Economics is a social science concerned with the study of the consumption, production and exchange of goods and services. Economists develop mathematical models to describe real-world economic phenomena. These models can be expressed using equations, words or diagrams. Economics lends itself to mathematical expression because many of the things economists deal with are quantitative, such as amounts or money or interest rates.
The equation of exchange describes the relationship among the supply of money, the velocity of money, the price level and income. It is usually written as MV = PY, where "M" is the quantity of money, "V" is the velocity of money, "P" is the price level and "Y" is the income level. The velocity of money refers to the number of times a particular unit of money, e.g. a dollar bill, changes hands in a particular period of time. The price level is the average price level for all products in the economy. If Y and V are held constant the equation of exchange can be used to find the level of inflation caused by an increase in the money supply. The equation of exchange is a mathematical identity, which means that it is necessarily true.
The Fisher equation describes the relationship between real and nominal interest rates. The Fisher equation is written as i = r + π, where "i" is the nominal interest rate, "r" is the real interest rate and "π" is the rate of inflation. The nominal interest rate is the amount of money paid in interest as a proportion of the amount of money borrowed. The real interest rate is the amount paid in interest with the effect of inflation removed. The inflation rate is the average change in the price of goods and services over time. The Fisher equation is named after economist Irving Fisher.
Elasticity equations describe how much one variable changes when a different variable changes. The changes are usually expressed as percentages. The things that elasticity equations describe are usually wages and the prices of various goods. Important elasticity equations include price elasticity of demand (PED) and income elasticity of demand (IED). PED measures the relationship between a change in the amount of a particular product people buy and the percentage change in the price of that product. IED measures the relationship between the percentage change in the amount of a product people buy and the percentage change in their income.
The national accounts equation describes components of gross domestic product, which is the total value of all the goods and services produced in a country in a year. The national accounts equation is Y = C + I + G + NX. "Y" is gross domestic product, "C" is private consumption, "I" is investment, "G" is government spending and "NX" is exports less imports. The national accounts equation is used to explore the relationship between all these factors and gross domestic product.