Answer to Question #278281 in Microeconomics for Arlind

Question

(1)(a) What is 3 rd degree price discrimination? Briefly identify the conditions necessary for a successful

implementation of this profit maximizing strategy.

(b) A seller produces output and sells in two distinct markets with the following demand curves:

Q1 = 16 – P1 , Q2 = 20 – 2P2. If the total cost for the firm is 10 + 2Q, determine the quantities of

output the firm would produce and sell in each market. What prices would the firm charge in each of

the two markets?

(c) Find the price elasticity of demand in each submarket and briefly comment on how the results relate

to the relative prices charged in each market.

Answer 1

Solution:

1.a.). Third degree discrimination involves charging a different price to different groups of consumers for the same good.

The three conditions necessary for a successful implementation of this profit maximizing strategy include the following:

·        The firm must have some degree of monopoly power.

·        The firm must be able to identify different market segments, such as domestic users and industrial users.

·        The firm must have the ability to prevent arbitration or resale of the product.

 

b.). Profit maximization: MR = MC

Inverse demand function for market 1: Q₁ = 16 – P₁

P₁ = 16 – Q₁

Inverse demand function for market 2: Q₂ = 20 – 2P₂

P₂ = 10 – 0.5Q₂

Derive TR:

Market 1: TR₁ = P₁ $\times$ Q₁ = (16 – Q₁) Q₁ = 16Q₁ – Q₁²

Derive MR₁:

MR₁ = $\frac{\partial TR_{1} } {\partial Q_{1} }$ = 16 – 2Q₁

MC₁ = 2

Set MR₁ = MC₁

16 – 2Q₁ = 2

16 – 2 = 2Q₁

14 = 2Q₁

Q₁ = 7

 

Substitute to derive price:

P₁ = 16 – Q₁ = 16 – 7 = 9

P₁ = 9

 

Market 2: TR₂ = P₂ $\times$ Q₂ = (10 – 0.5Q₂) Q₂ = 10Q₂ – 0.5Q₂²

Derive MR₂:

MR₂ = $\frac{\partial TR_{2} } {\partial Q_{2} }$ = 10 – Q₂

MC₂ = 2

Set MR₂ = MC₂

10 – Q₂ = 2

10 – 2 = Q₂

8 = Q₂

Q₂ = 8

 

Substitute to derive price:

P₂ = 10 – 0.5Q₂ = 10 – 0.5(8) = 10 – 4 = 6

P₂ = 6

 

c.). Price elasticity of demand: $\frac{\triangle Q_{1} }{\triangle P_{1} }$ $\times \frac{P}{Q}$

Market 1: $\frac{\triangle Q_{1} }{\triangle P_{1} }$ = -1

PED = -1 $\times$ $\frac{9 }{7}$ = -1 $\times$ 1.29 = -1.29

PED = -1.29

 

Market 2: $\frac{\triangle Q_{2} }{\triangle P_{2} }$ = -2

PED = -2 $\times$ $\frac{6 }{8}$ = -2 $\times$ 0.75 = -1.50

PED = -1.50