QuestionYou have \$100 for books (\$25 each) or movie tickets (\$10 each). How do changes in budget or prices affect combinations?
A: Budget increases to \$150, prices same. increase
B: Budget \$100, books \$25, tickets rise to \$20. decrease
C: Budget \$100, tickets \$10, books drop to \$15. increase

Studdy Solution

STEP 1

Assumptions1. The initial budget is \$100. The initial price of a book is \$253. The initial price of a movie ticket is \$104. The attainable set of combinations refers to the different combinations of books and movie tickets that can be bought with the given budget

STEP 2

For situation A, we need to check if the attainable set of combinations increases or decreases when the budget increases from \$100 to \$150 while the prices stay the same.
The number of books that can be bought is given by the budget divided by the price of a book. Similarly, the number of movie tickets that can be bought is given by the budget divided by the price of a movie ticket.
$Number\, of\, books = Budget / Price\, of\, a\, book$ $Number\, of\, movie\, tickets = Budget / Price\, of\, a\, movie\, ticket$

STEP 3

Plug in the values for the budget, price of a book, and price of a movie ticket to calculate the number of books and movie tickets that can be bought.
$Number\, of\, books = \$150 / \$25$ $Number\, of\, movie\, tickets = \$150 / \$10$

STEP 4

Calculate the number of books and movie tickets that can be bought.
$Number\, of\, books = \$150 / \$25 =6$ $Number\, of\, movie\, tickets = \$150 / \$10 =15$ Since the number of books and movie tickets that can be bought has increased, the attainable set of combinations has increased. $\hat{\imath}$

STEP 5

For situation B, we need to check if the attainable set of combinations increases or decreases when the budget remains \$100, the price of books remains \$25, but the price of movie tickets rises to \$20.
Repeat the calculations in steps3 and4 with the new values.
$Number\, of\, books = \$100 / \$25 =4$ $Number\, of\, movie\, tickets = \$100 / \$20 =5$ Since the number of movie tickets that can be bought has decreased, the attainable set of combinations has decreased. $\hat{v}$

STEP 6

For situation C, we need to check if the attainable set of combinations increases or decreases when the budget remains \$100, the price of movie tickets remains \$10, but the price of a book falls to \$15.
Repeat the calculations in steps3 and4 with the new values.
$Number\, of\, books = \$100 / \$15 \approx6.67$ $Number\, of\, movie\, tickets = \$100 / \$10 =10$ Since the number of books that can be bought has increased, the attainable set of combinations has increased. $\hat{\vee}$

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