Page 142 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Unit 8: Use of Differentiation in Economics

MR = 80 10 8 u 0 Note
1
90
MR = 180 58 u 29 0
2
90 90 90
u
p = (60 8) (5 8 8) 160u u u u 29 u 50
29 29 29
u
14400 8100
= 240 320 50
29 29
14400 8100

= 130
29
6300 7
= 130 130 217

29 29
7
= 87
29
Example 14: Demand and Total Cost of a monopoly in two markets are as under
P =2 – q 1
1
P =9 – 6q 2
2
C = q + q 2
1
In case of price difference in two markets determine the price, production (sale quantity), marginal
revenue and profit of monopoly. Also find out the elasticity of demand for Market A and market
B.
Solution: We know that
P =2 – q 1 ...(i)
1
P =9 – 6q ...(ii)
2 2
C = q + q 2 ...(iii)
1
Total Revenue for Market A R = P q =2q 1 – q 2 1 ...(iv)
1
11
Total Revenue for Market B R = P q =9q 2 – 6q 2 2 ...(v)
22
2
Separately differentiating equation (iv) and (v) separately with respect to q and q :
2
1
w R 1
22q
MR = q w 1 1 ...(vi)
1
w R 2
912q
MR = q w 2 2 ...(vii)
2
Total profit
p = R R C
2
1
= q 1 q 1 2 9q 2 6q 2 2 q 1 q 2

= q 1 q 1 2 8q 2 q 2 2 ...(viii)

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