1. A firm decides to bundle products A and B with the following inverse demand c

ID: 1122484 • Letter: 1

Question

1. A firm decides to bundle products A and B with the following inverse demand curves: PA = 1000 – 20A + 3B PB = 500 – 5B + A

The firm’s joint fixed cost is $10000 and marginal costs of MCA = 200 and MCB = 100

a. Calculate the joint-profit maximizing quantity of each product in the bundle (QA and QB).

b. Calculate the joint-profit maximizing price of each product in the bundle (PA and PB).

c. Calculate total profit of the firm.

d. Calculate MRA with respect to B and MRB with respect to A. Explain the economic meaning of each value.

a) profits = revenue - costs

= price* quanity - costs

= (1000 - 20A + 3B)A + (500 - 5B +A)B - (200A +100B +10000)

differentiating wrt to A

0 = 1000 - 40A + 3B +B - 200

0 = 800 - 40A +4B

A = (800 + 4B)/40.....1

differentiating wrt to B

0= 3A + 500 - 10B +A - 100

0 = 4A +400 -10B.....2

puttimg value of A in 2

0 = 4(800+4B)/40 + 400 - 10B

0 = 3200 + 16B + 16000 - 400B

0 = 19200 - 384B

384B = 19200

QB = 50

QA=25

PA = 1000 - 20A +3B = 1000 -20*25 + 3*50 = 650

PB = 500 - 5(50) +25 = 275

C) PROFITS = 650*50 + 275*25 - 10000 - 200*25 - 100*50 =19375

d) mra = DTR / DA

tr = TOTAL REVENUE = P*Q

MRA= 1000 - 40A + 3B +B - 200

MRb =DTR/DB . = 3A + 500 - 10B +A - 100

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