Question

uppose that demand is given by qa = 32 – pa in Market A and by qb = 40 – pb in Market B where pi, and qi are price and output in market i = a, b, respectively. Marginal cost is constant and equal to 4. Fixed costs are zero.

b)   . Find the profit maximizing prices, quantities and profit if the monopolist can price discriminate.

c)   . Find the profit-maximizing price, quantity and profit if the monopolist cannot price discriminate. Determine whether it is more profitable to serve both markets or to serve only Market B.

Answer 1

b)

In case of price discrimination, monopolist will maximize profit in each market.

qa=32-pa

or pa=32-qa

Total revenue in market a=TRa=pa*qa=32qa-qa²

Marginal Revenue=MRa=dTRa/dqa=32-2qa

Set MRa=MC for profit maximization

32-2qa=4

qa=14 -----profit maximizing output in market a

pa=32-qa=32-14=$18 ----profit maximizing price in market a   

qb=40-pb

or pb=40-qb

Total Revenue in market b=TRb=pb*qb=40Qb-qb²

Marginal Revenue=MRb=dTRb/qb=40-2qb

Set MRb=MC for profit maximization

40-2qb=4

qb=18 ----profit maximizing output in market b

pb=40-qb=40-18=$22   ----profit maximizing price in market b

Profit=TRa+TRb-MC*(qa+qb)

Profit=18*14+22*18-4*(14+18)=$520

c)

qa=32-pa for pa32 or qa=0 for pa>32

qb=40-pb for pb40 or qb=0 for pb>40

Combined demand is given by

q=(qa+qb)  p32

q=72-2p for p32

q=qb for

q=40-p for

q=0 for p>40

Let us consider

q=40-p for

We have calculated in part b that profit maximizing price is $22, So, we ignore this function.

Let us consider

q=72-2p for p32

On rearranging we get

2p=72-q

p=36-0.5q

Total Revenue=TR=p*q=36q-0.5q²

Marginal Revenue=MR=dTR/dq=36-q

Set MR=MC for profit maximization

36-q=4

q=32 ----profit maximizing output

p=36-0.5q=36-0.5*32=20  ----profit maximizing price

Profit=TR-TC=20*32-4*32=$512

In case of uniform pricing policy, we can see that it is more profitable to serve both markets