Question

Suppose that market ( inverse) demand is linear and given by p(y) = 120-y

Two firms compete in this market. Firm 1 has cost function
c_{a}(y) = 30y while its competitor, Firm B, has cost
c_{b}(y) = y2

i. Suppose that firm 1 is acting alone and acting as a monopolist. Find the market price and quantity sold assuring firm 1 maximizes its profits.

ii. Suppose that both firms are Cournot competitors. Find the quantity produced by each firm and the market price.

iii. Now assume they are Stackelberg competitors. Firm A is the leader and sets its quantity firm first. What quantity is produced by each firm and the market price?

Answer #1

Two firms, a and b, compete in a market to sell homogeneous
products with inverse demand function P = 400 – 2Q where Q =
Qa + Qb. Firm a has the cost function
Ca = 100 + 15Qa and firm b has the cost
function Cb = 100 + 15Qb. Use this
information to compare the output levels, price and profits in
settings characterized by the following markets:
Cournot
Stackelberg
Bertrand
Collusion

Two firms, a and b, compete in a market to sell homogeneous
products with inverse demand function P = 400 – 2Q where Q = Qa +
Qb. Firm a has the cost function Ca = 100 + 15Qa and firm b has the
cost function Cb = 100 + 15Qb. Use this information to compare the
output levels, price, and profits in settings characterized by the
following markets:
a, Cournot
b, Stackelberg
c, Bertrand
d, Collusion

1) Suppose the monopoly has broken up into two separate
companies. The demand function is P=105-3Q. The firms do not
collude and the firms have identical marginal cost functions
(MC1=MC2=40.). Also assume they are Cournot duopolists. Determine
the quantity and price of each firm.
Quantity for firm 1: ________
Quantity for firm 2: ________
Price in each market: $_________
2) Now assume these firms are acting like Bertrand duopolists. What
quantity will each firm produce and what will be the...

Suppose a drug manufacturer sells a new drug for twitchy feet.
The market demand curve for the drug is P=110-2Q, where P is the
market price and Q is the market quantity. Also suppose the
marginal cost for manufacturing is 10/ unit.
A) Assuming the firm is an unregulated monopolist, what
quantity and price should the firm offer?
Quantity =.
Price = $
B) Now suppose, the manufacturer has identified two separate
classifications of cusC) Suppose the monopoly has broken...

3. Consider an oligopoly in which firms choose quantities. The
inverse market demand curve is given by P = 280 - 2(X + Y ), where
X is the quantity of Firm 1, and Y is the quantity of Firm 2. Each
firm has a marginal cost equal to 40. What is the Stackelberg
equilibrium, when Firm 1 acts as the leader? What is the market
price at the Stackelberg equilibrium? What is the profit of each
firm?

Consider a market with demand p = a − bq. There are two firms.
Both firms produce the same homogeneous product but have different
technologies. Firm A has a cost function cA(qA) = cA × qA and firm
B has a cost function cB(qB) = cB × qB. If necessary, assume that
cA < cB.
(a) Find the equilibrium quantities produced by each firm, the
total equilibrium quantity, and the equilibrium price as a function
of a, b, cA, and...

Suppose a drug manufacturer sells a new drug for twitchy feet.
The market demand curve for the drug is P=105-3Q, where P is the
market price and Q is the market quantity. Also suppose the
marginal cost for manufacturing is 40/ unit.
C) Suppose the monopoly has broken up into two separate
companies. The demand function is still P=105-3Q as part A. The
firms do not collude and the firms have identical marginal cost
functions (MC1=MC2=40.). Also assume they are...

1. Consider a market with inverse demand P (Q) = 100 Q and two
firms with cost function C(q) = 20q.
(A) Find the Stackelberg equilibrium outputs, price and total
profits (with firm 1 as the leader).
(B) Compare total profits, consumer surplus and social welfare
under Stackelberg and Cournot (just say which is bigger).
(C) Are the comparisons intuitively expected?
2. Consider the infinite repetition of the n-firm Bertrand game.
Find the set of discount factors for which full...

Suppose a drug manufacturer sells a new drug for twitchy feet.
The market demand curve for the drug is P=120-4Q, where P is the
market price and Q is the market quantity. Also suppose the
marginal cost for manufacturing is 20/ unit.
A) Assuming the firm is an unregulated monopolist, what quantity
and price should the firm offer?
Quantity =
Price =
B) Now suppose, the manufacturer has identified two separate
classifications of customers for their twitchy feet product.
Because...

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...

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