Page 125 - DECO401_MICROECONOMIC_THEORY_ENGLISH

Microeconomic Theory

Notes Formula

According to price elasticity formula—
___
P __
E = × ∆Q

d Q
∆P
It is clear that, change brought in quantity ∆Q = Q – Q and change in price ∆P = P – P. But what are the
1
1
costs of P and Q? Because there are different costs of P and Q on the different points of AC arc, so it is
not necessary to use the fixed value of one of these. According to law, average of P and Q is used so that:
(Q + Q) (P + P)
1
1
and P =

Q = ________ _______

2
2
Therefore, arc price elasticity of demand is determined by the help of following formula—
Change in Quantity
Change in Price

E = __________________ + _______________

1 __
d 1 __
Sum of Quantities Sum of Price
2
2
1 __
(P + P)
∆Q
∆Q
∆P
1

E = (–) __________ ÷ __________ = (–) __________ × 2 _________

d 1 __ 1 __ 1 __ ∆P
(Q + Q) (P + P) (Q + Q)

2
2
2
1
1
1
or
1 __

Q – Q (P + P) Q – Q P + P
1
1
1
1
= (–)

E = (–) __________ × 2 _________ _______ ______

×

d 1 __ P – P Q + Q P – P
(Q + Q) 1 1 1

2
1
Here, Q = Initial Demand; Q = New Demand; P= Initial Price; P = New price
1
1
According to Arc Elasticity Method, if proportion of price of a commodity increases or decreases and as
a result of that there is contraction or relaxation in that proportion in the demand of commodity also,
and then the elasticity of demand will be the same. But if percentage method is used, then elasticity of
demand will be different in above condition. In first, this will be more than the unit (6) or elastic and in
3 __
second, this will be less than the unit ( ) or inelastic.

4
Therefore, arc elasticity method is more actual and dependent method in comparison to percentage
elasticity method.
There is also difference between arc elasticity of demand and point elasticity. Arc elasticity is the
average cost of elasticity on a special portion of demand curve while point elasticity is the the cost of
elasticity on a special point of demand curve. According to Baumol, “Point elasticity of demand is the
corresponding concept, for each point on the demand curve. But at any such point there is no change
in price (∆P = 0) or in quantity (∆Q = 0). We, therefore, take point elasticity to be the limit of the arc
elasticity figure as the arc is made smaller and smaller.”
5. Revenue Method
Revenue method is the fifth method of determining the elasticity of demand. Whatever the selling price
is earned by the factory of its production that is called revenue income. Suppose a company earns 50
by selling 10 m of cloth. So, this 50 will be called as total revenue of the factory. If total revenue is
divided by the quantity of units of production, then the quotient will be known as Average Revenue
50
___
or Per Unit Price. Average Revenue of above factory will be = 5 per metre. Therefore, average

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revenue and price are the synonyms. The difference comes in total revenue by selling a more units of any
commodity that is called the Marginal Revenues. If the factory earns 54 by selling 11 metre cloth, then
it means the marginal revenue of 11th metre cloth will be 54 – 50 = 4. An average revenue curve of
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