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 this essay, we will delve into a hypothetical economy to explore the dynamics of money supply, GDP, and the effects of monetary policy actions. The given economy has a nominal GDP of $1.2 trillion, a real GDP of $600 billion, and a money supply of $60 billion. Commercial banks are mandated to maintain a reserve requirement of 10% of deposits, without holding excess reserves.
The money multiplier represents the increase in money supply resulting from a change in the monetary base. It can be calculated using the formula: Money Multiplier = 1 / Reserve Requirement. In this case, the reserve requirement is 10%, so the money multiplier is 1 / 0.1 = 10.
Now, if the central bank buys $1 billion of government bonds, it injects money into the economy. This initial injection gets multiplied by the money multiplier. The change in money supply (ΔM) can be calculated as ΔM = Initial Injection × Money Multiplier = $1 billion × 10 = $10 billion. Therefore, the money supply would increase to $60 billion + $10 billion = $70 billion.
The Quantity Theory of Money states that MV = PY, where M is the money supply, V is the velocity of money, P is the price level, and Y is the real GDP. Before any central bank action, we can use this equation to find the initial values of the price level and velocity of money.
Given: M = $60 billion, V = ?, P = ?, Y = $600 billion.
Since V = (PY) / M, substituting the values, we get V = ($600 billion * P) / $60 billion = 10 * P.
Given that V is constant, we can rearrange the equation to solve for P: P = V / 10 = (10 * P) / 10. Solving for P, we find P = $1 (since V = 10).
With a constant velocity of money and a 2% increase in real GDP, we can predict the changes in nominal GDP and the price level. If money supply remains unchanged at $60 billion, the equation MV = PY implies that if Y increases by 2%, P must decrease by 2% to maintain the equation’s balance.
Therefore, if real GDP increases by 2%, nominal GDP will also increase by 2% (assuming no change in money supply), but the price level will remain the same.
To prevent any change in the price level despite a 2% increase in real GDP, the central bank must adjust the money supply. Using the equation MV = PY, where V and Y are known and P should remain constant, we can calculate the required money supply.
$60 billion * V = $600 billion * P.
Substituting V = 10 and P = 1, we find the required money supply M = ($600 billion * 1) / 10 = $60 billion.
If the central bank aims for 5% inflation while real GDP increases by 2%, we need to find the new required money supply to accommodate the increased nominal GDP. In this case, the new P would be 1.05 (5% increase from the initial P of 1).
$60 billion * V = $600 billion * 1.05.
Solving for V, we find V = 10.5.
Since V = (PY) / M, we can rearrange the equation to solve for the new required money supply: M = PY / V = ($600 billion * 1.05) / 10.5 = $63 billion.
In conclusion, this hypothetical scenario demonstrates the intricate interplay between money supply, GDP, and the price level in response to different monetary policy actions. Through these calculations, we’ve explored the consequences of central bank interventions, the impact on inflation, and the measures required to maintain stability in the economy.
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