Calculating the Profit Maximising Price

 If you would have studies economics, you would be familiar about the concept of marginal cost (MC) and marginal revenue (MR). Profit is maximized when MR = MC.


There are two equations which would be used to determine the profit maximising price:


Equation 1:
     P = a - b x q ,
           where P = Price
                     Q=Quantity Demanded
                     A=The price at which demand would be Nil
                     B= change in price / change in quantity


Calculation of A:
        current price + ( current quantity at current price / change in quantity when price is changed by $b  x $b)


Equation 2:
      MR = a - 2b x q
                 all the variables are the same.




Lets calculate a profit maximizing price by using this methods,


Current Price charged by the company: $20
Current demand at current price: 1000 units
Change brought about in price by: $3
Change in quantity demanded due to change in price: 250 units
Variable cost per unit (marginal cost) $8


Required:
Calculate the profit maximizing price.


First lets calculate a, 20 + (1000/250 x 3)   =   $32
calculate b = 3/250 =  0.012


Substituting the values in the Marginal Revenue equation:


As profit is maximized when MR=MC, therefore as MC = $8 therefore MR is also $8.


      MR=a - 2b x q
      $8 = $32 - 2(0.012)q
        q = 1000, this is the quantity that should be demanded for profit maximizing price.


Substituting 'q' in price equation:
       
       P=a - b x q
       P = $32 - 0.012(1000)
       P = $20


To sum it up, if a price of $20 is charged at a demand of 1000 units than the company will maximize it profit to the maximum. $20 is the profit maximizing price and 1000 units are the profit maximizing demand.