1. Muhammad enjoys going to the aquarium (x) and playing basketball (y). His preferences on x and y are described by his utility function: U(x, y) = 100x23y3. He has a budget of £120 per week to spend on playing basketball and going to the acquarium. Knowing that p,=10 and py=10: 2/3,,1/3 (A) Find the optimal combination of x and y so that Muhammad maximizes his utility subject to the budget constraint. Show this graphically. (B) Consider now that the price of going to the aquarium increases to £20, the price of playing basketball is now £15 and the income did not change. How does this modify Muhammad's optimal bundle? Show this graphically. (C) Compare the optima in (A) and (B): has the valuation of y in terms of x changed? Explain.

1. Muhammad enjoys going to the aquarium (x) and playing basketball (y). His preferences on x and y are described by his utility function: U(x, y) = 100x23y3. He has a budget of £120 per week to spend on playing basketball and going to the acquarium. Knowing that p,=10 and py=10: 2/3,,1/3 (A) Find the optimal combination of x and y so that Muhammad maximizes his utility subject to the budget constraint. Show this graphically. (B) Consider now that the price of going to the aquarium increases to £20, the price of playing basketball is now £15 and the income did not change. How does this modify Muhammad's optimal bundle? Show this graphically. (C) Compare the optima in (A) and (B): has the valuation of y in terms of x changed? Explain.

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

See similar textbooks

Similar questions

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?
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?
5
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.
1) Elaine wants to keep a good balance of soup and Jujyfruit (a delicious fruit flavored candy) in her diet. Her preferences over bundles of soup and Jujyfruit are represented by the quasi-linear utility function U(S,J) = J0.5 + S, where S and J denote the quantities of soup and Jujyfruit, respectively (Assume fractional quantities of each good can be consumed). Let Ps & Pj denote the prices of the goods and Y denote Elaine's monthly income for spending on these goods. For this exercise, treat soup as the x-axis good. a) Find Elaine's Marshallian demand for soup and Jujyfruit. Is soup a normal or an inferior good? Justify your answer using calculus. Also, calculate the derivative of Marshallian demand for Jujyfruit with respect to income and briefly explain what this implies about the relationship between the demand for Jujyfruit and income for Elaine. b) Now, assume Pj = $5 and Ps Marshallian demanded quantities of Jujyfruit and soup given these prices and income. Use your answers…
Ellie spends £20 on Energy drink (E) and Juice (J). Her preferences for these goods can be described by the following utility function: U ( E,J) = 2E + J^2 ( J squared) - J (MUt = 2, MUj = 2J - 1) Suppose that one energy drink costs £1.60 while one carton of Ellie’s favourite Juice costs £4.00. a) Find Ellie’s optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how Ellie’s optimal consumption choice would change when her disposable budget changes. c) If the price of energy drinks increases to £2.00 per can, how should the price of Juice change so that Ellie can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ellie’s optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ellie’s demand for Energy drink and/or Juice.
Huang is determining how much Coke and Pepsi he will buy. Use the information in italics to answer the bolded question below. • Huang's preferences for Coke (C) and Pepsi (P) are represented by the following utility function: U = 2C + 3P • Huang has $12 to spend on soft drinks. • The price of Coke (P) is $0.50/can. • The price of Pepsi (Pp) is $1.00/can. Which of the following statements referring to Huang's preferences is incorrect. O Huang does NOT experience diminishing MRS. If Huang gives up two cans of Pepsi, he needs to purchase 3 cans of Coke to remain equally satisfied. Pepsi and Coke are perfect substitutes for Huang O None of the above statements are incorrect.
1. Sam is going to Baltimore for the day to watch his favorite baseball team (Orioles). Sam loves his Orioles, but he is addicted to drinking beer (B) and eating hotdogs (D) while watching his team. His utility function is: U = (B*D)1/2 a. Suppose Sam has $50 to spend on beer and hotdogs. Beer costs $5 a mug and a hotdog costs $4. Draw Sam's budget constraint. b. Suppose Sam spends all of his income on beer. How many mugs of beer can he buy? What is his utility? c. Will Sam's income allow him to reach a U = 5? d. If Sam buys 4 hotdogs, how many mugs of bear can he buy? What is his utility? e. What is the combination of beer and hotdogs that yield the highest utility? 2. Firm A's Price $20 $15 $20 $40 profit $35 profit Firm B's Price $37 profit $39 profit $15 $49 profit $38 profit $30 profit $35 profit a. Firms A and B are member of an oligopoly. Which solution will Firm A and B select? b. Is there a Nash equilibrium? If so, what is it? c. Which solution will Firm A and B select if Firm…
Please answer carefully and explain in as much detail as possible.
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…
Alex, who was convinced that "Football is coming home", was very excited for the World Cup last year. Unfortunately, he realized that his favourite Paul Gascoigne jersey from Euro 1996 was getting old, so he wanted to buy a new one before England's first game the following week. He could either buy a 2014 James Milner shirt from retailer A, which would make him totally happy (utility=1), or a 2006 David Beckham shirt from retailer B, which gives him a utility of 0.8. However, the shirts are not available today. There is a 50% chance that retailer A will have the shirt on the week-end, and 70% chance that retailer B will have theirs on the week-end. Due to time and work constraints, Alex can only visit one of these retailers before the tournament starts, otherwise he will have to keep his old 1996 shirt, which gives him a utility of 0.5. He can also ask his friend Nathan to check both places in the morning. But being a Welsh supporter, Nathan will not do it for free and wants some money…
Lucas likes lemon soda (X) and chips (Y). His utility function is given by: U (X, Y) = X0.2Y0.8 He earns $40 per week to spend on lemon soda (X) and chips (Y). The prices of lemon soda and chips are $2 and $4 respectively. Find out Lucas’s utility-maximizing bundle of lemon soda and chips (X*, Y*). Set up the utility-maximization problem and find out the price ratio of these two goods. Find out Lucas’s marginal utility of lemon soda (MUX) and marginal utility of chips (MUY). Calculate the MRSXY . Set up the optimal tangency condition and solve for Y in terms of X. Solve for Lucas’s optimal consumption bundle of lemon soda (X*) and chips (Y*). Draw the optimal consumption bundle on the budget constraint BC1 in Q1. Denote it as Bundle A. Make sure to indicate the optimal consumption of lemon soda (X*) and chips (Y*). Draw an indifference curve that is tangent to the budget constraint at Bundle A. Calculate the value of the MRSXY (the value not the formula) at the optimal…