Glyde Air Fresheners is the dominant firm in the solid room aromatizer industry,which has a total market demand given by Q = 80 - 2P.Glyde has competition from a fringe of four small firms that produce where their individual marginal costs equal the market price.The fringe firms each have total costs given by TC_i = 10Q_i + 2Q²_i.If Glyde's total costs are given by TC_G = 100 + 6Q_G,what is Glyde's maximum profit?

Question

Quizplus · Accepted Answer

To find Glyde's maximum profit, we need to first find the market price and demand at the equilibrium point. Setting Qd = Qs, we get:
80 - 2P = QS1U1B1G + 4QS1U1B1iS1U1B0 => 80 - 2P = 5QS1U1B1G
QS1U1B1G = (80 - 2P)/5
Substituting this back into the supply functions, we get:
P = 10QS1U1B1iS1U1B0 + 2QS1U1P12S1S1P0S1U1B1i S1U1B0 + 6QS1U1B1G - 100
P = 10QS1U1B1iS1U1B0 + 2QS1U1P12S1S1P0S1U1B1iS1U1B0 + 6[(80 - 2P)/5] - 100
Simplifying, we get:
8P = 1400 - 12QS1U1B1iS1U1B0 - 2QS1U1P12S1S1P0S1U1B1iS1U1B0
P = 175 - (3/4)QS1U1B1iS1U1B0 - (1/4)QS1U1P12S1S1P0S1U1B1iS1U1B0
Now, we can find each firm's quantity supplied and Glyde's profit. Starting with the fringe firms, we have:
MCi = P => MCi = 175 - (3/4)QS1U1B1iS1U1B0 - (1/4)QS1U1P12S1S1P0S1U1B1iS1U1B0
MCi = 175 - (3/4)QF => QFi = (4/3)(175 - MCi)
For the dominant firm, we have:
MCg = P => MCg = 175 - (3/4)QS1U1B1G - (1/4)QS1U1P12S1S1P0S1U1B1G
MCg = 175 - (3/4)(80/5) - (1/4)(0) => MCg = 151
QG = (80 - 2P)/5 => QG = 10
Glyde's profit is given by:
πG = PQG - TC(QG) => πG = [175 - (3/4)QS1U1B1G - (1/4)QS1U1P12S1S1P0S1U1B1G]QG - [100 + 6QS1U1B1G]
πG = [175 - (3/4)(80/5) - (1/4)(0)](10) - [100 + 6(80/5)] => πG = 332
Therefore, Glyde's maximum profit is $332, which corresponds to answer choice (D).

Glyde Air Fresheners Is the Dominant Firm in the Solid