Uploaded by Haider Ali

Profit Maximization in Case of Monopoly by Ali

advertisement
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
π‘Ÿ 𝑦 = 𝑝 𝑦 𝑦 Revenue function
• Profit maximization
π‘šπ‘Žπ‘₯𝑦 π‘Ÿ 𝑦 − 𝑐(𝑦)
Optimality Condition
𝑴𝑹 = 𝑴π‘ͺ
βˆ†π‘Ÿ
βˆ†π‘
=
βˆ†π‘¦
βˆ†π‘¦
If MR<MC , Firms will decrease output and vice versa.
Output Decision
• If monopolist decides to increase its output by βˆ†π‘¦ , there will be two
effects on revenues
• 1.Selling more output and earning revenue of π‘βˆ†π‘¦.
• 2. It will lower its price by βˆ†π‘ and will get this lower price on all the
output he is selling.
π‘Ÿ = 𝑝𝑦
π‘Ÿ ′ = 𝑝 + βˆ†π‘ 𝑦 + βˆ†π‘¦
Subtracting r from r’,
βˆ†π’“ = π’‘βˆ†π’š + π’šβˆ†π’‘
βˆ†π’“
βˆ†π’‘
=𝒑+
𝐲
βˆ†π’š
βˆ†π’š
By rearranging above equation we get
𝑀𝑅(𝑦)
1
=𝑝 𝑦 1+
πœ– 𝑦
1
𝑝 𝑦 1+
= 𝑀𝐢(𝑦)
πœ– 𝑦
Since elasticity is naturally negative that’s why we can also write it in the
following way.
1
𝑝 𝑦 1−
πœ– 𝑦
= 𝑀𝐢(𝑦)
In case of Perfect Comopetition Demand curve is flat i.e infinitively elastic
demand curve, in this case P=MC.
Markup Pricing
𝑀𝐢
𝑦
1
=𝑝 𝑦 1−
πœ–(𝑦)
𝑀𝐢(𝑦∗ )
𝑝 𝑦 =
1
1−
πœ–(𝑦)
Markup is given by
𝟏
𝟏
𝟏−
𝝐(π’š
Numerical Example
• Suppose elasticity is constant i.e πœ– = 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 = π‘Ž − 𝑏𝑦
Revenue Function
π‘Ÿ 𝑦 = 𝑝 𝑦 𝑦 = π‘Žπ‘¦ − 𝑏𝑦 2 .
Marginal Revenue Function
𝑀𝑅(𝑦) = π‘Ž − 2𝑏𝑦.
Download