Question

In: Economics

In market 1, let demand be given by q1 = A−5p. In market 2, let demand...

In market 1, let demand be given by q1 = A−5p. In market 2, let demand be given by q2 = 500−10p. Let Q = q1 + q2. Let total costs be C(Q) = 20 + 2Q. Let A < 250.

If a monopolist is forced to charge the same price in both markets what price will that be?
What is the price in each market if the monopolist can charge different prices in each market?
As a consumer in market 1, which of the above do you prefer (i.e. prices being forced to be the same, or allowing the monopolist to set different prices), if A = 40?
At what value of A does this preference change?

Solutions

Expert Solution

If the monopolist charges same price, he would just add the demands of both the markets, and then follow the profit maximization rule for Equilibrium Q i.e MR= MC

Q= q1+q2

Q= A- 5p+ 500- 10p

Q= A + 500- 15p.

p= 1/15 ( A+500 -Q).....................Total demand from both markets

TR= PQ

= 1/15 (A+500 -Q ) Q

= 1/15 (AQ + 500 Q - Q² )

MR = 1/15 ( A + 500 - 2Q)

TC= 20+ 2Q

MC= 2

MR = MC

1/15 ( A + 500 - 2Q) = 2

A+ 500- 2Q= 30

A+ 470 = 2Q

1/2 (A + 470) = Q................. Profit maximizing Q

p = 1/15 ( A + 500 - Q)........................(1)

Putting the value of Q in (1)

p = 1/15 ( A + 500 - 1/2 A - 235)

p = 1/15 ( 1/2 A + 265)

p = 1/30 A + 53/ 3.................... Price charged without discrimination.

When the monopolist charges different price, he will maximize his profit in each market separately.

MR1 = MC..................... Profit maximizing condition in market 1

TR1 = p q1

= 1/5 ( A - q1) q1

= 1/5 ( A.q1 - q1²)

MR1 = 1/5 ( A - 2q1 )

MC= 2

MR1 = MC

1/5 ( A - 2q1) = 2

A- 2q1= 10

A- 10 = 2q1

1/2 ( A- 10 ) = q1

q1= A- 5p....................(2)

Putting the value of q1 in (2)

1/2 (A- 10) = A- 5p

A- 10 = 2A - 10 p

10p = A + 10

p = A/ 10 + 1.............. Price in market 1 in case of price discrimination.

TR₂ = p .q₂

= 1/10 ( 500- q₂) q₂

= 1/10 ( 500 q₂ - q₂²)

MR₂ = 1/10 ( 500 - 2q₂)

MR₂ = MC

1/10 ( 500 - 2 q₂) = 2

500 - 2 q₂ = 20

480 = 2 q₂

240 = q₂

q₂ = 500 - 10p .................................. (3)

Putting the value of q₂ in (3)

240= 500 - 10p

10 p = 260

p = 26...................price in market 2 in case of price discrimination

If A= 40, then prices in market 1 will be 5, in case of price discrimination. And 19, if there is no price discrimination. So a consumer in market 1 will want price discrimination to proceed.
when prices in both the cases are same, or when the prices in case of same price charged is less than the case of price discrimination.

A/10 +1 > A/30 + 53/3

(3A - A)/ 30 > (53-3)/3

2A /30 > 50/3

A> 250.

When A is greater than 250 , then consumer will prefer same prices in both markets

Rahul Sunny answered 1 year ago

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