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Butoxors [25]
3 years ago
11

An industry demand curve faced by firms in a duopoly is P = 69 - Q, where Q = Q1 + Q2. MC for each firm is 0. How many units sho

uld each firm produce? How much money will each firm make?
Mathematics
1 answer:
emmasim [6.3K]3 years ago
7 0

You first need to establish the benefits function B. For each firm it is equal to the amount produced (q1 for firm 1 and q2 for firm 2) multiplied by the price P, minus cost C. It is

B1 = P.q1 - C1 = (69 - q1 - q2)q1 - C1

B2= P.q2 - C2 = (69 - q1 - q2)q2 - C2

As firma Will maximize benefits we need the derivative in q1 and q2 for firms 1 and 2 respectively. This will give us

69 - 2q1 - q2 = 0

69 - q1 - 2q2 = 0

Note that the derivative of cost is null as marginal cost is null.

Thus,

q2= 69 - 2q1

Replacing on the second equation:

69- q1 - 138 + 4q1 = 0

-69 + 3q1= 0

q1= 69/3=23

Replacing in the q2 equation:

q2=69- 46= 23

To find the money they make replace in benefits function. First we find piece P=69-23-23=23. Thus:

B1=23*23-C1

B2=23*23-C2

As we don't have a value for C1 and C2 we can't compute a number for benefits. If you have these values you will have the benefits.

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