Question

Question 3 Suppose that the market demand curve for golf balls is described by Q = 90 – 3P where Q is measured in kilos of balls. There are 2 firms that supply the market. Suppose first that golf balls produced by the 2 firms are identical. Firm 1 can produce a kilo of balls at a constant unit cost of $15 whereas firm 2 has a constant unit cost of $10. (a) Suppose firms compete in quantities. How much does each firm sell in a Cournot equilibrium? What is market price and what are the firms’ profits? Show your work. (b) Suppose firms compete in price. How much does each firm sell in a Bertrand equilibrium? What is market price and what are the firms’ profits? (c) Would your answer in (b) change if there were 3 firms , one with unit costs = $20 and 2 with unit costs = 10. Explain why or why not. (d) Would your answer in (b) change if firm 1’s golf balls were green and endorsed by Tiger Woods whereas firm 2’s are plain and white? Explain why or why not.

Answer #1

Suppose that market demand for golf balls is described by Q = 90
− 3P, where Q is measured in kilos of balls. There are two firms
that supply the market.
Firm 1 can produce a kilo of balls at a constant unit cost of $15
whereas firm 2 has a constant unit cost equal to $10.
a)Suppose the firms compete in quantities. How much does each firm
sell in a Cournot equilibrium? What is the market price and what...

Consider an asymmetric duopoly. The market demand is p = 1 − Q.
Firm 1 has zero cost while Firm 2 has constant marginal cost c
distributed over the interval 0, 1/2.
a. Find the equilibrium when firms compete in quantities.
b. Suppose a regulator can marginally decrease c. Will this change
increase social welfare and why? Give your answer in terms of the
market share of Firm 2.
c. Suppose now that firms compete in prices. Find the Bertrand...

Two firms compete in a Bertrand setting for homogeneous
products. The market demand curve is given by Q = 100 – P, where Q
is quantity demanded and P is price. The cost function for firm 1
is given by C(Q) = 10Q and the cost function for firm 2 is given by
C(Q) = 4Q. What is the Nash-Equilibrium price? What are the profits
for each firm in equilibrium?

Suppose that demand for soccer balls is given by ?=120 – ?.
There are only two firms that produce soccer balls, they both have
cost function ??=60+q?^2, where ?=1,2 denotes the factory. Total
production of soccer balls is equal to output from the two
firms.
a. Suppose the two firms compete on quantities. Find the Nash
equilibrium price and output of each firm. How much profit does
each firm make?
b. Suppose that firm 1 gets their product to market...

Consider a market with only two firms. Demand on this market is
given by D(p)= 90 - 3p. Initially both firms have the same constant
per-unit cost, specifically c1 = c2 = 20 .
(a) What is the Nash equilibrium in this market if firms behave
as Bertrand competitors? How much does each firm produce, what
price do the firms charge, and what are their profits?
(b) Now suppose that firm 1 acquires a new production technique
that lowers its...

Consider the market for electricity in New York State. Suppose
that the demand for electricity is given by Q=16-0.2P (P=80-5Q)
where Q is measured in billions of kwh and P is measured in cents.
The marginal cost of producing electricity in NYS is MC=5+Q.
Suppose that there are three firms in this market who are
competing on the wholesale market by choosing prices (Bertrand
Competition). Firm 1 has a MC=15, Firm 2 has a MC=12, and Firm 3
has a...

Two firms compete in a market with inverse demand P = 120 − Q.
Firm 1 has cost function C(q1) = 20q1 and Firm 2 has cost function
C(q2) = 10q2. Solve for the Bertrand equilibrium in which firms
choose price simultaneously.

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 that two firms compete in the same market producing
homogenous products with the following inverse demand function:
P=1,000-(Q1+Q2)
The cost function of each firm is given by:
C1=4Q1
C2=4Q2
Suppose that the two firms engage in Bertrand price
competition. What price should firm 1 set in equilibrium? What
price should firm 2 set? What are the profits for each firm in
equilibrium? What is the total market output?
Suppose that the two firms collude in quantity, i.e.,
acting together...

24. Cournot duopolists face a market demand curve given by P =
90 - Q where Q is total market demand. Each firm can produce output
at a constant marginal cost of 30 per unit. There are no fixed
costs. Determine the (1) equilibrium price, (2) quantity, and (3)
economic profits for the total market, (4) the consumer surplus,
and (5) dead weight loss.
25. If the duopolists in question 24 behave according to the
Stackelberg Leader-Follower model, determine the...

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