Questions: On April 1, the price of gas at Bob's Corner Station was 4.95 per gallon. On May 1, the price was 5.45 per gallon. On June 1, it was back down to 4.95 per gallon. Between April 1 and May 1, Bob's price increased by . Between May 1 and June 1, Bob's price decreased by , or . Suppose that at a gas station across the street, prices are always 20% higher than Bob's. In absolute dollar terms, the difference between Bob's prices and the prices across the street is when gas costs 5.45 than when gas costs 4.95. Some economists blame high commodity prices (including the price of gas) on interest rates being too low. Suppose the Fed raises the target for the federal funds rate from 2% to 2.75%. This change of percentage points means that the Fed raised its target by approximately .

On April 1, the price of gas at Bob's Corner Station was 4.95 per gallon. On May 1, the price was 5.45 per gallon. On June 1, it was back down to 4.95 per gallon.

Between April 1 and May 1, Bob's price increased by .

Between May 1 and June 1, Bob's price decreased by , or .

Suppose that at a gas station across the street, prices are always 20% higher than Bob's. In absolute dollar terms, the difference between Bob's prices and the prices across the street is  when gas costs 5.45 than when gas costs 4.95.

Some economists blame high commodity prices (including the price of gas) on interest rates being too low.

Suppose the Fed raises the target for the federal funds rate from 2% to 2.75%. This change of  percentage points means that the Fed raised its target by approximately .
Transcript text: On April 1, the price of gas at Bob's Corner Station was $\$ 4.95$ per gallon. On May 1 , the price was $\$ 5.45$ per gallon. On June 1 , it was back down to $\$ 4.95$ per gallon. Between April 1 and May 1, Bob's price increased by $\qquad$ $\qquad$ . Between May 1 and June 1, Bob's price decreased by $\qquad$ , or $\qquad$ . Suppose that at a gas station across the street, prices are always 20\% higher than Bob's. In absolute dollar terms, the difference between Bob's prices and the prices across the street is $\qquad$ when gas costs $\$ 5.45$ than when gas costs $\$ 4.95$. Some economists blame high commodity prices (including the price of gas) on interest rates being too low. Suppose the Fed raises the target for the federal funds rate from $2 \%$ to $2.75 \%$. This change of $\qquad$ percentage points means that the Fed raised its target by approximately $\qquad$ .
failed

Solution

failed
failed

Solution Steps

Step 1: Percentage Change in Gas Prices at Bob's Station

The percentage change in gas prices at Bob's station is calculated using the formula: \[\frac{P_{final} - P_{initial}}{P_{initial}} \times 100\] Substituting the given values, we get: \[\frac{5.45 - 4.95}{4.95} \times 100 = 10.1\%\]

Step 2: Price Difference Between Stations

Given the fixed percentage increase at the competitor's station, we calculate the competitor's prices and the absolute and percentage differences. The competitor's initial and final prices are calculated as: \[P_{competitor} = P_{Bob} \times (1 + \frac{percentage\_increase}{100})\] For the initial prices, the absolute difference is \[$0.99\] and the percentage difference is \[20\%\]. For the final prices, the absolute difference is \[$1.09\] and the percentage difference is \[20\%\].

Step 3: Impact of Federal Funds Rate Change

The change in the federal funds rate and its impact as a percentage of the initial rate is calculated as follows: \[r_{final} - r_{initial} = 0.75\] \[\frac{r_{final} - r_{initial}}{r_{initial}} \times 100 = 37.5\%\]

Final Answer:

The percentage change in gas prices at Bob's station is 10.1%. The absolute and percentage differences between the stations initially are $0.99 and 20%, respectively. Finally, the change in the federal funds rate as a percentage of the initial rate is 37.5%.

Was this solution helpful?
failed
Unhelpful
failed
Helpful