Math & GDP
Money isn’t everything but everything needs money - Anonymous
When we think about real life problems, being a part of a developing country, money and finances comes first in mind. These thoughts of money or in a broader sense finance and economics act as driving force for a nation to excel. Living in the era of technology and computers , the theory of differential equations have become an essential tools for economic analysis
Today I’ll talk about (real)GDP . The change of GDP with time is a fine example of how ODE(Ordinary Differential Equations) in Finance.
What is GDP and why is it so significant?
GDP (in simple terms) is the measurement of productivity of a country. It is the total monetary or market value of all the finished goods and services produced within a country’s borders in a specific unit of time. To a greater mass, GDP is viewed as an important measure of national success.
How do we calculate GDP?
A differential equation expresses the rate of change of the current state as a function of the current state. A simple illustration of this type of dependence is changes of the Gross Domestic Product (GDP) over time. Consider state x of the GDP of the economy. The rate of change of the GDP is proportional to the current GDP
x’(t) = gx(t),
where t stands for time and x’(t) the derivative of the function x with respect to t. The growth rate of the GDP is x’/x.
If the growth rate g is given at any time t, the GDP at t is given by solving the differential equation. The solution is
x(t) = x(o)e^gt
The solution tells that the GDP decays (increases) exponentially in time when g is negative (/ positive).
Let us consider a practical example.
Suppose a country produces Oranges (only;for the sake of example)
Now how can we say whether the worth of the country increased or decreased following the previous data?
Let us assume that the price of each orange did not increase the second year.
Assuming P1= P2 =Rs 20
Then accordingly the GDP2’ = Rs (1010*20)
= Rs 20200
Hence even if our prices were held constant
we would have made this improvement
(or real growth)
Hence Real Growth= Rs (20200–20000)
= Rs 200 (It is denoted by the Orange dotted lines)
Here GDP2’ is considered the Real GDP (Today I won’t discuss on the Nominal GDP; Comment below if you’re interested)
For References I consulted lecturer from Swayam and Khan Academy and various sites on Google and a paper “ODE and Economics” by Dr Sanjay Kumar.
