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?
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Understand the Problem
The question is asking how much prices might rise given the increase in total reserves by the Federal Reserve. It specifies a direct relationship between the increase in money supply and price level changes, and it includes a reserve requirement that needs to be considered for the calculation.
Answer
$0.36\%$
Answer for screen readers
The price level might rise by $0.36%$.
Steps to Solve
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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.
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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:
$$ \text{Number of increments} = \frac{200}{100} = 2 $$
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Determine the total increase in price level Now, we multiply the number of increments by the increase per increment:
$$ \text{Total increase in price level} = 2 \times 0.2 = 0.4% $$
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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:
$$ \text{Effective increase in reserves} = 200 \times (1 - 0.10) = 200 \times 0.90 = 180 $$
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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:
$$ \text{New price level increase} = 1.8 \times 0.2 = 0.36% $$
The price level might rise by $0.36%$.
More Information
This calculation shows how monetary policy, specifically changes in reserves, has a direct effect on the price level. Understanding the reserve requirement is crucial as it reduces the effective increase in money supply.
Tips
- Forgetting to adjust for the reserve requirement when calculating the money available for lending.
- Miscalculating the number of increments when determining the total price increase.
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