Long-run equilibrium Problem. Suppose we have a market where all firms and poten
ID: 1104269 • Letter: L
Question
Long-run equilibrium Problem. Suppose we have a market where all firms and potential entrants are identical. Each firm’s marginal cost is MC(q) = 40 2q + 0.03q2, and each firm’s average cost is AC(q) = 40 q + 0.01q2. The aggregate demand curve is Q = D(p) = 25000 1000p. Find the long-run equilibrium, including: • The equilibrium price p • The equilibrium quantity q supplied by each firm • The number of firms N and the aggregate quantity Q = Nq supplied by the industry.Long-run equilibrium Problem. Suppose we have a market where all firms and potential entrants are identical. Each firm’s marginal cost is MC(q) = 40 2q + 0.03q2, and each firm’s average cost is AC(q) = 40 q + 0.01q2. The aggregate demand curve is Q = D(p) = 25000 1000p. Find the long-run equilibrium, including: • The equilibrium price p • The equilibrium quantity q supplied by each firm • The number of firms N and the aggregate quantity Q = Nq supplied by the industry.
Long-run equilibrium Problem. Suppose we have a market where all firms and potential entrants are identical. Each firm’s marginal cost is MC(q) = 40 2q + 0.03q2, and each firm’s average cost is AC(q) = 40 q + 0.01q2. The aggregate demand curve is Q = D(p) = 25000 1000p. Find the long-run equilibrium, including: • The equilibrium price p • The equilibrium quantity q supplied by each firm • The number of firms N and the aggregate quantity Q = Nq supplied by the industry.
Explanation / Answer
In long-run equilibrium, price equals minimum AC.
AC is at its minimum when it is equal to MC
Equating AC and MC to ascertain output at which AC is at its minimum
AC = MC
40 - q - 0.01q2 = 40 - 2q + 0.03q2
q - 0.02q2 = 0
q = 50
AC is at its minimum when q = 50
Calculate the minimum AC -
AC = 40 - q - 0.01q2
AC = 40 - 50 - 0.01(50)2
AC = 15
The minimum AC is $15 per unit.
As stated above, in long-run equilibrium, price equals minimum AC.
So, the long-run equilibrium price is $15 per unit.
The equilibrium quantity supplied by each firm (q) is 50 units.
Calculate aggregate quantity (Q) -
Q = 25,000 - 1,000P
Q = 25,000 - (1,000 * 15)
Q = 25,000 - 15,000
Q = 10,000
Aggregate quantity, Q, is 10,000 units.
Calculate the number of firms, N -
N = Q/q = 10,000/50 = 200 firms
The number of firms, N, is 200 firms.
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