If velocity does not change when the money supply of a country increases, will nominal GDP definitely increase? Will real GDP definitely increase? Briefly explain.

Imagine money as a baton in a relay race; the frequency with which that baton is passed between runners is akin to the velocity of money. It measures the rate at which money circulates in the economy and is used for purchasing goods and services over time. Calculated by dividing nominal GDP by the money supply, it reflects the economic activity efficiency: the higher the velocity, the more transactions are occurring, suggesting a more dynamic economy.

In terms of exercise understanding, if the velocity of money stays the same and the money supply increases, more money is moving at the same pace. This indicates that more transactions could be happening, likely increasing the nominal GDP, but the effect on real GDP, which accounts for inflation, is less certain and will depend on various factors such as economic policies and the responsiveness of the market.

When you read a total that reflects the value of all goods and services produced in a country without adjusting for inflation, you're looking at nominal GDP. It’s the raw economic output. Nominal GDP can be helpful to get a snapshot of economic activity within a given year, but it doesn't tell the whole story—especially when comparing economic performance over multiple years. Higher nominal GDP usually signals a growing economy, but it can also be due to inflation.

So, in our exercise, an increase in the money supply, with an unchanged velocity, directly implies an increase in nominal GDP. However, this doesn’t necessarily mean that the country’s economy is producing more; it could also mean prices have gone up.

To determine if an economy is genuinely expanding, economists look at real GDP. This version of GDP is adjusted for inflation and represents the true growth in goods and services produced. It allows comparisons over time by expressing all years’ economic output in terms of a base year's prices, removing the distortion of inflation.

Back to our initial question – can an increased money supply definitively increase real GDP? Not necessarily. Increment in real GDP relies not just on the amount of money but how it's used to generate real products and services. So unless the increased money supply leads to increased production rather than just higher prices, real GDP might not see a significant change.

The Quantity Theory of Money is a classical economic theory that links the money supply and price levels over the long term. It’s famously summarized by the equation \( M \times V = P \times Y \) where \( M \) is the money supply, \( V \) is the velocity of money, \( P \) is the price level, and \( Y \) is the real GDP. According to this theory, if the velocity of money (\( V \) ) and real GDP (\( Y \) ) are constant, then an increase in the money supply (\( M \) ) will lead to a proportional increase in the price levels (\( P \)).

The implication for our exercise is that a boost in the money supply should logically lead to an increase in nominal GDP without necessarily impacting the real GDP, which adjusts for price changes, unless the extra money prompts growth in actual output.