If the price level increases by 0.2 percent for every $100 billion increase in the money supply, by how much might prices rise if the Fed increases total reserves by $200 billion a... If the price level increases by 0.2 percent for every $100 billion increase in the money supply, by how much might prices rise if the Fed increases total reserves by $200 billion and the reserve requirement is 0.10? Read more

Steps to Solve

1. Identify key variables We know that the price level increases by 0.2% for every $100 billion increase in the money supply. The Federal Reserve is increasing the total reserves by $200 billion.

2. Calculate the increase in price level For every $100 billion increase, the price increases by 0.2%. Since the Fed is increasing reserves by $200 billion, we can find how many $100 billion increments are in $200 billion:

   $$ \text{Number of increments} = \frac{200}{100} = 2 $$

3. Determine the total increase in price level Now, we multiply the number of increments by the increase per increment:

   $$ \text{Total increase in price level} = 2 \times 0.2 = 0.4% $$

4. Adjust for the reserve requirement Since the reserve requirement is 0.10 (or 10%), we need to account for how much of the reserves are actually available for increasing the money supply. The money available for lending is calculated as follows:

   $$ \text{Effective increase in reserves} = 200 \times (1 - 0.10) = 200 \times 0.90 = 180 $$

5. Calculate the final increase in price level Now, we find out how many $100 billion increments fit into $180 billion:

   $$ \text{Effective increments} = \frac{180}{100} = 1.8 $$

   Finally, we calculate the new price level increase:

   $$ \text{New price level increase} = 1.8 \times 0.2 = 0.36% $$