Question

Consider two firms competing to sell a homogeneous product by setting price. The inverse demand curve is given by P = 6 − Q. If each firm's cost function is Ci(Qi) = 6 + 2Qi, then each firm will symmetrically produce _________ units of output and earn ___________.

Multiple Choice

2 units; profits of $2

4 units; profits of $6

4 units; losses of $2

2 units; losses of $6

Answer 1

The correct answer is (d) 2 units; losses of $6

Marginal Cost = d(Ci)/dQi = 2

Hence Marginal Cost of both firms = 2

This is like a Bertrand competition. Suppose firm 1 charges price greater than MC(marginal cost = 2). Then firm 2 will charge price just lesser than Firm 1 price and will take all the market demand and hence Firm will not charge price greater than its marginal cost. Firm 1 will definitely not charge price lesser than its marginal cost because it will result in unnecessary loss. Hence Firm 1 will charge price equal to its Marginal cost (i.e.P = 2).

Similarly Firm 2 will also charge Price equal to its marginal cost = 2.

Both Will charge P = $2 and divide the market equally

Hence Nash equilibrium will occur when Both will charge there Price = MC and hence Market Price = 2

Market Quantity = 6 - P = 6 - 2 = 4 and hence Each firm's quantity = Market quantity/2 = 4/2 = 2

Hence Each firm's quantity = 2.

Profit = TR - TC = PQ - C = 2*2 - (6 + 2*2) = -6 i.e. loss of $6.

Hence, the correct answer is (d) 2 units; losses of $6