Question

Two firms Apple and Samsung in the smart phone market have combined demand given by Q = 200 – P. Their total costs are given by TC _Apple = 4  Q _Apple +   Q ²_Apple and TC _Samsung = 4  Q _Samsung +   Q ²_Samsung . If they cannot successfully collude and instead produce where the market price equals marginal cost, their total output will be:

Answer 1

Given, Q = 200 - P so P = 200 - Q

where, Q = Q_A + Q_S (A- Apple and S - Samsung)

P = 200 - Q_A - Q_S

and TC_A = 4Q_A+ Q_A²

TC_S= 4Q_S+ Q_S²

If they cannot successfully collude and instead produce where the market price equals marginal cost, then for Apple

P = MC_A

MC_A = dTC_A/dQ_A = 4 + 2Q_A

So,

200 - Q_A - Q_S = 4 + 2Q_A

3Q_A + Q_S = 196....(i)

And for Samsung,

P = MC_S

MC_S = dTC_S/dQ_S = 4 + 2Q_S

So,

200 - Q_A - Q_S = 4 + 2Q_S

Q_A + 3Q_S = 196....(ii)

Solving equations (i) and (ii) simultaneously, we get

Q_A = 49 units and Q_S = 49 units

Thus, the total output is

Q = Q_A + Q_S = 49 + 49 = 98 units

Therefore, If they cannot successfully collude and instead produce where the market price equals marginal cost, their total output will be 98 units.