Question

Suppose that with a budget of $100, Deborah spends $60 on sushi and $40 on bagels when sushi costs $2 per piece and bagels cost $2 per bagel. But then, the price of bagels falls to $1 per bagel.

b. At the new prices, how much money would it have cost Deborah to buy those same quantities (the ones that she consumed before the price change)?

c. Given that it used to take Deborah’s entire $100 to buy those quantities, how big is the income effect caused by the reduction in the price of bagels?

Answer 1

Part A) The quantities are
`30\ piece\ of\ sushi` and
`20\ bagels`

Part B)
`\$80`

Part C) The income effect is a loss of
`\$20`

Explanation:

Part A)

Let

x-----> the number of piece of sushi

y----> the original number of bagels

we know that

`2x=60` ------>
`x=30\ piece\ of\ sushi`

`2y=40` ------>
`y=20\ bagels`

Part B) At the new prices, how much money would it have cost Deborah to buy those same quantities (the ones that she consumed before the price change)?

Bagels

`20(1)=\$20`

Sushi

`30(2)=\$60` -----> is the same

The total cost is

`\$20+\$60=\$80`

so

The same quantities would have cost
`\$80`

Part C) Given that it used to take Deborah’s entire $100 to buy those quantities, how big is the income effect caused by the reduction in the price of bagels?

Find the difference

`\$100-\$80=\$20`

therefore

The income effect is a loss of
`\$20`