 9. Draw his budget line (in blue). Sketch theindifference curve that passes through the point (9, 0). What is the slopeof his indifference curve at the point (9,0)?(9) What is the slope of his budget line at this point?_(h) Which is steeper at this point, the budget line or the indifferencecurve?.(i) Can Ambrose afford any bundles that he likes better than the point(9,0)?- 5.3 (0) Ambrose, the nut and berry consumer, has a utility functionU(21,x2) = 4/T +x2, where ¤; is his consumption of nuts and r2 is hisconsumption of berries.%3D(a) The commodity bundle (25,0) gives Ambrose a utility of 20. Otherpoints that give him the same utility are (16, 4), (9, ), (4,-), (1, –), and (0, ). Plot these points on theaxes below and draw a red indifference curve through them.(b) Suppose that the price of a unit of nuts is 1, the price of a unit ofberries is 2, and Ambrose's income is 24. Draw Ambrose's budget linewith blue ink. How many units of nuts does he choose to buy?(c) How many units of berries?(d) Find some points on the indifference curve that gives him a utility of25 and sketch this indifference curve (in red).(e) Now suppose that the prices are as before, but Ambrose's income is34. Draw his new budget line (with pencil). How many units of nuts willhe choose?How many units of berries?

U(x1,x2) = 4x1+x2 MUx1=2x1MUx2=1

Answered: 5.3 (0) Ambrose, the nut and berry…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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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?
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You currently have (x, y) = (8, 2) and the utility function U(x, y) = min(x, 4y ). How many units of X are you willing to give up to get another unit of Y?
Jackie has a budget of $36 per month to spend on snacks. She can spend this budget on bags of potato chips (C) and Hershey chocolate bars (H). Potato chips cost $4 per bag, while Hershey bars cost $1 per bar. The utility that Jackie receives from consuming potato chips and Hershey bars is represented by the following utility function: U=3C2 H. Given that Jackie seeks to maximize her utility, find the number of potato chip bags and Hershey chocolate bars that Jackie will purchase each month.
Assume, as in Exercise 22.1, that a consumer has utility function F or fruit and chocolate. Determine the consumer's demand functions q1(P1, P2, M) and q2(P1, P2, M). Determine also It* in terms of P1, P2 and M. Find the indirect utility function and show that It* = 8Vj8M. Suppose, as before, that fruit costs $1 per unit and chocolate $2 per unit. If the income is raised from $36 to $36.5, determine the precise value of the resulting change in the indirect utility function. Show that this is approximately equal to (O.5)λ*, where λ* is evaluated at P1 = 1,P2 = 2 and M = 36. Exercise 22.1 A consumer purchases quantities of two commodities, fruit and chocolate, each month. The consumer's utility function is For a bundle (X1, X2) of X1 units of fruit and X2 units of chocolate. The consumer has a total of $49 to spend on fruit and chocolate each month. Fruit cost $1 per unit and chocolate costs $2 per unit. How many units of each should the consumer buy…
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.) C Utility (pleasure units) AU 200- 150- 100- 50- 0 (1,67) (2,106) I (3,134) (4,156) 2 Number of units of product 4 X
Problem 1 (25pts) Benjamin spends his time either watching movies (x1) (he uses "on demand" option, cable TV) or listening to songs MP3 downloaded from the Internet (x2). His preferences are described by - U(x1, x2) = ln(x1) + In(x2) - a) Derive Benjamin's demand for movies and MP3 files as a function of prices p1, p2 and his income m. (do not use Cobb Douglas formula but rather derive demand using "two secrets of happiness"). b) Fix the price of MP3 at p2 = 1, and income on m = 10. Find the price offer curve (give an exact formula x2 = f(x1)) and plot it in the commodity space. Find the demand curve x1 = f(p1) and plot it in the graph (with p₁ on vertical axis and x1 on horizontal axis). == c) Is x1 an ordinary good or a Giffen good? Explain. d) Now fix p₁ = 1 and p2 = 1. In the commodity space, plot the income offer curve. In addition, in two separate graphs, plot Engel curves for both movies and MP3 files. Argue that the two commodities are normal (not inferior). e) For the demand…
You consume music (M) and concert tickets (C). Your utility function is U(M, C) = M1/4C3/4. The marginal utility for concert tickets, MUC is MUC =3/4C-1/2M1/4 and the marginal utility for music, MUM is MUm = 1/4C3/4M-3/4 (a) Calculate MRSMC using only the given marginal utilities. (b) Solve for the utility of bundle A where M = 16 and C = 16. Solve for your utility at bundle B where M = 128 and C = 8. Are the utilities the same? (c) Calculate MRSMC at bundle A and at bundle B. Are they the same? (d) Are your indifference curves convex? Draw the ICs. Make sure to label the quantities of the consumption bundles, the axis, and the MRS at those bundles.
Part A . Consider an economy with the following features. • There are 100 identical consumers that derive utility from consuming three different goods: software, computers, and good m. • Each consumer decision utility function is given by U (c, 8) = 4c¹/48¹/4+m, where e denotes the amount of computers that she consumes, s denotes the amount of software that she consumes, and m denotes the amount of good m that she consumes. cand s must be non-negative, but m can take any real value. • Computers are produced by 20 identical competitive firms with a total cost function given by 10c². • Software is produced by 40 identical competitive firms with a total cost function given by 20s². . QUESTION 1: What are the equilibrium prices for software and comput- ers in equilibrium? Part B • Suppose that there is a positive technology shock in the software industry so that that the new cost function of the software firms becomes 10s². Let C and S denote, respectively, the aggregate level of…

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