Question

In the Bertrand model with homogenous product, how does the Nash equilibrium change if the two firms have different marginal/average cost?

Answer #1

In the Bertrand model with product differentiation, suppose that
the two Bertrand firms face the following symmetric demand
curves:
q1 = 96 - 2p1+1/2 p2
q2 = 96 - 2p2 + 1/2p1
where q1, q2 ≥ 0 and p1, p2 ≤ 48. MC for both firms is 12.
Is product differentiation more or less significant in this
example than in the example given in the text in Equations 10.3A
and 10.3B? Why?
Find the Bertrand equilibrium.

Consider the following variant of the Bertrand Model of Duopoly.
Suppose there are two firms producing the same good and they
simultaneously set prices for their product. If firm i sets a price
pi and firm j sets a price pj, the total quantity demanded for firm
i’s product is given by:
qi= 10–pi+ ½ pj
Each firm produces exactly the qi demanded by the market. Both
firms have the same marginal cost of production: c=4. For example,
if a...

A homogenous good industry consists of two identical firms (firm
1 and firm 2). Both firms have a constant average total cost and
marginal cost of $4 per unit. The demand curve is given by P = 10 –
Q. Suppose the two firms choose their quantities simultaneously as
in the Cournot model.
(1) Find and plot each firm’s best-response curve. (Be sure to
clearly label your curves, axes and intercepts.)
(2) Find each firm’s quantity and profit in the...

In a Bertrand duopoly with product differentiation explain how a
change in one firm's marginal cost can have an effect on the price
charged by the other firm.

1. In class, we found that the only Nash equilibrium outcome of
the homogeneous goods Bertrand duopoly model was p1 = p2 = MC. We
then noted that if we changed some of the assumptions this result
would no longer hold. Explain one assumption which will alter this
result such that two firms competing on prices will have market
power? 2. What is the Herfindahl-Hirschman Index (HHI)? You must
provide the formula for full credit. Would the Competition Bureau
be...

a. i. If a game has a dominant strategy equilibrium, does it
have a Nash equilibrium?
ii. If a game has a Nash equilibrium, does it have a dominant
strategy equilibrium?
iii. If one firm has a dominant strategy, can another firm take
advantage of that fact in deciding on its optimal strategy?
iv. Can a game have more than one dominant strategy
equilibrium?
v. Can a game have more than one Nash equilibrium?
b) There are only two firms...

what sort of insight does folk theorem provides to firms seeking
to escape the Nash Equilibrium of the static Prisoners’ Dilemma
game played in highly competitive (Cournot or Bertrand) markets.
Can some one explain with example?

) Suppose two identical firms with the constant marginal cost
produce the same product and compete in the market. (10) under
which model the equilibrium profit for each firm must be zero?
Bertrand or Cournot model, or neither

Two firms, A and B, engage in Bertrand price competition in a
market with inverse demand given by p = 24 - Q. Assume both firms
have marginal cost: cA = cB = 0. Whenever a firm undercuts the
rival’s price, it has all the market. If a firm charges the same
price as the rival, it has half of the market. If a firm charge
more than the rival, it has zero market share. Suppose firms have
capacity constraints...

Two firms are involved in Bertrand competition. The marginal
cost for firm 1 and 2 are mc1=1 and mc2=0. As
usual, the consumers purchase only from the firm with a lower
price. If p1=p2, then each firm will sell to
50% of the consumers. Find any two Nash Equilibria of the game. And
explain why they are Nash Equilibria.

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