Question

Suppose that an industry consists of two firms. These firms are Bertrand competitors. The inverse market demand equation for the output of the industry is P = 33 − 5Q, where Q is measured in thousands of units. Each firm has a marginal cost of $3. Based on this information we can conclude that:

• P = $1.5 and each firm will sell 6,300 units.
  
  

• P = $5 and each firm will sell 2,800 units.
  
  

• None of the options.
  
  

• P = $3 and each firm will sell 6,000 units.
  
  

P = $3 and each firm will sell 3,000 units.

Answer 1

Bertrand competition is the price in which firms set their price. Here since marginal cot of each firm is $3 hence nash equilibrium will be P1 = P2 = MC = $3

Any firm trying to deviate from this price will be in loss as

if price set up is greater than its MC then the other firm will set its own price equal MC and capture the whole market & hence the first one will be worse off.

price can't be set up lower than the MC as it will generate loss.

hence P1 = P2 = MC = $3 is the nash equilibrium

NOW,

P = 33 - 5Q

=> 3 = 33 - 5Q

=> 5Q = 30 = Q = 6 in thousands units

Q = q1+q2 = 6000

since their cost structure is equal

hence q1 = q2 = 6000/2 = 3000 units

hence P = $3 and each firm will sell 3,000 units. is the answer i.e. option D