Assume that there are 10 firms in the oil industry producing a specific type of processed petroleum.
The industry demand curve is given by P=100-2Q.
Six out of ten enter into an agreement to limit their production to increase the price.
Assume that each non-cartel firm has the total cost function of TC(qi)= 4qi 2 (i=1,2,3,4) and that they act as price takers. The cartel as a whole has a MC=qc.
a) Given the price P, how much will each non-cartel firms produce? i.e. what is (q1 q2 q3 q4)?
b) Using part a, knowing that non-cartel firms would produce q1, q2, q3 and q4 at any price p, what is the cartel’s Revenue function (in terms of P and qc ONLY)?
c) Using the optimal rule MR=MC, find the optimal quantity produced by the cartel and the market price P.
d) Calculate the quantity produced by all non-cartel firms.