Suppose This Year's Money Supply Is 500 Billion Nominal

3 Suppose That This Years Money Supply Is 500 Billion Nominal Gdp

Suppose that this year’s money supply is $500 billion, nominal GDP is $10 trillion, and real GDP is $5 trillion. a. What is the price level? What is the velocity of money? b. Suppose that velocity is constant and the economy’s output of goods and services rises by 5 percent each year. What will happen to nominal GDP and the price level next year if the Fed keeps the money supply constant? c. What money supply should the Fed set next year if it wants to keep the price level stable? d. What money supply should the Fed set next year if it wants inflation of 10 percent?

Paper For Above instruction

The relationship between money supply, price level, real GDP, and the velocity of money is fundamental in understanding macroeconomic stability and monetary policy. This paper explores these concepts through the context provided, employing the Quantity Theory of Money to analyze the implications of changes in economic variables and the Fed’s monetary policy decisions.

Calculation of the Price Level and Velocity of Money

Given the data: Money supply (M) = $500 billion, Nominal GDP (Y) = $10 trillion, Real GDP (Y_r) = $5 trillion. The Price Level (P) is calculated as the ratio of Nominal GDP to Real GDP:

P = Nominal GDP / Real GDP = $10 trillion / $5 trillion = 2.

Thus, the price level in the economy is 2.

The velocity of money (V) is given by the equation:

V = (Nominal GDP) / (Money Supply) = $10 trillion / $500 billion = 20.

This indicates that, on average, each dollar circulates 20 times within a year to support the transactions equivalent to the nominal GDP.

Projected Outcomes if the Velocity Remains Constant and Output Grows by 5%

If the velocity of money remains steady and real GDP grows by 5% annually, the new real GDP (Y_r_next) will be:

Y_r_next = $5 trillion * 1.05 = $5.25 trillion.

Assuming the velocity (V) remains at 20 and the money supply remains unchanged at $500 billion, the new nominal GDP (Y_next) can be determined by:

Y_next = V M = 20 $500 billion = $10 trillion.

However, since the real GDP has increased, nominal GDP must also increase proportionally if the velocity remains constant. Therefore, the new nominal GDP (Y_next) should be:

Y_next = P_next * Y_r_next.

But since V and M are steady, and nominal GDP stays at $10 trillion, the only plausible scenario is that the price level will adjust accordingly. Alternatively, considering the equality: Nominal GDP = Price Level * Real GDP, with the initial data and a constant velocity, the price level in the next year is determined by:

P_next = Nominal GDP / Y_r_next = $10 trillion / $5.25 trillion ≈ 1.90.

This indicates a slight decrease in the price level, reflecting the economic growth with stable money supply and constant velocity.

Implications for the Price Level if Money Supply is Kept Constant

Since the question is about what happens next year if the Fed maintains the same money supply ($500 billion) and the output increases by 5%, the model indicates the price level would decrease slightly from 2 to approximately 1.90, due to increased productivity and demand for money. Nominal GDP would, therefore, continue to reflect the unchanged velocity and money supply, remaining around $10 trillion, or adjusting marginally based on actual price level changes.

Monetary Policy Adjustments for Price Stability

If the Fed aims to keep the price level stable at 2 next year, given the increased real GDP of $5.25 trillion, the target nominal GDP should be:

Nominal GDP_target = Price level Real GDP = 2 $5.25 trillion = $10.5 trillion.

Using the quantity theory formula, the money supply (M_next) needed to achieve this at constant velocity (V = 20) is:

M_next = Nominal GDP / V = $10.5 trillion / 20 = $525 billion.

Thus, the Fed should set the money supply at approximately $525 billion next year to maintain the same price level.

Adjusting Money Supply for an Inflation Target of 10%

To achieve a 10% inflation rate, the price level next year should be:

P_next = P_current (1 + inflation rate) = 2 1.10 = 2.2.

The desired nominal GDP corresponding to this price level and the projected real GDP of $5.25 trillion is:

Y_next = P_next Y_r_next = 2.2 $5.25 trillion = $11.55 trillion.

To fund this level of nominal GDP at the same velocity (V = 20), the required money supply (M_next) is:

M_next = Y_next / V = $11.55 trillion / 20 = $577.5 billion.

Therefore, to induce a 10% inflation rate, the Fed should increase the money supply to approximately $577.5 billion next year.

Conclusion

This analysis demonstrates how the quantities of money, economic output, price levels, and velocity interact according to the Quantity Theory of Money. The Federal Reserve's monetary policy decisions—whether to keep the money supply constant, aim for price stability, or target inflation—are crucial tools for managing macroeconomic stability. By adjusting the money supply accordingly, the Fed can influence inflation rates and maintain the desired level of economic stability, illustrating the importance of understanding the mechanics of monetary economics in shaping policy outcomes.

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