Mathwizurd.com is created by David Witten, a mathematics and computer science student at Vanderbilt University. For more information, see the "About" page.

# Introduction

How do we quantify the success of an economy? A good way would be to see how much money the country is making. How do we do this? Through gross domestic product.

# Gross Domestic Product

Gross domestic product, or GDP, refers to the total value of all final goods and services produced in one year. This equals the sum of (products multiplied their price) in order to get the entire value.

### Final good

A final good does not include intermediate purchases. A guitar string is not a final product, but a guitar is, because guitars need guitar strings.

## Nominal vs. Real GDP

Nominal GDP uses current prices. Real GDP uses prices at the beginning of the year. The nominal GDP is affected by inflation.

A crucial formula is Nominal GDP = Real GDP + Inflation

So, if nominal GDP increases by 5% and inflation is 1%, real GDP is 4%. To be exact, it’s 1.05/1.01, which is 1.039 or 3.9%.

## GDP per Capita

This is GDP per person, and it is the best measure of well-being. That is because it’s not fair to compare the US’s GDP to Singapore’s. We are magnitudes larger than Singapore. We should compare GDP per person. Real GDP is a more reliable way of measuring well-being, so Real GDP per capita is even better. This is good because it accounts for inflation and the population of the country.

# What goes into GDP?

MathJax TeX Test Page $$GDP = \text{Consumption} + \text{Investment} + \text{Government Spending} + \text{Exports} - \text{Imports}$$ Why do we subtract imports? Well GDP only wants to track what is produced in the United States. Let's rewrite this $$GDP = \left(\text{US Goods consumed} + \text{Imports consumed}\right) + \left(\text{US Investment} + \text{Foreign investment}\right) + \\ \left(\text{Gov't Spending on US prod.} + \text{Gov't Spending on Foreign}\right) + \text{Exports} - \text{Imports}$$ $$=\text{US Goods Consumed} + \text{Investment} + \text{Government Spending} + \text{Exports}$$ This should make sense. It's only American products. $$\boxed{\text{GDP} = C + I + G + (EX - IM)}$$

## Consumption 68%

Consumption is just what people buy: food, clothes, cars, etc. This includes American-made and foreign-made products. Note that this has to be the consumption of newly created goods. Buying someone else’s house doesn’t increase GDP. Otherwise, person A could buy person B’s house then A could buy it back … and GDP could increase without bound.

## Investment 16%

Investment is spending on new buildings, factories, etc. These should be considered part of the United States’ product, because they have value. The main difference between this and consumption is this reaps long-term benefits, whereas consumption gives short-term benefits. Buying food, for example, is part of consumption. After you eat it, it’s gone. You cannot get any more benefits. Buying a house, however, will give you value for twenty to thirty years.

## Gov’t Spending on Goods and Services 18%

This is money the government spends on goods and services from local to federal. This includes the military, highway, and education.

Social security, unemployment, while government services, do not count for the GDP. Why is this? There is no value being added. Transferring money from one person (taxes) to another (unemployment checks) does not generate any value for the United States.

## Exports 13%

This is composed of all of the goods that America produces and ships abroad.

## Imports -15%

This is what the US buys from other countries. The reason it is subtracted is it’s accounted for in consumption, investment, and gov’t spending, and we only want to consider products created in the US.

# Example Problems

A man buys a Lamborghini. What does that do the GDP?

The GDP doesn’t change at all. While consumption increases by 300K, imports also increase by 300K. An important thing to remember is GDP only includes the value of products made in your country. Lamborghini’s are not made in the US, so they don’t count for the GDP.

What’s the largest portion of the GDP?

Consumption, or what citizens bought.

# Problems with GDP

GDP is a good measure for well-being. However, it still comes with problems. First of all, it doesn’t measure non-market activity. When an economy is doing well and incomes are high, people can afford to work less, therefore spending more time on leisure. This doesn’t add to GDP but it still indicates well-being. Additionally, if someone mows their own lawn, this doesn’t count toward GDP, but if someone does it for them, it does. Additionally, it doesn’t quantify income inequality, which is definitely relevant. Finally, if prices increase, GDP will increase regardless of whether or not the country is doing well.