Step 1:Start by finding the amount produced by each small firm, if the market price is P.Glyde Air Fresheners is the dominant rm in the solid room aromatizer industry, which has a total market demand given by Q = 80 - 2P. Glyde has competition from a fringe of four small rms that produce where their individual marginal costs equal the market price. The fringe rms each have total costs given by TCi = 10Qi +2Q2 . If Glyde's total costs are given by TC.G = 100 + 6QG, what price should Glyde establish for air fresheners? -
You are told that they produce at Marginal Cost = Price
MC = 10 + 4Q
P = 10 + 4Q
There are 4 identical small firms, so the total they produce is
Step 2 Find the demand curve faced by the large firm
The demand curve faced by the large firm is the totla market demand, less the amount produced by the other firms:
Qd = 80 - 2P - (P-10)
Qd = 90 - 3P
P = (90-Qd)/3
Step 3 Find the Total revenue function of the large firm.
The demand curve is the average revenue. Muliply by Q to get the Total Revenue.
P = (90-Q)/3
PQ = TR = Q(90-Q)/3
TR = 90Q - Q^2
Now you have the total revenue and total cost functions for the large firm. Find the price by equating MC = MR