Chapter 10: Problem 362

Suppose that real GNP doubles while the quantity of money increase by \(80 \%\). If the velocity of money is constant, what happens to the price level?

Short Answer

Expert verified

With real GNP doubling and the quantity of money increasing by 80% while the velocity of money remains constant, the price level goes down by 10%. In other words, under these assumptions, there is a slight decrease in the price level.

Step by step solution

Determine the initial equation of exchange

The initial equation, before any changes occur, is: \(M_1V_1 = P_1Q_1\) Where: - \(M_1\) is the initial quantity of money - \(V_1\) is the initial velocity of money (will remain constant) - \(P_1\) is the initial price level - \(Q_1\) is the initial real GNP

Determine the final equation of exchange

The final equation, after the changes occur, is: \(M_2V_2 = P_2Q_2\) Where: - \(M_2\) is the final quantity of money (80% increase) - \(V_2\) is the final velocity of money (constant) - \(P_2\) is the final price level (what we want to determine) - \(Q_2\) is the final real GNP (double) Since the velocity of money is constant, we can write \(V_2 = V_1\).

Find the changes in quantity of money and real GNP

We are given that real GNP doubles, meaning \(Q_2 = 2Q_1\), and that the quantity of money increases by 80%, so \(M_2 = 1.8M_1\).

Substitute the changes into the final equation of exchange

Now, we'll substitute these changes back into the final equation of exchange: \(1.8M_1V_1 = P_2(2Q_1)\) Recall that \(M_1V_1 = P_1Q_1\). So, we can rewrite the equation as: \(1.8(P_1Q_1) = P_2(2Q_1)\)

Solve for the final price level

We want to find \(P_2\), so now we will solve for it: \(P_2 = 1.8(P_1Q_1) / (2Q_1)\) Notice that \(Q_1\) cancels out: \(P_2 = 1.8P_1 / 2\) \(P_2 = 0.9P_1\)

Interpret the results

We found that \(P_2 = 0.9P_1\), which means that, with real GNP doubling and the quantity of money increasing by 80% while the velocity of money remains constant, the price level goes down by 10%. In other words, under these assumptions, there is a slight decrease in the price level.

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