Consider an industry in which n firms produce a homogeneous product. Demand for
ID: 1196963 • Letter: C
Question
Consider an industry in which n firms produce a homogeneous product. Demand for the product is given by p = a Q, where a is a positive constant and Q is the industry output. Each producer is identical, having a constant marginal cost c. Assume a > c. (a) If this industry is perfectly competitive, what is the equilibrium price and quantity? (b) Suppose n = 1 (so, it is a monopoly market). Find the equilibrium price and quantity. (c) Suppose these n producers are engaged in Cournot competition. Find the symmetric equilibrium. (An equilibrium is symmetric if all the firms are producing the same amount.) What happens to the equilibrium price as n approaches infinity? (d) Suppose one firm is a von Stackelberg leader and all the rest are followers and engaged in Cournot competition. Find the equilibrium price and quantity. What happens to the equilibrium price as n approaches infinity
Explanation / Answer
Q = nq or q = Q/n
For a firm,
TR = P.q = (a – qn).q = aq – nq^2
MR = a – 2qn
MC = c
In eq, MR = MC
a – 2qn = c or q = (a - c)/2n
P = a – n.[ (a - c)/2n] = (a + c)/2
TR = (a – Q)Q = aQ – Q^2
MR = a – 2Q
MC = c
In eq, MR = MC
a – 2Q = c or Q = (a – c)/2
P = a - (a – c)/2 = (a + c)/2