Question

Consider a Cournot market with two firms that have TC(Q) =5Q. Demand is given by P= 200−2(Q1+Q2).

A) Find firm 1’s profit as a function of Q1 and Q2

B) Find the equilibrium price, quantity sold by each firm, and profit for each firm.

Answer #1

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)....

Q1.
Consider a Cournot oligopoly in which the market demand curve is
Q = 60 - P. There are two firms in this market, so Q =
q1 + q2. The firms in this market are not
identical: Firm 1 faces cost function c1(q1)
= 2q12, while firm 2's cost function is
c2(q2) = 28q2.
In the space below, write down a function for Firm 1's profit,
in terms of q1 and q2.
Q2.
Refer back to the Cournot oligopoly...

Consider a market with two identical firms. The market demand is
P = 26 – 2Q, where Q = q1 + q2. MC1 = MC2 = 2.
1. Solve for output and price with collusion.
2. Solve for the Cournot-Nash equilibrium.
3. Now assume this market has a Stackelberg leader, Firm 1.
Solve for the quantity, price, and profit for each firm.
4. Assume there is no product differentiation and the firms
follow a Bertrand pricing model. Solve for the...

Consider a Cournot duopoly operating in a market with inverse
demand P(Q) = a - Q, where Q = q1 + q2 is the aggregate quantity on
the market. Both firms have total costs ci(qi) = cqi, but demand is
uncertain: it is High (a = aH) with probability theta and low (a=
aL) with probability 1 - theta. Furthermore, information is
asymmetric: firm 1 knows whether demand is high or low, but firm 2
does not. All this is...

2. Consider two identical firms in a Cournot competition. The
market demand is P = a – bQ. TC1 = cq1 = TC2 = cq2 . a. Find the
profit function of firm 1. b. Maximize the profit function to find
the reaction function of firm 1. c. Solve for the Cournot-Nash
Equilibrium. d. Carefully discuss how the slope of the demand curve
affects outputs and price.

N firms, in a Cournot oligopoly are facing the market demand
given by P = 140 – 0.4Q, where P is the market price and Q is the
market quantity demanded. Each firm has (total) cost of production
given by C(qi) = 200 + 10qi, where qi is the quantity produced by
firm i (for i from 1 to N).
New firms would like to enter the market if they expect to make
non-negative profits in this market; the existing...

Consider two identical firms (no. 1 and no. 2) that face a
linear market demand curve. Each firm has a marginal cost of zero
and the two firms together face demand:
P = 50 - 0.5Q, where Q = Q1 + Q2.
a. Find the Cournot equilibrium Q and P for each firm. Calculate
the results rounded to the second digit after the decimal point
b. Find the equilibrium Q and P for each firm assuming that the
firms collude...

Fill in the blanks.
Consider two firms facing the demand curve: P=60-5Q
where Q=Q1+Q2. The firm's cost functions are
C1(Q1)=15+10Q1 and C2(Q2)=15+20Q2
Combined, the firms will produce __ units of output, of which
firm 1 will produce __ units and firm 2 will produce __ units.
If the firms compete, then firm 1 will produce __ units of
output and firm 2 will produce __ units of output.
Draw the firms' reaction curves and sho the equilibrium. Then,
indicate the...

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)...

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...

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