Two firms compete in a market by selling differentiated
products. The demand equations are :
q1 = 75 – p1 +p2/2
q2 = 75 – p2 +p1/2
Assume that each firm has a marginal cost and average
costs of 0
What market model do we use if each firm competes by
simultaneously choosing price
Are the two goods substitutes?
. Solve for firm 1’s best response
function.
Solve for the equilibrium price and
quantity.
Would firm 1 still be able...
Two firms produce differentiated products and set prices to
maximize their individual profits. Demand functions for the firms
are given by
Q1 =64–4P1 +2P2
Q2 =50–5P2 +P1
where P1, P2, Q1, Q2, refer to prices and outputs of firms 1 and
2 respectively. Firm 1’s marginal cost is $5 while firm 2’s
marginal cost is $4. Each firm has a fixed cost of $50.
Assuming that the two firms decide on prices independently and
simultaneously, calculate the best response function...
Consider a differentiated Bertrand market with three firms,
whose demand curves are:
Q1 = 300-10P1+3P2
+2P3
Q2 = 300-8P2 +2P1 +
P3
Q3=
50-3P3+P1+P2.
Firms 1 and 2 both have marginal costs of 10 and Firm 3 has a
marginal cost of 15.
P1 = 26.80; P2 = 28.66; P3 = 25.07.
a. Calculate the market shares of each product
If Firm 2 and 3 merge Firm 3’s marginal cost will fall to 10 as
a result of the merger....
1. Consider a differentiated Bertrand market with three firms,
whose demand curves are:
Q1 = 300-10P1+3P2 +2P3
Q2 = 300-8P2 +2P1 + P3
Q3= 50-3P3+P1+P2.
Firms 1 and 2 both have marginal costs of 10 and Firm 3 has a
marginal cost of 15.
a. Calculate the equilibrium prices and quantities.
b. Calculate the market shares.
c. By specific reference to the HMGLs, would the two lead
federal agencies be likely to regard a merger between Firm 2 and
Firm...
Consider two firms that provide a differentiated product, which
they produce at the same constant marginal cost, MC = 3 (no fixed
cost). The demand function for Firm 1 is q1 = 10 – p1 + 0.5p2 and
for Firm 2 is q2 = 20 – p2 + 0.5p1, where p1 is Firm 1’s price and
p2 is Firm 2’s price.
a) Write the profit functions for these firms.( 8 marks)
b) What are the equilibrium prices and quantities? (...
There are two firms, A and B producing differentiated products.
Their demand curves are:
qA=100-2PA+3PB
qB=120-2PB+2PA
and both have MC=5. Note that demand
curves are not symmetric. Assuming that firms are engaged in
Bertrand price competition:
(a)Write down the profit function of
firm A and find its price response function
Hint:
πA=(PA-5)(100-2PA+3PB)
(b) Write down the profit function of
firm B and find its price response function
(c) Find equilibrium prices
PA and PB; equilibrium quantities
qA and qB; and...
A monopolist has two segmented markets with demand
curves given by
P1 = 160- Q1 and P2 = 130 - 0.5Q2
where p1 and p2 are the prices charged in each market
segment, and Q1 and Q2 are the quantities sold. Its cost function
is given by c(Q) = 2Q2, where Q = Q1 + Q2.
a. What type of price discrimination does this
entail?
b. Find the monopolist's profit-maximizing price and
quantity for each segment.
c. What is the...
Q2. Consider a Bertrand game with differentiated products in
which two firms simul- taneously choose prices. The marginal cost
for each firm is zero and there are no fixed costs. The demand
functions for each firm are:
Q1 = 80 − 2P1 + 2P2,
Q2 = 80 − 2P2 + 2P1.
where P1 is the price set by firm 1, P2 is the price set by firm
2, Q1 is the quantity demanded of firm 1’s product and Q2 is...
Consider an industry with three firms, with demand curves as
given below.
Q1 =
140-12P1+3P2+3P3
Q2=
130-10P2+3P1+2P3
Q3 =
135-9P3+2P1+2P2.
Each firm has a marginal cost of 4.
1. Calculate the pre-merger prices.
2. Assume that firms 1 and 2 merge, to form a new firm “M”.
Assume also that the merger allows M to reduce marginal cost from 4
to 2. Firm 3’s marginal cost remains at 4. What are the new
equilibrium prices?
3. Calculate the UPPIs for...
Consider two firms that sell differentiated products and compete
by choosing prices. Their demand functions are Q1 = 72 – 3P1 + 2P2
and Q2 = 72 – 3P2 + 2P1 where P1 and P2 are the prices charged by
firm 1 and 2, respectively, and Q1 and Q2 are the corresponding
demands. All production costs are assumed to be zero.
(a) Suppose the two firms set their prices simultaneously and
non-cooperatively. Find the resulting Bertrand-Nash equilibrium.
What price does...