Page 146 - DECO403_MATHEMATICS_FOR_ECONOMISTS_ENGLISH

Unit 8: Use of Differentiation in Economics

Putting the value of q in equation (i) Note
1
80 + 0.5q =95
2
15
Or 0.5q = 95 80 15 or q 2 0.5 7.5
2
Putting the value of q and q in demand and profit
1 2
P = 100 – (q + q )
2
1
= 100 – 0.5 (80 + 7.5)
= 100 – 0.5 × 87.5 = 100 – 43.75 = 56.25
π = 95 × 80 – (0.5 × 80 × 80) – (0.5 × 7.5 × 80)
1
= 7600 – 3200 – 300 = 4100
π = 100 × 7.5 – 0.5 × 7.5 × 80 – 7.5 × 7.5
2
= 75 – 300 – 56.25 = – 281.25
Second condition
wS 1 = – 1 < 0
q w 1 2
2
wS 2 = – 2 < 0
q w 2 2
By reciprocal method (i) and (ii)
q = 95 – 0.5q
1 2
100 0.5q

and q = 2 1 50 0.25q 1

2
Since the slope of these curves is negative, therefore in case of increase in productivity of a firm,
productivity of second firm will go down.
Self Assessment

2. State whether the following statements are True or False:
6. With the help of differentiation, level of equilibrium in monopoly is assessed.
dR d ( )
()
c
7. dq z dq
8. MR = MC
TC TVC

9. AVC
x
TC TFC

10. AVC
x
8.2 Summary

z Differentiation is used in economics to determine elasticity.
z Demand product shows that demand of any commodity is the product of price of that
commodity. But demand of any commodity is also related to price of other related commodity.
Cross demand tells that if the price of related commodity changes, in that case demand of that
commodity also changes.

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