Suppose Ann likes both pancakes (P) and waffles (W) and is always willing to substitute twopancakes for one waffle.Write the equation for Ann's utility function.a.b.Given her preferences, what is Ann's marginal utility of an additionalpancake? What is Ann's marginal utility of an additional waffle?с.With pancakes on the horizontal axis and waffles on the vertical axis, graphAnn's indifference curves for U=4 and U=8.d.What is Ann's marginal rate of substitution?

There is two goods pancakes (P) and waffles (W), they are substitute to each other. Ann is willing…

Answered: Suppose Ann likes both pancakes (P) and…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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QUESTION ONE The only source of income available to Doreen, a level 200 student of UEW is her monthly stipend (M) from her parents. She neither saves nor borrows. Assuming she spends all her income on only two goods food (F) and Clothes (C), with Pr and Pc being the prices of the two goods respectively and having a utility function of the form: U = 6F°C i. Write an expression for Doreen's budget constraint. ii. Assuming good Fis on the vertical axis, produce a sketch of her budget constraint and determine the slope. iii. Find Doreen's monthly equilibrium demand functions for both goods. iv. With Pr and Pcgiven as ¢12 and ¢15 respectively and income of ¢300, calculate the equilibrium quantities of both goods. v. Compute the price elasticity of demand for both goods and interpret your results. vi. If income and prices of the two goods increase by 50%, calculate the equilibrium quantities of Food and Clothing.
1. Suppose Frank enjoys traveling and his utility is a function of the number of airplane trips he takes and the number of bus rides he takes. His utility function is given by U(b,p) = 3b0-4p0.8. A trip on a plane costs $400, a trip on the bus costs $50 and Frank has $3,000 to spend on travel. a. Draw Frank's budget line on a graph with bus trips on the vertical axis. b. Calculate AND INTERPRET the slope of Frank's budget line. c. Draw a representative indifference curve on your graph and provide a function that describes the slope of this indifference curve (i.e., find Frank's marginal rate of substitution). What is the INTERPRETATION of the marginal
2)Ben is choosing between cookies and soda. Denote the marginal utility of cookies is MUc, and the marginal utility of soda is MUs. Which of the following relationship is true regarding the marginal utility of substitution (MŘS) of cookie in terms of soda? A) MRS= MUc B) MRS = MUS C) MRS = MUS / MUC D) MRS = MUc / MUs
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2. Sally consumes two goods, X and Y. Her utility function is given by the expression U = 3XY². The current market price for X is £10, while the market price for Y is £5. Sally's current in come is £500. (a) Sketch a set of two indifference curves for Sally in her consumption of X and Y. (b) Write the expression for Sally's budget constraint. Graph the budget constraint and determine its slope. (c) Determine the X,Y combination which maximises Sally's utility, given her budget constraint. (d) Calculate the impact on Sally's optimum market basket of an increase in the price of X to $15. What will happen to her utility as a result of the price increase?
Xia's utility function is U = TC, where T is baskets of tomatoes and C is bags of carrots. One of Xia's indifference curves will go through points: Baskets of 10 tomatoes 9 8 7 6 5 4 3 2 1 0 a. B, C, and F. O b. B, D, and E. O c. A, D, and E. O d. A, B, and F. A D B C F E 123 4 5 6 7 8 9 10 Bags of carrots
Mary's indifference map and budget constraint for goods X and Y are shown below. If Mary spends all her money on X and Y, which bundle will she choose to maximize her utility? Good Y с A E B A D B U3 U₂ U₁ E Good X
1,
Solve these consumer choice problems: a. Suppose a consumer has a utility function u(x, y) = xy + 7y facing prices p,=S1 and p,=$2 and income I = $10. Draw a diagram and find the consumer's optimal consumption of goods x and y. b. Suppose that you are in a situation where you can afford purchasing 3 units of good x and 4 units of good y. You discover that another affordable bundle of 5 units of good x and 2 units of good y causes you to reach the same level of utility. Assume that your utility function and budget line are both well behaved. Are you maximizing your utility by consuming your original bundle? Why or why not? Propose an alternative, affordable bundle that would yield a higher utility level than either of the original bundles.
Jennifer likes her tea, but only if prepared with 4 teaspoons of honey for every cup of tea. The price of tea is $2, and the price of honey is $0.50. Jennifer has a $12 budget for tea and honey. a. Write down a utility function that reflects her preferences for tea (T) and honey (H). b. What bundle should Jennifer choose to maximize her utility given her budget constraint? c. Graphically illustrate Jennifer's utility maximizing bundle given her budget constraint.
1. In a simple but delicious world, Joey eats only sandwiches, s, and jam, j. He has a Cobb-Douglas utility function U(j, s) = Nj1-asª, where 0 0. The price of jam is pj, the price of sandwiches is Ps, and Joey has a monthly budget Y to spend on lunch. a. Explain why you can safely use a simpler Cobb-Douglas utility function, V(j, s), to represent Joey's preferences, which is the same as U(j, s) except for replacing N with 1. b. Transform V(j,s) by taking natural logs and bringing down exponents. Explain why it is useful to do this for a Cobb-Douglas utility function, but not for a quasi-linear utility function. Use In(V(j, s)) and the substitution method to derive the formulas for Joey's optimal amount of jam, j*, and sandwiches, s*, to buy and consume per month. Simplify your answers so that you arrive at the С. (1-a)Y aY formulas j* = and s* Ps d. What fraction of his income does Joey spend on jam, and what fraction on sandwiches?
Question 3 (Demand). Carlos really likes pizza. His utility function for Little Caesar's (xi) and Woodstock's (x.) is given by: U(xi, x2) = x;+2x2 The price of x,is $10 and Carlos spends $50 on pizza. a) Graph the demand curve for x1, with pi (the price of x) on the y-axis and x, on the x-axis. (Hint: There will be a range of prices where the demand for x, will be 0). Explain you graph. Page 2

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