Answer:
Each firm produces a quantity of 50 in long run equilibrium.
Explanation:
If a perfectly competitive industry of many identical firms has a long-run average total cost of LATC = 800 – 10Q + 0.1Q² and long-run marginal cost of LMC = 800 – 20Q + 0.3Q², for long run equilibrium to occur, LATC must be equal to LMC i.e LATC = LMC.
Equating both cost equation to get quantity Q each firm produces gives;
800 – 10Q + 0.1Q² = 800 – 20Q + 0.3Q²
Bringing all the terms to one side of the equation, we will have;
800-800-10Q+20Q+0.10Q²-0.3Q² = 0
10Q-0.2Q² = 0
Factorizing out Q, the equation becomes;
Q(10-0.2Q) = 0
From the resulting equation;
10-0.2Q = 0
10 = 0.2Q
Q= 10/0.2
Q = 50
This shows that each firm produces a quantity of 50 in long run equilibrium.
