Question

SCENARIO 3: Consider an industry consisting of two firms producing an identical product. The inverse market demand equation is P = 100 − 2Q. The total cost equations for firms 1 and 2 are TC1 = 4Q1 and TC2 = 4Q2, respectively.

Refer to SCENARIO 3. Suppose that the two firms are Bertrand rivals. The equilibrium level

of output for firm 1 is:

a. 8.

b. 10.

c. 12.

d. 24.

e. None of the above.

Answer 1

Answer - 24 (Option D )

* In Bertrand model firms determine price simultaneously. When product is homogenous/identical then each firm will charge price equal to marginal cost. This is because if one firm charges price greater than MC then competitors can reduce price slightly to get entire market. This is because products are perfect substitutes. In this situation there will be no incentive for any firm to deviate from their pricing strategy. In that sense it is Nash equilibrium. This result is also known as Bertrand Paradox because despite having only two firm the outcome is similar to competitive market output.

P = MC
100 - 2Q = 4
96= 2Q
Q = 48
For Firm 1 output is Q₁ = Q / 2
= 24