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

Rearranging==> P-MC/P=-1/Ed

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 :

**P=MC/1+(1/Ed)**

Hence, we can use these equations to check whether a particular output level and price are at its optimum level of not.

### Practical Example

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).