Question

In Market A, one unit sells for $10 and the quantity demanded goes up one unit for Every $2 price decrease. In Market B, the demand price for one unit is $6, and quantity Demanded goes up one-unit for every $1 price decrease. If you were a price Discriminator with constant marginal cost of $2, what price would you charge in each Market? Hint, you may need to draw a table here to find your answers.

Answer 1

Demand function: P = a - bQ

(I) Market A

When P = 10, Q = 1 and when P = 8, Q = 2

10 = a - b...........(1)

8 = a - 2b.........(2)

(1) - (2):

b = 2

a = 10 + b = 10 + 2 = 12

Demand: PA = 12 - 2QA

TRA = PA x QA = 12QA - 2QA2

MRA = dTRA/dQA = 12 - 4QA

Setting MRA = MC,

12 - 4QA = 2

4QA = 10

QA = 2.5

PA = 12 - 2 x 2.5 = 12 - 5 = $7

(II) Market B

When P = 6, Q = 1 and when P = 5, Q = 2

6 = a - b...........(1)

5 = a - 2b.........(2)

(1) - (2):

b = 1

a = 6 + b = 6 + 1 = 7

Demand: PB = 7 - QB

TRB = PB x QB = 7QB - QB2

MRB = dTRB/dQB = 7 - 2QB

Setting MRB = MC,

7 - 2QB = 2

2QB = 5

QB = 2.5

PB = 7 - 2.5 = $4.5