Economics variables and their functional relationships
There are two categories of economic variables such as micro and
macro economic variables. Firstly, we discuss micro economic variable and their
relationships. After that we will study macro economic variables and their
relationships.
Micro economics variables and their functional relationships
Revenue (R), costs(C), utility (U), quantity supplied (QS),
quantity demand (QD) and price (P) etc. are the most important micro economic
variables. The following functional relationship exists between these
variables:
1.
Demand Function
The quantity demand (Qd) depends on price (P). This type of
relationship between demand and price is name as of demand function. It is
shown as:
Qd = f(P)
As regards to demand function, a law is presented known as law
of demand which states that “other things remaining the same the quantity
demanded varies inversely with change in price”. Thus to represent such
relationship and behavior between Q and P in the presence of certain
assumptions a standard demand function is presented as: Q= a-bp where P
and Q are variables, a and b are parameters (assumptions of the law of demand)
and the negative sign (-) represents the negative relationship between price
and demand. Therefore the demand function is a decreasing function. It is shown
as:
P increase, Qd decrease
and P decrease, Qd
increase
The standard demand function is linear. Hence its graph is a
straight line.
The average demand function = Q/p
Marginal demand function = slope of the demand curve
= demand function derivation= dQ/dp
2.
Supply Function
The quantity demand (Qs) depends on price (P). This type of
relationship between supply and price is name as of demand function. It is
shown as:
Qs = f(P)
As regards to supply function, a law is presented known as law
of supply which states that “other things remaining the same the quantity
supply varies directly with change in price”. Thus to represent such
relationship and behavior between Q and P in the presence of certain
assumptions a standard supply function is presented as: Q= a + bp where P
and Q are variables, a and b are parameters (assumptions of the law of d
supply) and the positive sign (+) represents the positive relationship between
price and supply. Therefore the supply function is an increasing function. It
is shown as:
P increase, Qs increase
and P decrease, Qs
decrease
The standard supply function is linear. Hence its graph is a
straight line.
The average supply function = Q/p
Marginal supply function = slope of the supply curve
= supply function derivation= dQ/dp
3.
Utility function
The utility (U) derived from any good depends on the units (Q) of
the good consumed. This type of functional relationship between U and Q is name
as the utility function. It is shown as:
U= f (Q)
As regard to utility function, a law is presented which is name as Law
of Diminishing Marginal Utility which states that “other thing remaining
the same, along with increase in the units of the commodity consumed the total utility
(U) increases at a decreasing rate, hence the marginal utility (MU) decreases”.
Thus to represent such relationship between U and Q in the presence
of certain assumption, a standard utility function is presented as:
U = aQ – bQ2
Where U and Q are variables, a and b represent parameters
(assumption of the law) and negative sign along with the square power on Q
shows that utility increase at a
decreasing rate. The rate of change of utility function or slope of utility
function is called marginal utility. It is shown as:
MU = dU/dQ
The standard utility function is Quadratic. Hence its graph is a
parabola.
4.
Production function
According to classical economists the production of any good (Q)
depend upon the units of labor (L). Such functional relationship between Q and
L is known as production function. It is shown as:
Q = f (L)
As regard to production function, a law is presented which is known
as Law of Variable Proportions which states that “ other thing remaining
the same, along with increase in the units of the labor the total production
increases at different rates, for
example , it increase at a constant rate , at a decreasing rate and at an
increasing rate”. Thus to represent relationship and behavior between Q and L
in the presence of certain assumptions, a standard production function
is follows as:
Q = aL – bL2 + cL3
Where Q and L are variables, a, b and c are represent parameters.
The average production function is called Average Product of Labor. It
is as:
APL = Q/L.
However, the slope of production function or derivative of
production function is given the name of Marginal Product of Labor. It
is shown as:
MPL = dQ/dL
The standard production function is cubic. Hence its graph is a cubic curve.
5.
Cost function
The cost of production (C) of any firm depend upon the quantity (Q)
produced by the firm. Such functional relationship between C and Q is known as cost
function. It is shown as:
C = f (Q)
As regard to cost function, we have a behavior which states that
“along with increase in the units of a
good produced the costs or total cost increase
at different rates, for example , it increase at a constant rate , at a
decreasing rate the cost increase at a constant rate and the cost increase at
an increasing rate”. Thus to represent relationship and behavior between C and Q
in the presence of certain assumptions, a standard cost function is
follows as:
C = aQ – bQ2 + cQ3
Where C and Q are variables, a, b and c are represent parameters.
The average cost function is called Average costs. It is shown as:
AC = C/Q.
However, the Marginal-Cost Function = slope of cost function=
derivative of cost function is given the name of marginal cost. It is shown as:
MC = dC/dQ
The standard cost function is cubic. Hence its graph is a cubic curve.
