Jamal only consumes two things: lift tickets at the local ski hill (S), and a compositegood (Y). The composite good costs $1 per unit. He has an annual income of $55,000,and his utility function and associated marginal utilities are as follows:U = 10s0lYMUS = S-0.9YMUy = 10S1%3DThe local ski hill offers the following three pricing options:(i) Pay-as-you-go: In this option, each lift ticket costs Jamal $100.(ii) Member discount: In this option, Jamal pays a $540 membership fee at the startof the year, then each lift ticket costs $90.(iii) Season Pass: In this option, Jamal pays $9000 membership fee at the start of theyear, then each lift ticket costs $0.Note that, given the length of the ski season, the maximum mumber of lift ticketsJamal can consume per year is 100.For each option, find Jamal's optimal consumption bundle and its associated utility.Which option should Jamal pick?

Recall that to find the optimum bundle we need to check for two conditions: MUsMUY=pSpY=pS1=pS (if…

Answered: Jamal only consumes two things: lift…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Kai spends his income on lime (L) and ginger water (G). Lime is priced at $2, while ginger water costs $1. Suppose Kai has $30 to spend and his utility function can be represented as U(L,G) = L0.5 G0.5 What is the optimal number of lime and ginger water for Kai to purchase? b. How much utility does this combination bring him?
Suppose that David and his friend Wilson derive utility from consuming two types of snacks: onion rings (9₁) and chips (9₂). The utility function for each individual is U (9₁, 92) = 9192. Their indifference curves for these two goods are assumed to have the usual (convex) shape. Suppose David has an initial endowment of 35 onion rings and 10 chips, and Wilson's initial endowment consists of 5 onion rings and 20 chips. (1) Draw an Edgeworth box and show the initial allocation of goods, to be labelled e. Indicate the initial quantities of each person's goods on the four axes.
Please refer to the following information to answer the question (in bold) below: You enjoy consuming apples (A) and oranges (O). Suppose that your utility function over both goods is given by Your marginal utility function for apples is . Your marginal utility function for oranges is U (A, O) = AO³ MUA = 0³ MUO 3A0² . Currently, the price of apples is $10/peck, the price of oranges is $5/pound, and your income is $160. Assume that apples are your horizontal axis good and oranges are your vertical axis good. = When you set up the optimal decision rule for your consumer problem, which of the following statements best describes how much you will buy of apples and oranges at your consumer equilibrium? For each peck of apples, you will buy 1/3 pounds of oranges. For each peck of apples, you will buy 1 pounds of oranges. O For each peck of apples, you will buy 3 pounds of oranges. O For each peck of apples, you will buy 6 pounds of oranges.
1. Consider a consumer who consumes two goods. The utility function is given by u(x1, x₂) /2x1+1+√√√x₂, - where x > 0 denotes the amount of good i = the price of good 1 is 3, the price of good 2 is p2 > 0, and the income is 12. 1,2 consumed. Unless stated otherwise, (1) Calculate the marginal rate of substitution (measuring the value of good 1) at the consumption plan (x₁, x₂) = (3, 4). (2) Calculate the consumption plan that is optimal for the consumer. (3) Let v(p₂) denote the utility level at the optimal consumption plan. Calculate its derivative with respect to p2, i.e., v'(P2), at p2 = 3. (4) Suppose that p2 = 1 and the utility level is 10. Calculate the compensated demand for each good.
3*. Ms Smith likes to drink wine; in particular, a french bordeaux (f) at $40 per bottle and a California varietal wine (c) priced at $8. She allocates $600 to these two each month; and her utility is: U(ƒ, c) = ƒ²/³ c¹/³ (a) Write out her (constrained) utility maximization problem. Solve for the optimal consumption of wine f and c.
Economics Summer break is approaching! Suppose you derive utility from days spent traveling on vacation domestically, D, and days spent traveling on vacation in a foreign country, F. Your utility function over these two “goods” is: U(D, F) : 4D0.25F 0.75 Let your budget constraint be I(D, F) = pDD + pF F; where I is your income, pD is the price of domestic travel per day, and pF is the price of foreign travel per day. a. Determine the demand functions for domestic travel and foreign travel. Make sure you show your work – show the steps used. b. Suppose that you’ve saved $800 for your summer travel, the price of domestic travel per day is $25 and the price of foreign travel per day is $100. How many days of each type of travel will you embark on? c. Illustrate the indifference curve, budget constraint, and the utility maximizing bundle associated with (b). Make sure you show the level of utility, the budget constraint intercepts, and the optimizing equilibrium. Your answer
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…
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…
Focus on parts e-h
In the graph below, you initially maximize utility at point A relative to the B1 budget constraint. Your income changes, which puts you on a new budget constraint (B2). x2 14 13 12 10 w 10 11 12 13 14 15 If good 1 is normal and good 2 is inferior, then point 1st attempt Y Y W Z is the new optimal bundle of consumption.
Compute marginal utilities and marginal rate of substitution for each of the utility functions given below. a) U(X,Y)= 1- e-ax -e-by b) U(X,Y)= XY + 3X + 5Y c) U(X,Y)= (0.3Xm +0.78m)/1 X1-a y1-b d) U(X,Y)= + 1-a 1-b
4. Two individuals, Amir and Budi, consume two goods, clothes (X) and shoes (Y). The utility functions for the two individuals are given as: Utility function of Amir, UA = 15X0.25Y0.75Utility function of Budi, UB = 25X0.5Y0.5 The current price for clothes (Px) is Rp 100,000 and the current price for shoes (PY) is Rp 150,000 a. Determine marginal rate of substitution (MRSXY)between clothes (X) and shoes (Y) for Amir and Budi! Please explain. b. Amir is currently consuming 5 units of clothes (X) and 10 units of shoes (Y), whereas Budi is consuming 12 units of clothes (X) and 8 units of shoes (Y). At this current consumption, have Amir and Budi reached the efficient allocation of clothes and shoes? If they have, explain why. If they have not, calculate the optimal allocation and explain. c. Considering the relative price between of clothes and shoes, at the current consumption, have Amir and Budi reached exchange equilibrium? Please explain d. Use the Edgeworth Box to illustrate the…

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