Question

ECON M?C

There are two firms in an industry. The industry demand curve is given by p = 60 - q. Each firm has one manufacturing plant and each firm i has a cost function C(q) = 97, where qi is the output of firm i. The two firms form a cartel and arrange to split total industry profits equally. Under this cartel arrangement, they will maximize joint profits if Select one: O a. each firm produces 15 units in its plant. O b. they produce a total of 20 units, no matter which firm produces them. O c. each firm produces 10 units in its plant. O d. they produce a total of 30 units, no matter which firm produces them. O e. they shut down one of the two plants, having the other operate as a monopoly and splitting the profits.

Answer 1

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Solution,

If the firms form cartel & maximise joint profit

Total Revenue for first firm

TR₁ = P*q₁ = (60 - q₁)q₁ = 60q₁ - q₁²

TC = q₁²

Total Revenue for second firm

TR₁ = P*q₂ = (60 - q₂)q₂ = 60q₂ - q₂²

TC = q₂²

Joint profit = (TR₁ - TC₁) + (TR₂ - TC₂) = (TR₁ + TR₂ - TC₂  - TC₁)

t = 6091 6091 - of + 6042 - 92 - 91 - 42

$\small \pi = 60q_1 + 60q_2 - 2q_2^2 - 2q_1^2$

$\small \frac{\partial \pi}{\partial q_1} = 60 - 4q_1 = 0$

4q₁ = 60

q₁ = 60/4 = 15

$\small \frac{\partial \pi}{\partial q_2} = 60 - 4q_2 = 0$

4q₂ = 60

q₂ = 60/4 = 15

the correct option is a). Each firm produce 15 unit of goods in it's plant