A perfectly competitive industry consists of many identical firms, each with a long-run average total cost of LATC = 800 – 10Q + 0.1Q2 and long-run marginal cost of LMC = 800 – 20Q + 0.3Q2. In long-run equilibrium, each firm produces a quantity of .

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.

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