Question

Given 2 firms faced in a Bertrand Oligopoly with demand curves as follows: For Firm A QA = 400 – 4PA + 2PB For Firm B QB = 240 – 3PB + 1.5 PA Marginal cost for both firms is Zero Find the Bertrand Reaction Function for Firm A and the Price for firm A, PA with respect to PB

Answer #1

A city has two major league baseball teams, A and B. Demand for
each is as follows:
Qa=10-2Pa+Pb
Qb=20-2Pb+Pa
Each team chooses price simultaneously (Bertrand competition
with differentiated goods) in order to maximize its profit given
that the marginal cost of an extra spectator at each game is zero
for both teams.What price does each team charge for a ticket?

Managers at Firm A and Firm B must make pricing decisions
simultaneously. The following demand and long-run cost conditions
are common knowledge to the managers:
Qa = 72 – 4Pa + 4
Pb
LACa = LMCa = 2
Qb = 100 – 3Pb + 4
Pa
LACb = LMC b = 6.67
2.1. Derive the best response curve for firm A
2.2. Derive the best response curve for firm B.
2.3. What will be the prices charged by firms...

Managers at Firm A and Firm B must make pricing decisions
simultaneously. The following demand and long-run cost conditions
are common knowledge to the managers:
Qa = 72 – 4Pa + 4 Pb
LACa = LMCa = 2
Qb = 100 – 3Pb + 4 Pa
LACb = LMC b = 6.67
2.1. Derive the best response curve for firm A
2.2. Derive the best response curve for firm B.

Question 2: Managers at Firm A and Firm B must make pricing
decisions simultaneously. The following demand and long-run cost
conditions are common knowledge to the managers:
Qa = 72 – 4Pa + 4 Pb LACa = LMCa = 2
Qb = 100 – 3Pb + 4 Pa LACb = LMC b = 6.67
2.1. Derive the best response curve for firm A
2.2. Derive the best response curve for firm B.
2.3. What will be the prices charged by...

Consider the Bertrand competition where Firm A's profit function
is XA(PA, PB)= (pA)(QA(PA,PB))-(C(QA(PA,PB))) where QA(PA,PB) is
the demand for firm A's product given the posted prices. Firm A's
and B's products are identical, so consumers will go to the lowest
price. QA(PA,PB)= Q(PA) if PA<PB, (1/2)(Q(PA)) if PA=PB, and 0
if PA>PB. where Q(P)=15.5-0.5P. However, make the change that
firm B’s cost function is CB (Q) = 2Q. Firm A’s cost function
remains the same at CA (Q) = Q....

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...

Assume that you observe two firms operating in a Bertrand
oligopoly. The inverse demand function for the market is P = 200 –
2Q and each firm has the same cost function of C(Q) = 20Q. What is
the level of production for each firm, market price, and profit of
each firm? What would happen if both firms merge to form a single
monopoly with a cost function of C(Q) = 20Q?

Given the Inverse Demand function as P = 1000-(Q1+Q2) and Cost
Function of firms as Ci(Qi) = 4Qi calculate the following
values.
A. In a Cournot Oligopoly (PC, QC, πC)
i. Find the Price (Pc) in the market,
ii. Find the profit maximizing output (Qi*) and
iii. Find the Profit (πiC) of each firm.
B. In a Stackelberg Oligopoly (PS, QS, πS),
i. Find the Price (PS) in the market,
ii. Find the profit maximizing output of the Leader (QL*)...

The market demand is given by P = 90 − 2Q. There are only two
firms producing this good. Hence the quantity supplied in the
market is the sum of each firm’s quantity supplied (that is, Q = qA
+ qB), where qj is the firm j 0 s quantity supplied). Firm A has
zero marginal cost, while Firm B has the marginal cost of $30. Each
firm has no fixed cost, and simultaneously chooses how many units
to produce....

A firm produces two different goods, with demand given by the
following: Pa = 200 – 25Qa – 2Qb and Pb = 75 – 2Qb Where Pa = price
of good A, Pb = price of good B, Qa = quantity of good A and Qb =
quantity of good B.
The marginal costs for the two goods are 12 for good A and 20
for good B.
Determine optimal prices and quantities for each good.

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