Question

A market consists of two population segments, A and B. An individual in segment A has demand for your product Q= 50 - P. An individual in segment B has demand for your product     Q = 120 - 2P.
Segment A has 1000 people in it. Segment B has 1200 people in it. Total cost of producing Q units is TC = 5000 + 20Q.
a)What is total market demand for your product?
Assume that you must charge the same price to both segments.
b)What is the profit maximizing price?
c)What are your profits?
Imagine now that you can legally charge different prices to these people.
d) What price do you charge to people in segment A?
e) What price do you charge to those in segment B?

Answer 1

Individual Demand in Segment A:

qA= 50-P

Individual Demand in Segment B:

qB= 120-2P

a)

There are 1000 people in Segment A:

QA= 1000qA

QA= 50000-1000P Total Demand in Segment A

There are 1200 people in segment B:

QB= 1200qB

QB= 144000-2400P Total Demand in Segment B

Total Market Demand = QA+QB= 194000-3400P

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We can write total market demand as:

P= (194000-Q)/3400

TC= 5000+20Q

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b)

For profit maximization:

MR=MC

For MR:

TR= P x Q= (194000Q-Q2)/3400

MR= differentiation of TR with respect to Q= (194000-2Q)/3400

MC= differentiation of TC with rspect to Q= 20

Now Put:

MC=MR

20= (194000-2Q)/3400

68000 = 194000-2Q

2Q= 194000-68000

2Q= 126000

Q*= 63000 Profit maximizing quantity

Put Q*= 63000 in market demand curve:

P*= (194000-63000)/3400= 38.53 Profit maximizing price

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c)

Profit= P* x Q* - TC

Profit= 38.53 x 63000 - 5000-20(63000)

Profit= 2427390-5000-1260000= 1162390

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If Charging different price:

d) In segment A:

QA= 50000-1000P Total Demand in Segment A

PA= (50000-QA)/1000

PA is the price in segment A

TR of segment A= (50000QA-QA2)/1000

MR of segment A(MRA)= Differentiation of TR with respect to QA= (50000-2QA)/1000

MC= 20 (Already calculated in part b)

For profit maximization:

MC=MRA

20= (50000-2QA)/1000

20000= 50000-2QA

2QA= 30000

QA = 15000 Profit maximizing quantity in segment A

Put this value in PA= (50000-QA)/1000

PA= (50000-15000)/1000= 35 Profit maximizing price in segment A

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e)

In segment B:

QB= 144000-2400PB

PB= (144000-QB)/2400

TR= PB x QB= (144000QB-QB2)/2400

MR of segment B(MRB)= (144000-2QB)/2400

MC= 20

For profit maximization:

MC=MRB

20= (144000-2QB)/2400

48000= 144000-2QB

2QB= 96000

QB= 48000 Profit maximizing quantity in segment B

Put this value in:

PB= (144000-QB)/2400

PB=(144000-48000)/2400= 40    Profit maximizing price in segment B