Question 5 The following diagram illustrates two different m

Question 5 The following diagram illustrates two different market segments for a single seller. If the segments can be kept separated, what price will be set in each segment if the marginal cost is constant at $10? price price 100 60 Demand A Demand EB 40 Quantity 120 Quantity Segment A Segment B

Solution

We will find the demand function for each market.

For market A

We will derive the demand function using the points (P, Q) = (100,0) and (0,40).

(P -100) = -(100/40)(Q)

P = 100-2.5Q

In market A we will calculate the optimal quantity will be where marginal revenue equals marginal cost.

TR = (100-2.5Q)*Q = 100Q -2.5Q²

MR = dTR/dQ = 100-5Q.

In equilibrium MR =MC. This implies 60-Q = 10.Thus Q_a* = 18 and P_a* = 55

In Market B

For market B

We will derive the demand function using the points (P, Q) = (60,0) and (0,120).

(P -60) = -(60/120)(Q)

P = 60-0.5Q

In market B we will calculate the optimal quantity will be where marginal revenue equals marginal cost.

TR = (60-0.5Q)*Q = 60Q -0.5Q²

MR = dTR/dQ = 60-Q.

In equilibrium MR =MC. This implies 60-Q = 10 .Thus Q_b* = 50 and P_b* = 35