In: Economics
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?
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.
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
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