Q34. What is an economic identity?

An economic identity is a way to show an enduring relationship between two variables, which are equal by definition.

Identities pop up a lot in economics. The simplest are of the form: €1 = 100 cents, but some can be controversial. There is a theory called the quantity theory of money, which says that money supply M, times the velocity of circulation, V, is directly related to the price level P times the output of the economy, Y, all of which is expressed as:

This identity is controversial in economics, because the logical next step, if you believe this is a true representation of the world, is to try to control the economy's level of output by controlling the supply of money in the economy. It implies a restricted role for fiscal policy and government intervention in stabilising the economy. The set of policies this identity leads to is called 'monetarism'.

So, an identity in economics is extremely important, because from these basic assumptions or postulates comes an enormously beneficial or costly policy prescription, which can help or damage the lives of millions.

Q35. Why do economists use graphs?

A graph is one way to represent data and their relationship to one another. Graphs and diagrams are very important in economics. They are used to display economic data, to display the important economic forces at work (say in a supply and demand diagram), to work out the effects of changing these forces (say an increase in price), and to work out, without any mathematics, what the end result might be. Graphs in economics are used as representations of reality, and representations of economists' ideas about reality. Sometimes a graph will be used to illustrate a two-dimensional example of a larger economic problem, and sometimes as a corollary for much more abstract economic theorems.

Most importantly, figures and graphs are expository devices in economics. They are used to explain, to persuade, to teach, and to convince. As an example, here is the supply and demand diagram, the most famous graph in economics.

Here's how to read a graph of a variable changing over time - use the example figure below as a guide. First, look at the title of the thing: what does it think it is describing? Look for subjects, and for dates. For example, one would like to see Real Gross Domestic Product, 1967-2010, United States as a title. The line you'll be looking at, if it is a line graph, will tell you about the movement of inflation-adjusted GDP over a defined time range. The next thing to work out are the axes - what is being measured? It is billions of US dollars? Is it a change over time? It is on a logarithmic scale? Then look at the lines within the graph. Do they change abruptly? Does the line tend upwards or downwards over time?

The line in the graph represents an economic relationship.

The line in the graph represents an economic relationship.

Finally, because economics uses graphs endlessly; it is worth getting to know how they work, and how to construct one. When making a graph, first check the data. Remember the maxim: garbage in, garbage out. If your data are correct, then make sure to explain your encodings, label both the vertical and horizontal axes, and ensure you use and explain units, and make sure to keep your geometry in check. Show the source of your data, so those readers who are interested can check your findings, and expand on them if they like.

Q36. Why do economists use equations and functions to explain their theories?

Economists love equations. They make us feel like real scientists. Sadly, most of economic life is not well described by equations, but we persevere.

Equations are mathematical sentences, which say that the expression on the right-hand side of the equals sign is equal to the expression on the left-hand side. Models are causal stories economists generate to fit the patterns they see in the data; an equation is part of the modelling toolbox.

A function is a mathematical machine, a process that takes an input and produces an output. For every value of the independent variable, x, within the domain of the function, there is one value for the dependent variable, y.

Take the function y = x +2. For every number you pump in to the variable x (for example: x = 1, 2, 3, 4, 5), the function gives you a corresponding number for y (y= 3, 4, 5, 6, 7).

Why are functions useful? Economics is about relationships: between households and businesses, individuals and societies, government and markets, the past and the future, savings and investment, and many more. Functions help us to see these relationships, one variable to another (or many more), so we can talk of a consumption function, which tells us what level of consumption a household will be likely to do in a particular period, given its current level of disposable income.

Functions are used to try to estimate these relationships using real-world data and, most of the time, these functions are represented on graphs to illustrate the relationships.

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