Question

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

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.

Key concepts

Velocity of Money

The velocity of money is a key concept in economics that reflects how frequently money is used to purchase goods and services in an economy over a given period. It is essentially an indicator of the rate at which money circulates in the economy. In the equation of exchange, the velocity of money is symbolized by \(V\) and plays a fundamental role in understanding economic dynamics.

• When the velocity of money is high, it means money is changing hands quickly, which could indicate a more active economy.
• Conversely, a low velocity indicates that each unit of money is used less frequently, suggesting slower economic activity.

In our problem, we assumed that the velocity of money remains constant, which simplifies the calculation and allows us to focus on changes in other variables like the quantity of money and real GNP.

Real GNP

Real Gross National Product (GNP) measures the total economic output of a country's residents, adjusted for inflation or deflation. It provides insight into the real value of goods and services produced by a nation and is an important metric for assessing economic performance.

• Real GNP focuses on the production by a country's citizens, whether within its borders or abroad, and is adjusted for price changes, making it a better indicator of long-term economic growth than nominal GNP.
• This adjustment helps to provide a more accurate reflection of people's living standards over time.

In the given exercise, the real GNP doubles, which is important because it directly impacts the equation of exchange. A doubling of real GNP means that despite more money being available, the economy is producing significantly more goods, which in turn affects the price level.

Price Level

The price level in an economy is a measure of the average of current prices across the entire spectrum of goods and services produced in the economy. It plays a critical role in economic theory as it relates to inflation and the purchasing power of money.

• An increase in the price level indicates inflation, where money buys fewer goods and services.
• A decrease suggests deflation, implying more purchasing power for each unit of currency.

In our exercise scenario, the price level decreases by 10% despite the quantity of money increasing. This happens because the increase in real GNP (which doubles) surpasses the growth in the money supply. Having doubled the economic output, the effect on prices is a downward pressure as more goods are competing for each dollar, leading to a deflationary effect instead of inflation.

Quantity of Money

The quantity of money in an economy refers to the total amount of monetary assets available in the system at a given time. It includes cash, coins, and balances held in checking and savings accounts. Changes in the money supply can have wide-reaching effects on economic activity, influencing interest rates, inflation, and consumer spending.

• An increase in the quantity of money typically leads to more spending and demand, which can drive up prices if it outpaces the growth of real output.
• However, if the growth of money keeps pace with or lags behind the growth in real goods and services, its inflationary impact can be mitigated.

In our example, the quantity of money is increased by 80%. While this would traditionally suggest higher inflation, in the context of our exercise, this increase is balanced by a doubling of real GNP, leading to a decrease in the overall price level, showing that actual outcomes depend heavily on the interaction between money supply and real economic growth.