Question
In: Economics
Problem 1: Consider the following Bertrand duopoly: two firms (A and B) are operating in a...
Problem 1: Consider the following Bertrand duopoly: two firms (A and B) are operating in a market where they produce identical products and compete on price. Assume that the market demand can be written as ? = 50 − ?. Assume that neither firm is capacity constrained so that either firm can satisfy the market demand at any price. Suppose further that the profit function for each firm can be written as ? = ?? − ?? = (? − ?)? where V is the constant marginal cost which we will assume is 2. What will be the price in the market? What will be the profits of each firm?
B) Consider the following change to the Bertrand duopoly described in the previous problem: suppose that the marginal costs of each firm are not the same but instead ?A = 4 and ?B = 2. What will be the price in the market? What will be the profits of each firm?
Solutions
Rahul Sunny answered 1 year agoRelated Solutions
Two identical firms compete in a Bertrand duopoly. The firms produce identical products at the same...
Two identical firms compete in a Bertrand duopoly. The firms
produce identical products at the same constant marginal cost of MC
= $10. There are 2000 identical consumers, each with the same
reservation price of $30 for a single unit of the product (and $0
for any additional units). Under all of the standard assumptions
made for the Bertrand model, the equilibrium prices would be Group
of answer choices $10 for both firms $30 for both firms $50 for
both...
) Consider a Bertrand duopoly where ?? , ?? and ??(?? ) = ??? are quantity,...
) Consider a Bertrand duopoly where ?? , ?? and ??(?? ) = ???
are quantity, price and total cost, respectively, for firm ? ∈
{1,2} where ? > 0. Assume neither firm has a capacity
constraint.
a. Derive the equilibrium quantities and prices if the products
are undifferentiated.
b. Derive the equilibrium quantities and prices if the products
are differentiated such that residual inverse demand for firm ? is
?? = ?? − ???? + ???? given the price...
In the Bertrand duopoly, market demand is Q = ? ? Bp, and firms have no...
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,...
In the Bertrand duopoly, market demand is Q = a-Bp, and firms have no fixed costs...
In the Bertrand duopoly, market demand is Q = a-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, assume the...
In the Bertrand duopoly, market demand is Q = a-Bp, and firms have no fixed costs...
In the Bertrand duopoly, market demand is Q = a-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, assume the...
Consider the following variant of theBertrand Model of Duopoly. Suppose there are two firms producing the...
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...
Consider the following asymmetric-information model of Bertrand duopoly with differentiated products. Demand for firm i is...
Consider the following asymmetric-information model of Bertrand
duopoly with differentiated products. Demand for firm i is qi(pi,pj)
= a−pi + bi ·pj. Costs are zero for both firms. The sensitivity of
firm i’s demand to firm j’s price is either high or low. That is, bi
is either bH or bL, where bH > bL > 0. For each firm, bi = bH
with probability θ and bi = bL with probability 1−θ, independent of
the realization of bj. Each...
Assume that you observe two firms operating in a Bertrand oligopoly. The inverse demand function for...
Assume that you observe two firms operating in a Bertrand
oligopoly. The inverse demand function for the market is P = 200 –
2Q and each firm has the same cost function of C(Q) = 20Q. What is
the level of production for each firm, market price, and profit of
each firm? What would happen if both firms merge to form a single
monopoly with a cost function of C(Q) = 20Q?
Suppose two firms, "A" and "B," form a duopoly in the market for a special type...
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,...
Recall the static Bertrand duopoly model (with homogenous products): the firms name prices simultaneously; demand for...
Recall the static Bertrand duopoly model (with homogenous
products): the firms name prices simultaneously; demand for firm
i's product is a - pi if pi < pj, is 0 if pi > pj, and is
(a-pi)/2 if pi = pj; marginal costs are c < a. Consider the
infinitely repeated game based on this stage game. Show that the
firms can use trigger strategies (that switch forever to the
stage-game Nash equilibrium after any deviation) to sustain the
monopoly price...
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