Question

Q3. Two local ready-mix cement manufacturers, Here and There, have combined demand given by
Q = 105 − P, where Q = ????? + ??h??? . Their total costs are the following

?? = 5? + 0.5?2 and ?? = 5? + 0.5?2???? ???? ???? ?h??? ?h??? ?h???

a) Assume these two firms successfully collude. Compute the profit for each firm.

b) Draw the market demand, the cartel's marginal cost and marginal revenue functions in a diagram. Label properly both axes. Identify the equilibrium price and quantity for the cartel.

c) Now assume these two firms cannot collude, so they decide to start a price competition instead. Compute the profit for each firm in this case.

Answer 1

​​​​​​GIVEN DATA: -

Q = 105 − P, where Q = ????? +  ??h???

And their total coast are. .

?? = 5? + 0.5?2 and ?? = 5? + 0.5?2????

That the company could be the output will be optimal level that can be produced bt the MC that MC of firm Here = MC of firm There = MR of total demand
MR = dTR/dQ = d(P*Q)/dQ that inverse demand to that
P = 105-Q
TR = 105Q - Q2
MR = 105 - 2Q
MC of Here = dTC/dQHere = 5 + QHere and MCof there = 5 + QThere Equating
MCHere with MCThere 5+Qhere = 5+Qthere Qhere = QThere It means Total Q = Qhere + Qthere or Qhere = Q/2 .... eq
1 Thus at optimal output
105 - 2Q = 5 + QHere = 5 + Qthere eq 2 now from eq 1 and eq 2 105 - 2Q = 5 + Q/2
200 = 5Q Q = 40
Their fore total output would be 40 units.