The document discusses the concept of demand in mathematical terms. It states that the amount consumers demand of a product (Qx) is a function of the price of the product (Px), the price of other goods (Py), consumer tastes and preferences (T), consumer income (M), and the number of consumers (N). It provides examples of linear and nonlinear demand curves expressed as mathematical equations, and explains how to calculate the total market demand by adding individual demand curves.

1. MARKET DEMAND
FUNCTION
.

2. SEYAM RAYHAN
SHARKER

3. Demand in Mathematical Terms
.

4. Review
We know that how much of a product consumers want
depends on
1) the price of the product,
2) the consumer desire or taste and preference for the
product,
3) the level of prices of other goods,
4) the level of consumer income,
5) the number of consumers in the market.
In a general mathematical sense we may summarize this with
the following
Qx = f(Px, Py, T, M, N) .

5. general math form
On the previous screen
Qx = the amount people want of good x,
f means is a function, note the parentheses here is not a
multiplication sign,
Px = the price of good x, Py = the price of good y,
T = a measure of consumer taste, M = consumer income,
N = a measure of the number of consumers in the market.
So, the amount people want depends on or is a function of
these influences listed in parentheses.

6. Linear demand
A linear demand curve might be of the form
Qx = a0 + axPx + ayPy + aMM.
Note the a’s with subscripts just means we have a number here.
Many books use the greek letter alpha here. The a’s may be
positive or negative.
As an example say we have
Qx = 1000 - 3Px + 4Py - .01M

7. Linear demand
Now if Px = 1, Py = 1 and M = 50,000
Qx = 1000 – 3(1) + 4(1) - .01(50,000)
= 1000 – 3 + 4 – 500
= 501.
Once we have the from and coefficient values of the
relationship between the variables we can make “predictions”
about how much people want based on the value of prices and
income and other variables.

8. Market demand
The market demand is the demand from each individual
added together. Say in a market we have two buyers. The
demand from each is
Q = 10 – 1P, and Q = 20 – 2P, respectively. (you will notice I
only have the price term listed. All the other influences are
captured in the Q intercept.)
Now, if the price is $1 per unit, the demand is 9 and 18,
respectively. So the market demand is 27. Here is how we
add the demand functions of each individual to get the
market demand : (next screen)

9. Market demand
Q = 10 – 1P
Q = 20 – 2P
Q = 30 – 3P
Notice on the left side on the addition I
did not put 2Q. The reason is due to the
notation used. The Q for each person is
personal, but I just used Q. You can see
at a price of 1 the Q is not the same for
each person. (We just did this last
screen.)
Notice the market demand curve Q = 30 – 3P does add up the
demand from each individual at a given price. If P = 1 we
have a market demand of 27 (= 9 + 18).

10. Inverse Demand curve
We just saw a market demand curve of
Q = 30 – 3P. I could rewrite this as P = 30/3 – (1/3)Q. When
written with P on the left we call the demand curve the inverse
demand curve. We write it this way because in a graph we
typically have the price on the vertical axis and so the equation
follows that convention. In general we write
P = A – BQ.
(Note: do not add individual demand curves when written in
inverse form – you do not get what you want.)

11. Nonlinear demand
Demand may not be a linear function. A popular nonlinear
form takes the form
Qx = cPx
BxPy
ByMBMHBH. An example would be
Qx = 10Px
-1.2Py
3M.5H.3 . An interesting thing about this
form is if you take the natural log (sometimes written Ln)of
each side you get
log Qx = 10 – 1.2 log Px + 3 log Py + .5 log M + .3 log H .
This nonlinear demand is said to be linear in logs.

12. Natural log
On the previous screen you see we have the amount demanded
in the form of a natural log. To get the value in the terms you
and I are used to you would take the value given and make it
the exponent of the term e.
Microsoft excel has the the function ln to put values into
natural log form. To get out of natural log form use the exp
function.