Page 139 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Mathematics for Economists

Note 2
(B) Total Revenue R 15q 0.5q
R will become maximum, if
dR 0
dq 15q (0.5 2)q u
Or 15 – q = 0
Or q = 15
Putting the value of q in equation (i), (ii) and (iv)
π = 15 (0.5 15) u

= 15 7.5 7.5
R = 15 15 0.5 15 15u u u
= 225 112.5
= 112.5
π = (10 × 15) – (15 × 15) – 10
= 150 – 225 –10
= – 85.
q
Example 11: Linear demand of any monopoly is p = 12 – 0.4q and Demand C =0.6q 2 + 4 + 5 , then
calculate issue (q), price (p) and gross profit (ππ ππ π) under profit maximization method.
Solution: We know that
p = 12 – 0.4q ...(i)
C = 0.6q 2 4q 5 ...(ii)
Total Revenue
R = p × q
= (12 – 0.4q ) × q
=12q – 0.4q 2 ...(iii)
Total Profit
π = R – c
= (12q 0.4q 2 ) (0.6q 2 4q 5)

= 12q 0.4q 2 0.6q 2 4q 5
= 8qq 2 5 ...(iv)
For profit maximization

dS 0
82q
dq
Or 2q = 8
8
q 4
2
2
For second condition, d S 2 0
dq 2
Putting the value of q in equation (i) and (iv)
p = 12 (0.4 4) u
= 12 1.6 10.4

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