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 (smaller or greater) when gas costs $4.30 than when gas costs $3.80.

Question

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 2.5%. This change of (0.005 or 0.2 or 0.5 or 0.25) percentage points means that the Fed raised its target by approximately (50% or 0.5% or 25% or 20%).

Answer 1

1. First, let's determine the absolute dollar difference between Bob's prices and the prices across the street at the two different gas prices.

• For gas costing $4.30:

  • Bob's price = $4.30
  • Price across the street = $4.30 * 1.20 = $5.16
  • Absolute difference = $5.16 - $4.30 = $0.86

• For gas costing $3.80:

  • Bob's price = $3.80
  • Price across the street = $3.80 * 1.20 = $4.56
  • Absolute difference = $4.56 - $3.80 = $0.76

Now, comparing both:

• At $4.30, the difference is $0.86.
• At $3.80, the difference is $0.76.

Thus, the absolute dollar difference between Bob’s prices and the prices across the street is greater when gas costs $4.30 than when gas costs $3.80.

2. Next, let's analyze the change in the federal funds rate:

• The Fed raised its target from 2% to 2.5%.
• The change in percentage points = 2.5% - 2% = 0.5 percentage points.

To determine how this change translates to a percentage, we calculate it relative to the original rate:

• Percentage change = (Change / Original) * 100
• Percentage change = (0.5 / 2) * 100 = 25%

Thus, the Fed raised its target by approximately 25%.