PRICE AND MARGINAL REVENUE

1
PRICE AND MARGINAL REVENUE

• DEMAND CURVE AND REVENUE
• Ref Managerial Economics by E.J Dauglas

2
Relationship between price, quantity demanded and
revenue

• It is studied because of impact price and qty
  demanded on total sales revenue
• OR
• Revenue Implications of the Law of Demand

3
Consider the following table
4
Contd

• In this example
• Px 11 0.001 Qx
• SO, FOR EVERY 1 UNIT OF PRICE REDUCTION THE
  QUANTITY DEMANDED WILL INCREASE BY 1000
• MR CHANGE IN TOTAL REVENUE DUE TO ONE UN IT
  IN QUANTITY DEMANDED
• MR ROW TO ROW DIFFERENCE IN TOTAL REVENUE
  COLUMN DIVIDED BY CHANGE IN QUANTITY DEMANDED
  etc.

5
Px 11- 0.001Qx
D
TR
MR
QX
6

• Total Revenue increases first as prices are low
  and reaches a maximum and then declines.
• MR lt Price at each output level and will fall to
  zero when TR is at maximum.
• TO FIND THE RELATIONSHIP BETWEEN PRICE AND MR WE
  CONSIDER THE TOTAL REVENUE AS THE PRODUCT OF
  PRICE AND QUANTITY.
•  T R x Px . Qx ( 10 )
•  WE KNOW Px a bQx
•  ? TRx a Qx bQx 2 ( 11 )

7

• SINCE MR IS DEFINED AS THE CHANGE IN TR FOR
  ONE UNIT CHANGE IN Qx IT CAN BE EXPRESSED
  AS THE FIRST DERIVATIVE OF EQUATION (11) WITH
  RESPECT TO Qx .
• TRx a Qx b Qx2
• dTR/dQ a 2 b Qx (MR)
• INTERCEPT( a ) EQUALS THE INTERCEPT OF THE
  EQUATION Px a bQx AND
• SLOPE TWICE OF EARLIER SLOPE.

8

• EXAMPLE Px 11 - 0.001 Qx
• MR 11 - 0.002 Qx
•  CONDITIONS FOR MAXIMA MINIMA Y f (X)

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IN REVENUE AND COST MAXIMISATION / MINIMISATION
THE FIRST AND SECOND ORDER CONDITIONS ARE
MAX
MIN 1st Order dY/dX 0 ( M R)
dY/dX 0 ( M C) 2nd Order d2Y/dX2
negative d2Y/dX2 positive

• LET Y 14 5X - 7X2
• dy/dx 5 - 14x
• d2 Y/dX2 - 14

• Y 14 - 5X 7X 2
• dy/dx - 5 14x
•  
• d2 Y/dX2 14

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REVENUE MAXIMISATION

• TOTAL REVENUE (TRx) f (Price Quantity)
• LET TRx Px Qx 
• SUBSTITUTE THE FUNCTION OF Px i.e.
• Px a bQx
• So TRx (a bQx) Qx
• aQx bQ2X
• WHEN Px 11 - 0.001 Qx (in Example)
• TRx 11 Qx - 0.001 QX2

11

• dTR/dQ 11 - 2 (0.001) Qx
• 11- 0.002 Qx
• SETTING MR 0 AND FINDING
• d2TR/dQ2 11 - 0.002 Qx 0
• OR Qx 5.5 (thousands)
• d2TR/dQ2 - 0.002(signifies change is negative)
• THE ABOVE IMPLIES AT Qx 5.5 TRx IS
  THE MAXIMUM.