Question

6. (3 points) Suppose that a monopoly can price discriminate between two markets: market 1 where the demand curve is given by 91 = 2 – P1, and market 2 where the demand is given by q2 = 4 – P2. Assume that the monopoly produces each unit at a cost of c=1. (a) Find {qM, PM, q2, px}. (2 points) (b) Suppose that price discrimination is no longer possible. Find {qM, pM}. (1 point)

Answer 1

a) Demand for market 1 is q₁=2-p₁

or, p₁=2-q₁

Then, total revenue TR₁=p₁q₁=2q₁-q₁²

and marginal revenue MR₁= dTR₁/dq₁ = 2-2q₁

Similarly, Demand for market 2 is q₂=4-p₂

or, p₂=4-q₂

Then, total revenue TR₂=p₂q₂=4q₂-q₂²

and marginal revenue MR₂= dTR₂/dq₂ = 4-2q₂

Given: C=1 per unit

Then, MC=0

Now, for profit maximization in each market, MR₁=MR₂=MC

Then, 2-2q₁=0

or, q₁=1 and p₁=2-1=$1

and 4-2q₂=0

or, q₂=2 and p₂ = 4-2=$2

Then, p₁^M=$1,q₁^M=1 unit, p₂^M=$2,q₂^M=2 units

b) If price discrimination is no longer possible,

q=q₁+q₂

or, q=2-p+4-p (where p₁=p₂=p)

or, q= 6-2p

or, p=3-(q/2)

Then, Total revenue TR=pq=3q-(q²/2)

and marginal revenue MR=3-q

Now, for profit maximization, MR=MC

or, 3-q=0

or, q=3

and p=3-(3/2)=$1.5

Then, p^M=$1.5 and q^M=3 units