In: Economics

4. Al and bert each own gidgets producing firms, in a duopoly market. The gidgets produced by Al and Bert are identical and both the firms have identical costs.

These are the demand and cost conditions

Demand: P=248-4Qt=248-4QA-4Qb

Cost: ATCA=ATCB=MCa=MCb=$8

a. assume first that al and bert come to an agreement and collude to form a profit maximizing cartel. the firms split the output and profits equally. Find cartel output, and profits.

Cartel output=_____ Price=_____ Firm output=_____ Firm profits=______

b. Now assume the cartel splits up and al and bert start a price war. Now find price, output and profits

Price=_____ Total output=_____ Firm output=_____ Firm profits=_____

c. Al and bert come to their senses somewhat and decide to conduct their competition over quantity instead. (Cournot) Find price. output and profits.

Price=_____ Total output=_____ Firm output=_____ Firm profits=_____

d. compare the profits that they earn when they compete as Cournot rivals in part c, with their profits if they cooperate (part a). of course they are better off cooperating. But the problem is both firms have an incentive to cheat (renege) on the deal. Use the reaction functions you constructed for part c to find the profit maximizing output for one of the firms (the cheater) is the other (the victim) sticks with the agreed output and then find the price and respective profits.

Cheaters output=_____ total output=_____ price=____ cheaters profits=_____ victims profit=_____

e. now use the information to create a payoff table.

Suppose in a duopoly market there are two firms, 1 and 2, each
with a cost function given as TC1 = 10Q1 and
TC2 = 10Q2. The inverse demand in the market
is P = 100 – 2(Q1 + Q2). The firms are
homogeneous product duopoly.
Suppose the market is characterized by Cournot oligopoly.
Calculate each firm’s profit-maximizing output, price, and profit.
Be sure to show all steps needed for this question.
Now suppose the market is characterized by Stackelberg...

Consider the following variant of theBertrand Model of Duopoly.
Suppose there are two firms producing the same good and they
simultaneously set prices for their product. If firm i sets a price
piand firm j sets a price pj, the total quantity demanded for firm
i’s product is given by:qi= 10 –pi+ ½ pjEach firm produces exactly
the qidemanded by the market. Bothfirms have the same marginal cost
of production: c=4. For example, if a firm produces 5 units it...

In the Bertrand duopoly, market demand is Q = ? ? Bp, and firms
have no fixed costs and identical marginal cost. Find a Bertrand
equilibrium pair of prices, (p1 , p2 ), and quantities, (q1, q2),
when the following hold.
a. Firm1 has fixed costs F>0.
b. Both firms have fixed costs F > 0.
c. Fixed costs are zero, but firm 1 has lower marginal cost than
firm 2, so c2 > c1 > 0. (For this one,...

Consider a Cournot duopoly of two identical cigarette producing
firms, Warlboro and Cramel. They produce tobacco of same quality
and, ceteris paribus, each firm sells to 1 million smokers, making
$100 profits per smoker. These 2 million smokers are addicts (as
most smokers are). They may change which tobacco they smoke but
they do not quit. On the other hand, those who are not smokers will
not start even if they are encouraged (because they understand the
harm). In other...

Consider a Cournot duopoly of two identical cigarette producing
firms, Warlboro and Cramel. They produce tobacco
of same quality and, ceteris paribus, each firm sells to 1
million smokers, making $100 profits per smoker.
These 2 million smokers are addicts (as most smokers are). They
may change which tobacco they smoke but they do not quit. On the
other hand, those who are not smokers will not start even if they
are encouraged (because they understand the harm). In other...

In a duopoly market with two identical firms, the market demand
curve is: P=50-2Q And the marginal cost and average cost of each
firm is constant: AC=MC=2 a. Solve for firm 1’s reaction curve and
graph b. Solve for firm 2’s reaction curve and graph c. Solve for
each firm’s Q and P in a cournot equilibrium and show on your graph
i. What is the profit for each firm?

Suppose two firms, "A" and "B," form a duopoly in the market for
a special type of computer chip. Each firm has a constant marginal
cost of $2. The daily market demand for this chip is given by the
following equation:
P = 8 – 0.005 Q = 8 – 0.005 (qA+qB).
a. Find an expression for firm #A's revenue, as a function of
its own quantity and firm B’s quantity: RevA(qA,qB). [Hint: By
definition, RevA = P qA. Here,...

Two firms are participating in a Cournot duopoly. The demand
function in the market is given by Q=430−2P. Each firm’s total cost
is given by C(q)=5q+q2.
(1) Write down the inverse demand function and the maximization
problem for Firm 1 given that Firm 2 is expected to produce
q2^e.
(2) Write down the reaction function q1(q2^e) for Firm 1.
(3) Find the market price, quantities supplied, and firms’ profits
in the Cournot
equilibrium of this game.

Two firms are participating in a Stackelberg duopoly. The demand
function in the market is given by Q = 2000 − 2P . Firm 1’s total
cost is given by C1(q1) = (q1)^2 and Firm 2’s total cost is given
by C2(q2) = 100q2. Firm 1 is the leader and Firm 2 is the
follower.
(1) Write down the inverse demand function and the maximization
problem for Firm 1 given that Firm 2 is expected to produce
R2(q1).
(2) Compute...

The market for fertilizer is perfectly competitive.
Firms in the market are producing output but are currently
incurring economic losses.
a) How does the price of fertilizer compare to the
average total cost, the average variable cost, and the marginal
cost of producing fertilizer?
b) Draw two graphs, side by side, illustrating the
present situation for the typical firm and for the
market
c) Assuming there is no change in either demand or the
firms’ cost curves, explain what will...

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