Question

Suppose the supply of money, measured by M1, is $2.4 trillion, output, measured by real GDP, is $16.8 trillion, and the velocity of money is 6.0. Suppose the supply of money increases to $5.0 trillion but GDP and the velocity of money do not change. What is the percent by which prices change? Provide your answer as a percentage rounded to two decimal places.

Answer 1

The percent by which prices change when the money supply increases from $2.4 trillion to $5.0 trillion, with the velocity of money and real GDP remaining constant, is 78.57%.

Step-by-step explanation:

The question involves using the Quantity Theory of Money, which can be represented by the equation MV = PQ, where M is the money supply, V is the velocity of money, P is the price level, and Q is the real output or real GDP.

Initially, the money supply (M1) is $2.4 trillion, the velocity of money (V) is 6.0, and the real GDP (Q) is $16.8 trillion. The initial nominal GDP (PQ) can be calculated as $2.4 trillion × 6.0 = $14.4 trillion. When the money supply increases to $5.0 trillion, and GDP and the velocity do not change, the new nominal GDP will be $5.0 trillion × 6.0 = $30 trillion.

To find the percentage change in the price level, we take the new nominal GDP and divide it by the original real GDP. The new price level (P) is $30 trillion / $16.8 trillion = 1.7857. To find the percentage change, we calculate ((New P - Original P) / Original P) × 100. Assuming the original P was 1 (since we're using ratios), the percentage change is ((1.7857 - 1) / 1) × 100 = 78.57%, rounded to two decimal places.