It is known that there are 3 companies in the market. Every company has the same market
Question:
It is known that there are 3 companies in the market. Every company has the same market power. The demand function in the market is D(P): Q = 4000 – 4P. It should be noted that the quantity of goods supplied in the market (Q) is the sum of the quantities of each firm or Q = q1 + q2 + q3. Even though they have the same power, but the three companies have different total costs, the total costs of each company are as follows: Where: TC1 =100+4q21 +10q1; TC2 =150+4q22 +8q2; TC3 = 100+3q23 +10q3.
Question:
a. Find the profit equation for each company.
b. Calculate the total output (= production) of each firm at the time the maximum profit is reached. Use solving through matrices.
c. What is the equilibrium price and quantity in the market when each firm maximizes the advantage?