1) The document discusses applications of calculus concepts like marginal revenue, average revenue, and marginal cost in economics. 2) It provides examples of calculating marginal revenue from demand functions, finding the quantity where marginal revenue is zero, and deriving a demand function from a marginal revenue function. 3) One example shows calculating the total increase in cost from increasing production from 100 to 200 units using a given marginal cost function and total cost function.

1. APPLICATIONS OF CALCULUS IN
COMMERCE AND
ECONOMICS -II
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2. x
R
AR  Average revenue
Marginal Revenue =
dx
dR
Marginal Average Revenue =
dx
dAR
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3. The demand function is given by 2
21500 xxp 
Find the marginal revenue for any level of output x.
Also find the marginal revenue when x = 10
R = px
32
21500 xxxR 
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question 1

4. 2
341500 xxMR 
Marginal revenue when x = 10 is 1160
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5. The total revenue in rupees received from the sale of x units of
a product is given by
5
300)(
2
x
xxR  Find
i) The average revenue
ii) The marginal revenue
iii)The total revenue when MR = 0
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Question 2

6. 5
300)(
2
x
xxR 
5
300
x
AR 
5
2
300
x
MR 
5
2
3000
x
MR 
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7. x= 750
Total revenue when MR = 0 is 11250
5
750
)750(300
2

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8. The marginal revenue function of a commodity is given by
2
429 xxMR 
Find the demand function
 MRR
cxxxR  32
3
4
9
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Question 3

9. When x=0 , R= 0
32
3
4
9 xxxR 
2
3
4
9 xxp 
Hence c=0
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Demand function p=

10. A manufacturer’s marginal cost function is given by
406.0003.0 2
 xxMC where x is the number of
units of a product . If x increases from 100 to 200 units, find the
total increase in cost
xxxTC 403.0001.0 23

 MCTC
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Question 4

11. TC(200)-TC(100)= 2000
**************************
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