Question

You have just been hired as the chief economist for Aarons (an eraser manufacturer) who currently enjoys a patented technology that allows it to produce erasers faster and at a lower cost than your only rival, Zacharys. Aarons has used this advantage to be to enable them to be the first mover in the eraser market and as such can choose to operate at the profit-maximising output level. Aarons cost function is CA(QA) = 2QCA, where as Zacharys cost function is CZ(QZ) = 4QZ and the inverse demand function for erasers is P = 500 − 2Q.

(a) Given the above information calculate the profit-maximising output levels for both Aarons and Zacharys.

(b) Given the above information calculate the equilibrium price in this market. (

c) Calculate the amount of profit each firm earns.

(d) Your firm has decided to merge with Zacharys, determine the offer that would enable the merger to be profitable to you firm.

Answer 1

Solution :-

a) P = 500 - 2Q

or then again P = 500 - 2(qA+qZ) where Q = qA + qZ

Zacharys chooses qZ with the end goal that his benefit is expanded.

Benefit (Z) = P * qZ - C(Z) * q(Z)

π (z) = (500 - 2(qA+qZ)) * qZ - 4qz * qz

First request condition gives, 500 - 2qA - 4qZ - 8qZ = 0

or on the other hand qA+6qZ = 250

or on the other hand qZ = (250 - qA)/6

Presently qA will be chosen to boost π(A)

π (A) = (500 - 2(qA+qZ)) * qA - 2qA * qA

First Order condition: 500 - 4qA - 2qZ - 4qA = 0

or on the other hand qZ + 4qA = 250

or on the other hand (250 - qA)/6 + 4qA = 250

or on the other hand 23qA/6 = 625/3

or on the other hand qA = 54.35

qZ = (250 - 54.35)/6 = 32.61

So Profit Maximizing Quantity for Aaron = 54.35 and Profit boosting amount for Zacharys = 32.61

b) P = 500 - 2 ( qA+qZ) = 500 - 2* (54.35 + 32.61) = 326.08

So the balance cost in the market is 326.08

c) Profit for Aaron = P * qA - 2qA * qA = 326.08 * 54.35 - 2*54.35^2 = 11814.60

Benefit for Zacharys = P* qZ - 4qz * qz = 326.08 * 32.61 - 4 * 32.61^2 = 8506.64

d) If Aaron were to Merge with Zacharys, Aaron would turn into a monopolist.

The benefit boosting amount can be discovered by likening Marginal income to peripheral Cost for Aaron

or on the other hand 500 - 4Q = 2

or on the other hand 4Q = 498

or on the other hand Q = 124.5

P = 500 - 2*124.5 = 251

Benefit = 251 * 124.5 - 2 * 124.5 = 31000.5

So Aaron's Profit would ascend by = 31000.5 - 11814.60 = 19185.90

So the most extreme sum that Aaron can pay to Zacharys for the merger to be gainful to Aaron is 19185.90