A market contains two types of consumers, green and yellow. Each green consumer

Question

A market contains two types of consumers, green and yellow. Each green consumer has a demand of P = 20-Q. Each yellow consumer has a demand of P=16-Q. These are individual demand curves. The monopolist who sells to these individuals has a MC = 8 and FC =10. A. If the monopolist can recognize a consumer as either green or yellow, what bundle would they sell each kind of consumer? What total profit would the monopolist make? B. If the monopolist cannot recognize either group, what is the optimal bundle size(s)? C. How would your answer to 'B' change if their were three times as many green consumers? PLEASE SHOW WORK! THANK YOU

Explanation / Answer

Let q1 be the quantity demanded by green consumer. The respective price be p1

Let q2 be the quantiy demanded by yellow consumer. COrresponding price be p2

So we have

p1= 20 - q1

And p2 = 16 - q2

MC= 8, FC= 10

(If the monopolist can recognise the different consumers)

Profits, = p1q1+ p2q2 - MC*(q1+q2) - FC

= 20q1- q12 +16q2 - q22 - 8(q1+q2) - 10

/q1 = 20 -2q1 - 8 = 0

==> q1* = (20-8)/2 = 6

similarly, /q2 = 16 - 2q2 - 8 = 0

==> q2* = (16-8)/2 = 4

So p1* = 20-q1*=20- 6 = $14

p2* = 16- q2*= 16- 4 = $12

= p1q1 - p2q2 - 8(q1+q2) - 10

= 14*6 + 12*4 - 8*10 - 10

= 84 + 48 -80-10

= $42

B) If the monopolist cant recognise the consumers he will charge same price in both the markets.

So q1 = 20- P .....a

q2 = 16- P .....b

We will see total demand at price P is

q1 + q2 = 36 - 2P

Supose q1+q2 = Q

==> Q= 36-2P

==> P= 18 - (Q/2)

= PQ - 8(q1+q2) - 10

= 18Q - (Q2/2) - 8Q - 10 [Since q1+q2= Q]

Now,

/Q = 18 - Q - 8 = 0

==> Q* = 10

==> P* = 18 - (10/2) = 18 - 5 = 13

Putting this P in a and b to get q1 and q2, we get

q1*= 20-13= 7

q2* = 16-13 = 3

[Check that q1* +q2* = 10]

C) If there were three times as many green consumers, we have

3q1 = 60 - 3P

q2 = 16 - P

3q1+ q2 = 76 -4P

Q' = 76- 4P

P= 19 - Q'/4

= 19Q' - Q'2/4 - 8Q' - 10

/Q' = 19 - Q'/2 - 8 = 0

==> Q' = 16

P = 19 - 4 = 15

3q1 = 60 -3*15 = 15

q2 = 16- 15 = 1

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