Variables and Parameters

Introduction

Understanding variables and parameters is key to understanding economic models.

In these models,

Variables are the pieces of information in a function that can vary.
In equations, a variable represents a number or concept that is assumed to be of a varying value.
Parameters are the constants in a function.
Parameters set the context for the equation we are studying. When we alter the parameters of an equation, we create a new context for the function --- though it can often remain in a family of similar relationships.

How do I use variables and parameters in economics?

The diagram model below shows the market for surfboards.

Identify the variables.
Price and quantity demanded are variables.
Identify the parameters.
The slope of the demand curve is a parameter.
How does the parameter describe the relationship between the variables?
There is a negative (-1/2) relationship, and it is a linear (a straight line).

Show Variables and parameters in a mathematical model

Where are variables and parameters used in Microeconomics?

Demand Functions

Demand functions represent the relationship between the the quantity of a good demanded by consumers (Q^D) and the price of the good (P).

Show An example of a demand function

An example of a demand function

A demand curve might take the form of a linear function such as:

$Q^D = a - bP$

which shows that quantity demanded and price are inversely related. In this relationship, b is the slope of the demand curve and shows the amount by which quantity demanded (Q^D) by consumers will change for a given change in price (P). a is the quantity demanded by consumers when the price is zero.

In this example, Q^D and P are variables, and a and b are parameters.

Supply Functions

Supply functions represent the relationship between the quantity of a good supplied by sellers (Q^S) and the price of the good (P).

Show An example of a supply function

An example of a supply function

A supply curve might take the form of a linear function such as:

$Q^S = a + bP$

which shows that quantity supplied and price are positively related. In this relationship, b is the slope of the supply curve and shows the amount by which quantity supplied (Q^S) by sellers will change for a given change in price (P). a is the quantity supplied by sellers when price is zero.

In this example, Q^S and P are variables, and a and b are parameters.

Where are variables and parameters used in Macroeconomics?

Production Functions

An aggregate production function is a mathematical model that shows how the amount of output produced in a nation is related to the amount of capital and labor employed.

Show An example of a production function

An example of a production function

Suppose that total output (Q) is related to the amount of capital (K) and labor (L) employed in an economy as:

$Y = AL^aK^b$

where Y is total output, A represents technology, L and K are the amounts of labor and capital employed, and a and b are values that measure how output is related to labor and capital.

In this example, L and K are variables, and A, a and b are parameters.

Consumption Functions

Consumption functions summarize the relationship between consumer spending (C) and disposable income (Y).

Show An example of a consumption function

An example of a consumption function

A consumption function might take the form of a linear relationship such as:

$C = a + bY$

which shows that consumer spending and income are positively related. In this relationship, b is the slope of the consumption function (known as the "marginal propensity to consume"), and it shows the amount by which consumer spending (C) will increase for a given change in income (Y). a is the intercept (known as "autonomous consumption"), and it represents consumer spending when income is zero.

In this example, C and Y are variables, and a and b are parameters.