Page 176 - DMTH201_Basic Mathematics-1

Unit 6: Functions

Notes
8000 5000
Thus, we have C - 5000 = x 200 15(x 200)
400 200
or C = 15x + 2000, is the required cost function.
Further, the fixed cost is 2,000.

Example
The demand and supply of a commodity are given by x = 81000 – 160p and x = –4500 + 125p,
d s
where x denotes quantity and p denotes price. Find the equilibrium price and quantity.
Solution:
We know that x x in equilibrium
d s
81000 – 160p = –4500 + 125p

Thus, 285p = 85500 or – t = 300

Also equilibrium quantity x = 81000 - 160 × 300 = 33000 units.

Example

When price of a commodity is 30 per unit, its demand and supply are 600 and 900 units
respectively. A price of 20 per unit changes the demand and supply to 1000 and 700 units
respectively. Assuming that the demand and supply equations are linear, find
(i) The demand equation
(ii) The supply equation
(iii) The equilibrium price and quantity

Solution:
Note: In both the situations of demand or supply, the price is an independent variable and the quantity a
dependent variable. However, while plotting them, price is taken on vertical axis and quantity on the
horizontal axis. This is an exception to the convention followed in most of the other topics of
economics as well as in other branches of science, where the independent variable is taken along
horizontal axis and the dependent variable along vertical axis.
(i) The demand equation is the equation of line passing through the points (600, 30) and
(1000, 20). Thus, we can write
30 20
p – 30 = (x d – 600)
600 1000
On simplification, we get the demand equation as x = 1800 – 40p.
d
(ii) The supply equation is the equation of a line passing through the points (900, 30) and
(700, 20). Thus, we can write

30 20
p – 30 = (x s – 900)
900 700

On simplification, we get the supply equation as x = 300 + 20p.
s

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