Question

There is a single good industry. If one firm produces all the output Q, then total costs are C1 = 1 +Q2 . Suppose two firms provide the industry output, each using the same technology as the single firm. If they divide the industry output efficiently, what is the total cost C2 ? Find the level of output Q’ such that for all output levels below Q’ we have natural monopoly, but for outputs above Q’ we are better off with two firms.

Answer 1

1) Suppose that there are two identical firms, Firm 1 and 2. Let us assume, they produce widgets and that are the only firms in the market.

2) Their total cost are given by C_i = 30Q_i,

which means MC₁ = 30 and MC₂ = 30.

3) The Two firms choose their output levels simultaneously, and market demand is given by

P = 150 - Q,

where Q = Q₁ + Q₂.  

4) The Marginal revenue schedules for each firm are as follows:

MR1 = 150 - 2Q₁ - Q₂

  MR2 = 150 - 2Q₂ - Q₁

Thus, the level of output 'Q' for all output levels below 'Q' we have natural monopoly, but for outputs above 'Q' we are better off with two firms.