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.

Economics:

10th Edition

ISBN:9781285859460

Author:BOYES, William

Publisher:BOYES, William

Chapter21: Demand: Consumer Choic

Section: Chapter Questions

Problem 16E

See similar textbooks

Similar questions

You have $4,000 to spend on entertainment this year (lucky you!). The price of a day trip (T) is $40 and theprice of a pizza and a movie (M) is $20. Suppose that your utility function is U(T, M) = T3/4M1/4.a. What combination of T and M will you choose? b. Suppose that the price of day trips rises to $50. How will this change your decision?
EXERCISE 6 If Ginna spends her entire budget, she could buy a chosen set of groceries and also buy 10 notebooks. If she spends only half of her budget, she could only buy a set of groceries and could not afford any notebooks. Suppose Ginna's budget is £150. Her preferences for groceries (G) and notebooks (N) can be described by the following utility function: U(G, N) = 30G + 2N (MUG = 30, MUN = 2). a) Find Ginna's optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how the price of a notebook should change for Ginna to change her optimal consumption choice. c) If the price of a notebook increases by 50%, how should the price of the groceries drop so that Ginna can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ginna's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ginna's demand for groceries and/or notebooks.
Suppose you had a budget of $20.00 and the prices of a burger and a slice of pizza are $4.00 and $2.00 respectively. What is the marginal utility per dollar spent for the fourth burger?
2. Tom spends all his $100 weekly income on two goods, apples and bananas. His utility function is given by U (A, B) = AB, where A and B stand for the quantity of apples and bananas consumed by Tom. If PA = $4 and PB= $10, how many apples and bananas will he consume? Make sure you write out the utility maximization problem explicitly, including the decision variable(s). What if his utility function is given by U (A, B) = A0.5B 0.5?
Julio loves gardening. His favourite plants are tulips and hydrangeas. His utility function is ' u(t,h)= t +100h -h^2 where t is the number of tulipsin his garden and h is the number of hydrangeas in his garden. suppose he has a 500 square feet for his garden. each tulip takes up 1 square foot of space and each hydrangeas takes up 4 square feet. he gets both plants for free.If he wanted to maximize his utility, how many tulips should he plant, what about hydrangeas? b) if his yard was only 144 square feet, how many tulips would he plant? How many hydrangeas? C) In order to plant both tulips and hydrangeas, how big does his garden need to be. carfeully explain.
Rick eats only french fries and burgers at his office cafeteria. His weekly lunch budget is $48. Each burger costs $6 and each order of fries costs $3. When deciding how much of each good to buy, Rick knows that 2 burgers and 4 orders of french fries will give him a utility of 8. At his utility-maximizing point, Rick's utility is:
Styles 15. Damian Matthews is busy. He allocates his free time between watching movies and working out at the gym. The table below shows his utility from the number of times per week he watches a movie or goes to the gym. Damien has 14 hours a week to spend on movies or the gym (think of hours like $ of income here). Each movie takes 2 hours. Each gym trip takes 2 hours. Q of Gym Total Q of Movie Total Utility visits Utility from visits from Gym Visits movies 100 1 60 180 110 3 240 3 150 4 280 4 180 310 190 330 195 340 7 197 a) What bundles of gym visits and movies can Damien consume if he spends 1) all his time in the gym or 2) all his time watching movies? b) Calculate the marginal utility of each gym visit'and movie. Then calculate the Marginal Utility per hour of each activity. c) How should he allocate his time to maximize his utility? 12
How do your total and marginal utility change as you stay at home watching the same TV show (not necessarily the same episode) alone all day?
Suppose John decides to buy 4 units of food and 4 units of clothing with his $12 budget. Would his marginal utility per dollar spent on food be greater than or less than his marginal utility per dollar spent on clothing? What does this tell you about how he should substitute food for clothing if he wanted to increase his utility without spending any more money?
If Ginna spends her entire budget, she could buy a chosen set of groceries and also buy 10 notebooks. If she spends only half of her budget, she could only buy a set of groceries and could not afford any notebooks. Suppose Ginna's budget is £150. Her preferences for groceries (G) and notebooks (N) can be described by the following utility function: U (G, N) = 30G + 2N (MUG = 30, MUN = 2). a) Find Ginna's optimal consumption bundle. Provide both algebraic and graphical solution. Explain your reasoning. b) Discuss how the price of a notebook should change for Ginna to change her optimal consumption choice. c) If the price of a notebook increases by 50%, how should the price of the groceries drop so that Ginna can be as well off as before this change in prices? d) Discuss the implications of the price change from c) on Ginna's optimal choice. In your discussion, include the analysis of the substitution and income effects as well as Ginna's demand for groceries and/or notebooks.
Devon's utility function can be written as ?1^0.50?2^0.50, where ?1 is the quantity of hamburgers consumed and x2 is the quantity of milk shakes. His income is $2,400.00. 1) Hamburgers cost $8.00 each and the price of one milk shake is $4.00. If he is maximizing his utility, how much will Devon spend on hamburgers? $ 2)The price of hamburgers decreases to $7.37 each. Now, how much will Devon spend on hamburgers if he is maximizing his utility? $
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.