Below is the utility preferences for an individual: Movies Marginal Utility of Movies Marginal Utility of Movies per Dollar (PM=$10)PM=$10Books Marginal Utility of Books Marginal Utility of Books per Dollar (PB=$5)PB=$51 100 10 1 45 92 70 7 2 40 83 40 4 3 30 64 10 1 4 15 3 What is the utility-maximizing consumption bundle if the individual has $25 to spend?Multiple choice question.1 movie and 3 books5 books2 movies and 3 books2 movies and 1 book
Question
Below is the utility preferences for an individual: Movies Marginal Utility of Movies Marginal Utility of Movies per Dollar (PM=10Books Marginal Utility of Books Marginal Utility of Books per Dollar (PB=51 100 10 1 45 92 70 7 2 40 83 40 4 3 30 64 10 1 4 15 3 What is the utility-maximizing consumption bundle if the individual has $25 to spend?Multiple choice question.1 movie and 3 books5 books2 movies and 3 books2 movies and 1 book
Solution
To find the utility-maximizing consumption bundle, we need to compare the marginal utility per dollar for each good and allocate the budget accordingly.
- In the first round, the marginal utility per dollar for movies is 10 and for books is 9. So, the individual should buy a movie. This leaves 25-$10) in the budget.
- In the second round, the marginal utility per dollar for the second movie is 7 and for the first book is 9. So, the individual should buy a book. This leaves 15-$5) in the budget.
- In the third round, the marginal utility per dollar for the second movie is still 7 and for the second book is 8. So, the individual should buy another book. This leaves 10-$5) in the budget.
- In the fourth round, the marginal utility per dollar for the second movie is still 7 and for the third book is 6. So, the individual should buy another book. This leaves 5-$5) in the budget.
So, the utility-maximizing consumption bundle for the individual is 1 movie and 3 books.
Similar Questions
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Question 1Joe’s preferences are described by the following utility functionU (x, y) = xαyβwith α > 0 and β > 0.(a) Let I denote Joe’s income, and px and py denote the prices of good x and y, respectively.Find Joe’s optimal consumption bundle.(b) Now, suppose α = 6, β = 2, px = 2, py = 3 and I = 24. Evaluate Joe’s optimal choice.(c) Suppose px increases by 50%. What is Joe’s new optimal consumption bundle? Calculateboth the Income Effect and the Substitution Effect.Question 2Collin likes milkshakes (m) and sushi (s). His preferenes over these two goods are representedby the following utility functionU (m, s) = 2√m + s.Collin’s income is $100 and the price of sushi is $10.(a) Suppose the price of milkshakes is initially $2. Find Collin’s optimal consumption bundle.(b) Draw a graph (with m on the horizontal axis and s on the vertical axis) to show Collin’sbudget line, his indifference curve, and his optimal bundle.(c) Suppose the price of milkshakes increases to $5. How many units of milkshake and sushiare in Collin’s new optimal consumption bundle?(d) Draw a new graph for the new optimal bundle (or add it to the graph you have drawnabove in part (b)).(e) What are the substitution and income effects that result from the increase in the price ofmilkshake? Calculate these effects algebraically and illustrate them on a new graph.(f) What is the amount of additional income needed for Collin to achieve the initial level ofutility? What is the amount of additional income needed for Collin to purchase the initialbundle? What is the ideal cost of living index?
For a consumer, the marginal utility of good A is 25 and its price is $5. The marginal utility of good B is 60 and its price is $12. The consumer has allocated his entire budget. Is this consumer maximizing his total utility? Explain your answer
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