Question

1- Alpha (Brand A) and Beta (Brand B) are leading brand names of clothes. The direct demand functions facing each producer are given by qA = 180 – 2 PA + PB and qB = 120 – 2PB + PA Assume zero production cost (cA = cB = 0), and solve the following problems: (i) Derive the price best-response function of firm A as a function of the price set by firm B. Show your derivations, and draw the graph associated with this function. (ii) Derive the price best-response function of firm B as a function of the price set by firm A. Show your derivations, and draw the graph associated with this function. (iii) Solve for the Nash-Bertrand equilibrium prices. Then, compute the equilibrium output levels, the equilibrium profits, and aggregate industry profit. (iv) Suppose now that the two producers hold secret meetings in which they discuss fixing the price of clothes to a uniform (brand-independent) level of p = PA = PB. Compute the price p which maximizes joint industry profit, ?A + ?B. Then, compute aggregate industry profit and compare it to the aggregate industry profit made under Bertrand competition which you computed in part (iii). (v) Suppose now that the two firms merge. However, they decide to keep selling the two brands separately and charge, possibly, different prices. Compute the prices PA and PB which maximize joint industry profit, ?A + ?B. Then, compute aggregate industry profit and compare it to the aggregate industry profit made under Bertrand competition, which you have already computed under separate ownership.

Answer #1

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....

Bertrand competition - asymmetric cost question
Consider the Bertrand competition example in the lecture notes.
P(Q)=31-2Q , firm B’s cost function is CB(Q) = 2Q. Firm A’s cost
function remains the same at CA(Q) = Q. Furthermore, constrain
prices to be divisible only into cents. there is a discreteness
imposed on the strategy choice.
1) Determine firm A’s best response function PˆA (PB). Argue
your answer.
2) Determine firm B’s best response function PˆB (PA). Argue
your answer.
3) What...

(QUESTION 1)
Assume two firms that produce complementary components, X and
Y.
The components are always consumed in a fixed proportion, i.e.
for every
unit of X, two units of Y are required. The respective prices
are Px and Py.
Consequently, the package price is Pp = Px + 2Py. Assume that
the demand
function for the package is, Q = a – Pp, with a > 0 and where
Q = X = Y/2.
(i) Suppose that the X...

Question 4 Consider the following game. Firm 1, the leader,
selects an output, q1, after which firm 2, the follower, observes
the choice of q1 and then selects its own output, q2. The resulting
price is one satisfying the industry demand curve P = 200 - q1 -
q2. Both firms have zero fixed costs and a constant marginal cost
of $60. a. Derive the equation for the follower firm’s best
response function. Draw this equation on a diagram with...

Consider two sellers (“1” and “2”) of brand new, still in the
box iPhone X’s. Online
inverse demand for these iPhones is given by P(Q) = 60 ? Q.
The two sellers compete by choos-
ing prices, so we have Bertrand competition with identical
products. Because the products are
truly identical, consumers only buy from whichever seller has
a lower price. If they charge the same prices, half purchase from
one seller and half purchase from the other. Assume further...

Consider a Cournot model with two firms, firm 1 and firm 2,
producing quantities q1 and q2, respectively. Suppose the inverse
market demand function is: P = 450 – Q where Q denotes the total
quantity supplied on the market. Also, each firm i = 1,2 has a
total cost function c(qi) = 30qi. a) What is the Nash equilibrium
of this Cournot game ? What is the market prices ? Compute each
firm’s profit and the industry profit. b)...

(Static Cournot Model) In Long Island there are two suppliers of
distilled water, labeled firm 1 and firm 2. Distilled water is
considered to be a homogenous good. Let p denote the price per
gallon, q1 quantity sold by firm 1, and q2 the quantity sold by
firm 2. Firm 1 bears the production cost of c1 = 4, and firm 2
bears c2 = 2 per one gallon of water. Long Island’s inverse demand
function for distilled water is...

Industry Analysis
Scenario
In the island nation of Autarka, the government holds a monopoly
over the provision of airfreight services. Both the general public
and business groups regularly complain about high prices and poor
quality of service from the government owned monopoly, Autarka
Airfreight Services (AAS). In response to these complaints, the
national government commissioned the competi- tion authority to
recommend steps for improving the efficiency of the airfreight
market. The commission made two recommendations:
The airfreight services market should...

No scan of handwritten answers
1. A monopolist faces a market demand curve given by Q = 53- P.
Its cost function is given by C = 5Q + 50, i.e. its MC =$5.
(a) Calculate the profit-maximizing price and quantity for this
monopolist. Also calculate its optimal profit.
(b) Suppose a second firm enters the market. Let q1
be the output of the first firm and q2 be the output of
the second. There is no change in market...

I only want the answer of problem 2
1.There is only one least-cost way to make wooden boxes for
shipping tomatoes, and any firm that makes
them has a cost function given by C = 200 + q +.005q2. The
inverse market demand for boxes is given by
p = 10?.005Q. There is currently only one firm in the industry
and it is able to act as a monopolist.
(a) What is its output and what price does it charge...

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