Page 144 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Unit 8: Use of Differentiation in Economics

And Note
π = R – C
=36q – 5q – q – 6q – 5
2
2
=30q – 6q – 5 ...(v)
2
For profit maximization
dS
dq = 30 12q 0

12q =30
30 5
Or q = 2.5
12 2
Putting the value of q in equation (i), (iv) and (v)
5 25
P = 36 5 u 36 36 12.5 23.5

2 2
MR = 36 – 10q
5
= 36 10 u 36 25 11

2
π = 30q 6q 2 5
5 5 5
= 30u 6u u 5
2 2 2
75
= 75 5
2
= 37.5 5 32.5
P MR
Since here P > MR, therefore monopolistic capacity of the firm is u 100
MR
23.5 11

= u 100
11
12.5 100
u
= 113.6%
11
In this condition, firm has the monopolistic capacity to increase the price by 113.6%
P
Thus, elasticity of demand (e) =
P MR
23.5 23.5
=
23.5 11 12.5

= 1.8.
Example 16: If following is the Demand and Cost:
P = 100 – 0.5 (q + q )
2
1
C =5q 1
1
C = 0.5q 2 2
2

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