Suppose a typical firm’s marginal cost in a perfectly competitive industry is given by MC=10+ 0.001Q and there are 1000 identical firms in the industry. The demand for the total industry output is known to be P=110-0.001Q. Calculate the equilibrium price and output.
First, we need to find the industry's total supply function. Since there are 1000 identical firms, the total industry quantity supplied (Q) is:
Q = 1000Qf
where Qf is the quantity supplied by each individual firm. We can find Qf by setting marginal cost equal to price (since the industry is perfectly competitive):
10 + 0.001Qf = P
Rearranging this equation, we get:
Qf = (P - 10)/0.001
Substituting this expression for Qf back into the total supply function, we get:
Q = 1000[(P - 10)/0.001]
Now we can set demand equal to supply to find the equilibrium price and quantity:
110 - 0.001Q = 1000[(P - 10)/0.001]
Simplifying this equation, we get:
110 - Q/1000 = P - 10
P = Q/1000 + 120
Substituting this expression for P back into either the demand or supply equation and solving for Q, we get:
110 - 0.001Q = 1000[(Q/1000 + 110)/0.001]
Simplifying, we get:
Q = 100000
Therefore, the equilibrium quantity is 100,000 units. To find the equilibrium price, we can substitute this value back into either the demand or supply equation:
P = (100,000/1000) + 120 = $220
Therefore, the equilibrium price is $220 per unit.