Question

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) Consider a Stackelberg model where firm 1 chooses quantity before firm 2. What is the subgame perfect Nash equilbrium in quantities ? Compute each firm’s profit and the industry profit. c) Suppose there is only one firm supplying the market. What is the profit maximizing price and quantity of the monopolist ? Compute each firm’s profit and the industry profit. d) Suppose the market is a perfectly competitive market. What is the price and quantity supplied in equilibrium ? Compute each firm’s profit and the industry profit. e) What do you observe ?

Answer #1

A product is produced by two profit-maximizing firms in a
Stackelberg duopoly: firm 1 chooses a quantity q1 ? 0, then firm 2
observes q1 and chooses a quantity q2 ? 0. The market price is
determined by the following formula: P ( Q ) = 4 ? Q , where Q =
q(1) +q(2) . The cost to firm i of producing q i is Ci( qi ) =
q^2)i . (Note: the only difference between this problem and...

(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...

Suppose there are n firms in a Cournot oligopoly model.
Let qidenote the quantity produced by firm
i, and let Q = q1 + q2
+…+ qn be the aggregate quantity in the market. Let
P denote the market clearing price and assume that the
inverse market demand is given by P(Q)=a - Q (when
Q<a, else P=0). Assume that the total cost for
firm i of producing quantity qi is
C(qi) = cqi . That
is, there are no...

A homogenous good industry consists of two identical firms (firm
1 and firm 2). Both firms have a constant average total cost and
marginal cost of $4 per unit. The demand curve is given by P = 10 –
Q. Suppose the two firms choose their quantities simultaneously as
in the Cournot model.
(1) Find and plot each firm’s best-response curve. (Be sure to
clearly label your curves, axes and intercepts.)
(2) Find each firm’s quantity and profit in the...

Consider two firms with the cost function TC(q) = 5q (constant
average and marginal cost,of 5), facing the market demand curve Q =
53 – p (where Q is the total of the firms’ quantities, and p is
market price).
a. What will be each firm’s output and profit if they make their
quantity choices simultaneously (as Cournot duopolists)?
b. Now suppose Firm 1 is the Stackelberg leader (its decision is
observed by Firm 2 prior to that firm’s decision)....

1. (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...

Consider the following variant of the Bertrand 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
pi and firm j sets a price pj, the total quantity demanded for firm
i’s product is given by:
qi= 10–pi+ ½ pj
Each firm produces exactly the qi demanded by the market. Both
firms have the same marginal cost of production: c=4. For example,
if a...

Consider the infinitely repeated version of the Cournot duopoly
model where price in the market is given by
P = 100 – Q for Q= q1 + q2
and marginal cost of production for both firms is given by c=
10.
a) What is the Nash equilibrium of the static game? What is the
profit of each firm?
b) If there was only one firm in the market, and P = 100-q1, what
is the static monopoly optimum? What is...

Consider two firms, Firm A and Firm B, who compete as
duopolists. Each firm produces an identical product. The total
inverse demand curve for the industry is ? = 250 − (?? + ?? ). Firm
A has a total cost curve ?? (?? ) = 100 + ?? 2 . Firm B has a total
cost curve ?? (?? ) = 100 + 2??.
a. Suppose for now, only Firm A exists (?? = 0). What is the
Monopoly...

There is a Cournot duopoly competition between Firm 1 and Firm
2. The inverse demand function is given by P(Q)=100-q, where
Q=q1+q2 and qi denotes the quantity produced by firm i for all iÎ
{1, 2} and the cost function is given by ci(qi)=10qi. Describe this
problem as a normal-form game. Find pure-strategy Nash Equilibria
for both firms.

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