6.
Revenue function
The revenues (R) of any firm depend upon the quantity (Q) sold by
the firm. Such functional relationship between R and Q is known as revenue
function. It is shown as:
R = f (Q)
As regard to revenue function, we have a behavior which states that
revenue of the monopolist increase at a decreasing rate. Thus to represent
relationship and behavior between R and Q in the presence of certain assumptions,
a standard revenue function is follows as:
R = aQ – bQ2
Where R and Q are variables, a and b represent parameters. The revenue
cost function is called Average revenue. It is shown as:
AR = R/Q.
However, the Marginal revnue function = slope of revenue
function= derivative of revenue function is given the name of marginal revenue.
It is shown as:
MR = dR/dQ
The standard revenue function is quadratic. Hence its graph is a parabola.
Macro economics variables and their functional relationships
Transfer payments (R), Taxes (T), Government-Expenditure (G),
Imports (M), Exports (X), Rate of Interest (i), Investment (I), National Income
(Y), Savings (S) and Consumption (C). The following functional relationship
exists between these variables:
1.
Consumption function
According to Keynes the consumption expenditures (C) of an economy
depend upon income (Y) of the economy. Such functional relationship between C
and Y is known as consumption function. It is shown as:
C = f (Y)
It is an increasing function which states that “along with increase
in income, consumption expenditures increase and vice versa”. It is shown as:
Y increase, C increase
and Y decrease, C decrease
Regarding consumption function we have Keynes Law of Consumption
which states that there exists a non-proportional relationship between
consumption and income. Accordingly the standard short-run consumption
function is presented as:
C = Co + cY
Where Co is autonomous consumption and cY is induce consumption.
The evergae consumption function is called average propensity to consume = APC
= C/Y.
While the slop of consumption function or derivative of consumption
function is called Marginal Propensity to Consume = MPC = dC/Dy
The standard consumption function is linear. Hence its graph is a
straight line. It is told that in case of long run there exist a proportional
relationship between C and Y. Hence its standard form is as:
C = cy
2.
Saving function
According to Keynes the saving (S) of an economy depend upon income
(Y) of the economy. Such functional relationship between S and Y is known as
saving function. It is shown as:
S = f (Y)
It is an increasing function which states that “along with increase
in income, saving increase and vice versa”. It is shown as:
Y increase, S increase
and Y decrease, S decrease
The standard short run saving function is presented as:
S = -So + sY
Where -So is autonomous saving and sY is induce saving. The average
saving function is called average propensity to save = APS = S/Y.
While the slop of saving function or derivative of saving function
is called Marginal Propensity to save = MPS = dS/dy.
The standard saving function is linear. Hence its graph is a
straight line. It is told that in case of long run there exist a proportional
relationship between S and Y. Hence its standard form is as:
S = sy
3.
Income function
According to Keynes the national income (Y) of a country depends
upon investment (I). Such functional relationship between Y and I is known as
income function. It is shown as:
Y = f (I)
It is an increasing function which states that “along with increase
in investment, national income also increases and vice versa”. It is shown as:
I increase, Y increase
and I decrease, Y decrease
The derivative of income function is called ‘multiplier’ (K) or
investment multiplier which shows the ratio of change in income (ΔY) to change
in investment (ΔI). It is shown as:
K = ΔY/ΔI = dY/dI
4.
Investment function
According to Keynes investment (I) depends upon rate of interest (i).
Such functional relationship between I and i is known as investment function.
It is shown as:
I = f (i)
It is a decreasing function which states that “along with increase
in the rate of interest, investment decrease and vice versa”. It is shown as:
i increase, I decrease
and i decrease, I increase
5.
Investment function
According to Keynes investment (I) depends upon level of national
income (Y). Such functional relationship between I and Y is known as investment
function. It is shown as:
It is an increasing function which states that “along with increase
in thelevel of national income, the investment also increases and vice versa”.
It is shown as:
Y increase, I increase
and Y decrease, I decrease
The derivative of invest function is called accelerator coefficient
(w) which shows the ratio of change in investment (ΔI) to change in income
(ΔY). It is shown as:
w = ΔI/ΔY = dI/dY
6.
Import function
The imports (M) of an economy depend upon income (Y) of the
economy. Such functional relationship between M and Y is known as import
function. It is shown as:
M = f (Y)
It is an increasing function which states that “along with increase
in income (Y), the imports also increase and vice versa”. It is shown as:
Y increase, M increase
and Y decrease, M decrease
The standard import function is presented as:
M = Mo + mY
Where Mo is autonomous imports and mY is induce imports. The
average import function is called average propensity to import = APM = M/Y.
While the slop of import function or derivative of import function
is called Marginal Propensity to import = MPM = dM/dY.
The standard import function is linear. Hence its graph is a
straight line.