Page 325 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes 12.3.2 Law of Supply

Other things, like prices of other commodities price of factors of production, level of technology
etc. remaining constant, the quantity supplied (x ) of a commodity varies directly with its price.
s
Mathematically, we can say that x is a function of p. Using symbols, we can write
s
dx s
x = f(p). We note that 0.
s dp

Elasticity of Supply

The elasticity of supply is defined as ratio of proportionate change in quantity supplied to
s
proportionate change in price.
d log x dx p
=
s
d log p dp x

Example
(i) Find elasticity of demand of the function, x = 100 – 5p at (a) p = 10, (b) p = 15.
(ii) Find elasticity of demand of the function p = –2x + 3x + 150 at x = 8.
2
(iii) If p = a – bx is the inverse demand function, show that elasticity of demand is different at
different points on the demand curve. At what price the demand is unitary elastic?
(iv) p = f(x) is an inverse demand function such that x f(x) is constant. Show that elasticity of
demand is unity at every point on it. Explain the meaning of this result.
(v) Show that elasticity of demand can be expressed as the numerical value of the marginal
demand function to average demand function.

Solution:
dx dx p 10
(i) (a) x = 100 – 5p 5 and d 5 1
dp dp x 50
(x = 50 when p = 10, from the demand equation).
Hence, the elasticity of demand = 1.
d
d log x d log x dp 5p 50
Alternatively, 1
d
d log p dp d log p 100 5p 50
5 15
(b) When p = 15 we have, 3
d
25
dp
2
(ii) We have p = –2x + 3x + 150 4x 3 29 at x = 8.
dx
Also, p = –2 × 64 + 3 × 8 + 150 = 46
dx p 1 46 23
d 0.198
dp x 29 8 116

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