When we are talking about an Imperfect competitive firm who is a price taker and has enough market power to have its Products price above the Marginal cost, than we also need to find out what would be that correct price and output that a monopolist must use to have its MR=MC. Just like we discussed in our last discussion about the Output decision of Monopoly. So a rule of thumb is applied in this regard to ease the whole procedure.
MR=ΔR/ΔQ = Δ(PQ)/ΔQ
MR= P + Q (ΔP/ΔQ)
Note : Producing one extra unit and selling it a P gives us a revenue of (1)P=P. And as we said the the firm faces a downward sloping demand curve, so producing and selling this extra unit would lead to a small decrease in Price ΔP/ΔQ which would lower the revenue from all the sold units. ( change in revenue Q(ΔP/ΔQ)
As per our discussion in Elasticity of Demand , recall that the elasticity for demand was equal to Ed= (P/Q)(ΔQ/ΔP). Thus, the above equation is the reciprocal of elasticity of demand, 1/Ed, so ,
MR=P + P(1/Ed)
And setting marginal revenue =Marginal Cost, (substituting the above equation of Mr with MC)
P + P(1/Ed)=MC
In the above equation , the left side is considered to be the markup over marginal cost as a percentage of Price. And this should equal the minus inverse of demand elasticity. Any value placed in it would be positive because the elasticity of demand is negative. Addtionally, Price can also be a markup to Marginal cost in the form of :
Hence, we can use these equations to check whether a particular output level and price are at its optimum level of not.
If Ed = -4
Marginal Cost = Rs 9 per unit
Than using the above equation , the Price would be :
9(1-1/4) = 9/0.75 = Rs 12 per unit
Comparing the Price of Perfect Competition with with Monopoly
A monopolist charges its price above its Marginal Cost but by the amount that is dependent upon the inverse Elastic Demand. So if demand is extremely elastic , Ed will be a large negative number due to which the price will be close to MC. In such a case, the monopolist would look more like a competitive one because there will be little benefit for the monopolist due to the elastic demand. (People would be more responsive to the Price change).