Question

Suppose the price p and quantity q of a commodity are related by the equation q = 30 - 4p - p2 find

1. ed at p = 2
2. MR

Answer 1

Given:

q = 30 – 4p – p²
1. e_d = (\(\frac { p }{ x }\))(\(\frac { dx }{ dp }\))
If P = 2 then
x = 30 – 4 (2) – 2²
= 30 – 8 – 4
=20 – 12
x = 18
\(\frac { dx }{ dp }\) =30 – 4p – p²
= 0 – 4 – 2p
= 0 – 4 – 2 (2)
= -4 -4
= -8
e_d = \(\frac { 2 }{ 18 }\) (-8)
x = – \(\frac { 16 }{ 18 }\)
e_d = – 0.88

MR

TR = p ×q
TR = p (30 – 4p – p²)
= 30p – 4p² – p³
MR = \(\frac { d(TR) }{ dp }\)
= 30 – 8p – 3p²
If p = 2
MR = 30 – 8 (2) – 3 (2)²
= 30 – 16 12
MR = 2