Qualitative economics

# Qualitative economics

Discussion

Encyclopedia
Qualitative economics refers to representation and analysis of information about the direction of change (+, -, or 0) in some economic variable(s) as related to change of some other economic variable(s). For the non-zero case, what makes the change qualitative is that its direction but not its magnitude is specified.

Typical exercises of qualitative economics include comparative-static
Comparative statics
In economics, comparative statics is the comparison of two different economic outcomes, before and after a change in some underlying exogenous parameter....

changes studied in microeconomics
Microeconomics
Microeconomics is a branch of economics that studies the behavior of how the individual modern household and firms make decisions to allocate limited resources. Typically, it applies to markets where goods or services are being bought and sold...

or macroeconomics
Macroeconomics
Macroeconomics is a branch of economics dealing with the performance, structure, behavior, and decision-making of the whole economy. This includes a national, regional, or global economy...

and comparative equilibrium-growth states in a macroeconomic growth model
Exogenous growth model
The neoclassical growth model, also known as the Solow–Swan growth model or exogenous growth model, is a class of economic models of long-run economic growth set within the framework of neoclassical economics...

. A simple example illustrating qualitative change is from macroeconomics. Let:
GDP = nominal gross domestic product
Gross domestic product
Gross domestic product refers to the market value of all final goods and services produced within a country in a given period. GDP per capita is often considered an indicator of a country's standard of living....

, a measure of national income
M = money supply
T = total taxes.

Monetary theory
Quantity theory of money
In monetary economics, the quantity theory of money is the theory that money supply has a direct, proportional relationship with the price level....

hypothesizes a positive relationship
Direct relationship
In mathematics and statistics, a positive or direct relationship is a relationship between two variables in which change in one variable is associated with a change in the other variable in the same direction. For example all linear relationships with a positive slope are direct relationships...

between GDP the dependent variable and M the independent variable
Independent variable
The terms "dependent variable" and "independent variable" are used in similar but subtly different ways in mathematics and statistics as part of the standard terminology in those subjects...

. Equivalent ways to represent such a qualitative relationship between them are as a signed functional relationship and as a signed derivative
Derivative
In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much one quantity is changing in response to changes in some other quantity; for example, the derivative of the position of a...

:

where the '+' indexes a positive relationship of GDP to M, that is, as M increases, GDP increases, and vice versa.

Another model
Model (economics)
In economics, a model is a theoretical construct that represents economic processes by a set of variables and a set of logical and/or quantitative relationships between them. The economic model is a simplified framework designed to illustrate complex processes, often but not always using...

of GDP hypothesizes that GDP has a negative relationship
Inverse relationship
An inverse or negative relationship is a mathematical relationship in which one variable, say y, decreases as another, say x, increases. For a linear relation, this can be expressed as y = a-bx, where -b is a constant value less than zero and a is a constant...

to T. This can be represented similarly to the above, with a theoretically appropriate sign change as indicated:

That is, as T increases, GDP decreases, and vice versa.
A combined model uses both M and T as independent variables. The hypothesized relationships can be equivalently represented as signed functional relationships and signed partial derivative
Partial derivative
In mathematics, a partial derivative of a function of several variables is its derivative with respect to one of those variables, with the others held constant...

s (suitable for more than one independent variable):

Qualitative hypotheses occur in earliest history of formal economics but only as to formal economic models from the late 1930s with Hicks's model of general equilibrium
General equilibrium
General equilibrium theory is a branch of theoretical economics. It seeks to explain the behavior of supply, demand and prices in a whole economy with several or many interacting markets, by seeking to prove that a set of prices exists that will result in an overall equilibrium, hence general...

in a competitive economy. A classic exposition of qualitative economics is Samuelson, 1947. There Samuelson identifies qualitative restrictions and the hypotheses of maximization
Maxima and minima
In mathematics, the maximum and minimum of a function, known collectively as extrema , are the largest and smallest value that the function takes at a point either within a given neighborhood or on the function domain in its entirety .More generally, the...

and stability of equilibrium
Economic equilibrium
In economics, economic equilibrium is a state of the world where economic forces are balanced and in the absence of external influences the values of economic variables will not change. It is the point at which quantity demanded and quantity supplied are equal...

as the three fundamental sources of meaningful theorems — hypotheses about empirical data that could conceivably be refuted by empirical data.