8.Consider a hypothetical economy with a nominal GDP of $1.2 trillion, real GDP of $600 billion, and money supply of $60 billion. Suppose commercial banks are required to maintain a reserve requirement of 10% of deposits. Assume that banks do not hold excess reserves. (Total marks = 12)
A) Calculate the money multiplier for this economy. If the central bank buys $1 billion of government bonds, what is the effect on money supply? Show your work. (2 marks)
B) Using the quantity theory of money, calculate the price level and the velocity of money for this economy prior to central bank action. Show your work. (2 marks)
C) Assume that velocity is constant and real GDP increases by 2% each year. What will happen to nominal GDP and the price level next year if money supply does not change? Show your work. (2 marks)
D) In (c), what money supply should the central bank set next year to keep the price level unchanged? Show your work. (3 marks)
E) In (c), what money supply should the central bank set next year if it wants inflation of 5%? Show your work. (3 marks)
In the context of a hypothetical economy with a nominal GDP of $1.2 trillion, real GDP of $600 billion, and a money supply of $60 billion, let’s delve into the various scenarios and outcomes considering the given parameters.
Money Multiplier and Central Bank Action
The money multiplier represents the factor by which the money supply increases due to a change in reserves. In this case, with a reserve requirement of 10%, the initial potential money multiplier (m) can be calculated using the formula: �=1reserve requirement=10.1=10.
If the central bank buys $1 billion of government bonds, the reserve of banks increases by $1 billion, leading to a potential increase in the money supply by $1 billion * 10 (money multiplier) = $10 billion.
Quantity Theory of Money: Price Level and Velocity
The Quantity Theory of Money equation states that MV = PY, where:
Given the real GDP ($600 billion) and money supply ($60 billion), we can calculate the velocity (V) using the equation: �=���=$1.2 trillion$60 billion=20.
Assuming that velocity is constant, rearranging the Quantity Theory equation gives us: �=���=$60 billion×20$600 billion=2.
Therefore, the price level is 2.
Effect of Real GDP Increase on Nominal GDP and Price Level
If real GDP increases by 2% (i.e., $600 billion * 1.02 = $612 billion), and assuming the money supply remains unchanged at $60 billion, the equation MV = PY still holds. As velocity is constant, nominal GDP (PY) would also increase by 2%, resulting in nominal GDP of $1.224 trillion. However, the price level (P) would remain unchanged at 2.
Keeping Price Level Unchanged
To keep the price level unchanged, the central bank needs to adjust the money supply based on the equation MV = PY. Given the 2% increase in real GDP, the desired nominal GDP is $1.224 trillion. With constant velocity (V = 20), the required money supply (M) can be calculated: �=���=$1.224 trillion20=$61.2 billion.
Therefore, the central bank should set the money supply at $61.2 billion to maintain the price level.
Achieving 5% Inflation
If the central bank aims for 5% inflation, the desired increase in the price level would be 5% of 2, which is 0.1. Therefore, the new desired price level (P) would be 2.1.
Using the Quantity Theory equation, we can calculate the required money supply (M): �=���=$1.26 trillion20=$63 billion.
Thus, the central bank should set the money supply at $63 billion to achieve a 5% inflation rate.
In conclusion, the hypothetical economy’s dynamics demonstrate the intricate relationships between money supply, price level, and real GDP. Through the analysis of the money multiplier, Quantity Theory of Money, and adjustments to the money supply, the central bank can influence inflation and maintain stability in the economy.
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