Uploaded by Haider Ali

# Profit Maximization in Case of Monopoly by Ali

```1.Profit Maximization in Case
of Monopoly
2.Markup Pricing
3.Linear Demand Curve and
Monopoly
Haider Ali
Choosing Suitable Quantity to Maximize Profit
Profit Maximization
• Profit Maximization problem
• Let us 𝑝 𝑦 Market Inverse Demand Curve
• 𝑐 𝑦 Cost Function
𝑟 𝑦 = 𝑝 𝑦 𝑦 Revenue function
• Profit maximization
𝑚𝑎𝑥𝑦 𝑟 𝑦 − 𝑐(𝑦)
Optimality Condition
𝑴𝑹 = 𝑴𝑪
∆𝑟
∆𝑐
=
∆𝑦
∆𝑦
If MR&lt;MC , Firms will decrease output and vice versa.
Output Decision
• If monopolist decides to increase its output by ∆𝑦 , there will be two
effects on revenues
• 1.Selling more output and earning revenue of 𝑝∆𝑦.
• 2. It will lower its price by ∆𝑝 and will get this lower price on all the
output he is selling.
𝑟 = 𝑝𝑦
𝑟 ′ = 𝑝 + ∆𝑝 𝑦 + ∆𝑦
Subtracting r from r’,
∆𝒓 = 𝒑∆𝒚 + 𝒚∆𝒑
∆𝒓
∆𝒑
=𝒑+
𝐲
∆𝒚
∆𝒚
By rearranging above equation we get
𝑀𝑅(𝑦)
1
=𝑝 𝑦 1+
𝜖 𝑦
1
𝑝 𝑦 1+
= 𝑀𝐶(𝑦)
𝜖 𝑦
Since elasticity is naturally negative that’s why we can also write it in the
following way.
1
𝑝 𝑦 1−
𝜖 𝑦
= 𝑀𝐶(𝑦)
In case of Perfect Comopetition Demand curve is flat i.e infinitively elastic
demand curve, in this case P=MC.
Markup Pricing
𝑀𝐶
𝑦
1
=𝑝 𝑦 1−
𝜖(𝑦)
𝑀𝐶(𝑦∗ )
𝑝 𝑦 =
1
1−
𝜖(𝑦)
Markup is given by
𝟏
𝟏
𝟏−
𝝐(𝒚
Numerical Example
• Suppose elasticity is constant i.e 𝜖 = 3.
• By using markup formula , markup will
be equal to 1.5.
• A monopolist who faces a constant
elasticity of demand will charge a price
that is a constant mark-up (which is 1.5
when e = 3) on MC. This is illustrated in
Figure.
Linear Demand Curve and Monopoly
Linear demand curve
𝑝 𝑦 = 𝑎 − 𝑏𝑦
Revenue Function
𝑟 𝑦 = 𝑝 𝑦 𝑦 = 𝑎𝑦 − 𝑏𝑦 2 .
Marginal Revenue Function
𝑀𝑅(𝑦) = 𝑎 − 2𝑏𝑦.
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