In This Problem All Amounts Are Shown In Billions Suppose Th

In This Problem All Amounts Are Shown In Billionssuppose This Years

In this problem, all amounts are shown in billions. Suppose this year's money supply is $800 billion, NGDP is $20 trillion, and real GDP is $8 trillion.

A) What is the price level? What is the velocity of money?

B) Suppose the velocity is constant and the economy's output raises by 5% each year. What will be the NGDP 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) Suppose the output still raises 5% next year, what money supply should the Fed set next year if it wants inflation of -2%?

E) Because of the widespread use of credit cards and other electronic payments, the velocity changed to 27. How much percentage is the change in velocity? The Fed set the target for economic growth at 5% next year and the inflation to be -2%. How much percentage change in money supply does the Fed intend to conduct?

Paper For Above instruction

The analysis of the money supply, velocity, price level, and GDP entails understanding several fundamental concepts central to macroeconomics. This paper addresses each question systematically, providing calculations rooted in the Quantity Theory of Money and related macroeconomic principles.

Part A: Determining the Price Level and Velocity of Money

Given data: Money Supply (M) = $800 billion, Nominal GDP (NGDP) = $20 trillion, and Real GDP (Y) = $8 trillion.

First, converting all units to a consistent scale, note that $20 trillion = $20,000 billion. Similarly, the money supply is $800 billion.

The Price Level (P) is calculated using the formula:

P = NGDP / Real GDP

Substituting the known values:

P = $20,000 billion / $8,000 billion = 2.5

The price level is therefore 2.5.

The velocity of money (V) is derived from the Equation of Exchange:

MV = NGDP

Rearranged for velocity:

V = NGDP / M

Applying the figures:

V = $20,000 billion / $800 billion = 25

Thus, the velocity of money is 25.

Part B: NGDP and Price Level Next Year with Constant Velocity and 5% Growth in Output

Assuming velocity (V) remains constant at 25 and real GDP increases by 5%, then the new real GDP (Y') is:

Y' = Y × 1.05 = $8 trillion × 1.05 = $8.4 trillion.

The new NGDP (NGDP') is found using the velocity equation:

NGDP' = V × M

Since the money supply remains unchanged at $800 billion, NGDP' equals:

NGDP' = 25 × $800 billion = $20 trillion

The NGDP remains at $20 trillion because the velocity and the money supply are constant, but this conflicts with the earlier increase in real GDP. To accommodate the increase, NGDP should also increase proportionally, but since the question specifies constant M and V, the NGDP is held steady at $20 trillion, implying a potential rise in the price level.

Next, calculate the new price level:

P' = NGDP' / Y' = $20,000 billion / $8,400 billion ≈ 2.38

This indicates a slight decrease in the price level, reflecting the increased output relative to nominal GDP, assuming constant NGDP.

Part C: Required Money Supply for Stable Price Level

To keep the price level constant at its initial level of 2.5 when the real GDP grows to $8.4 trillion, NGDP must also increase proportionally. Since P remains at 2.5, the NGDP must be:

NGDP' = P × Y' = 2.5 × $8.4 trillion = $21 trillion.

Given V = 25, the required money supply (M') is:

M' = NGDP' / V = $21 trillion / 25 = $840 billion.

Therefore, the Fed should set the money supply at $840 billion next year to maintain a stable price level.

Part D: Adjusting Money Supply for 5% Growth in Output and -2% Inflation

Target inflation of -2% suggests the aim to decrease the price level. The initial price level is 2.5; a -2% change would reduce it to:

P' = P × (1 - 0.02) = 2.5 × 0.98 = 2.45.

The new NGDP is related to the price level and real GDP:

NGDP' = P' × Y' = 2.45 × $8.4 trillion ≈ $20.58 trillion.

Using the velocity of 25, the new money supply (M') should be:

M' = NGDP' / V = $20.58 trillion / 25 ≈ $823.2 billion.

Thus, the Fed should target a money supply of approximately $823.2 billion to achieve a -2% inflation rate with 5% output growth.

Part E: Impact of Changed Velocity and Policy Changes

Velocity has increased from 25 to 27. The percentage change is calculated as:

Percentage change in V = [(27 - 25) / 25] × 100% = (2 / 25) × 100% = 8%.

Regarding the targeted economic growth of 5% and inflation of -2%, the change in money supply (ΔM) can be approximated using the Quantity Theory adjustment:

Expected NGDP growth rate:

NGDP growth rate ≈ Money supply growth rate + Velocity growth rate + Inflation rate.

Rearranged to find the necessary change in M:

ΔM / M ≈ NGDP growth rate - V growth rate - Inflation rate.

Assuming NGDP needs to grow by 5% plus a -2% inflation, total NGDP growth is approximately 3%. Since velocity increases by 8%, the Fed needs to adjust the money supply accordingly:

Money supply growth rate ≈ NGDP growth rate - V growth rate - inflation rate = 3% - 8% + 2% = -3%.

This indicates the Fed should decrease the money supply by approximately 3% to meet the targets considering the velocity increase and inflation goal.

In conclusion, the analysis reveals how central banks must adjust the money supply to sustain economic objectives amidst evolving velocity and output conditions.

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