Question

Consider two identical firms competing in a market described by:

• (Inverse) Demand: P = 50 − Q , where Q = q1 + q2

• Cost Firm 1: C1 = 20q1 +q1^2

• Cost Firm 2: C2 = 20q2 + q2^2

a. (1 point) What is firm 1’s marginal cost? Firm 2’s marginal cost? What can you observe about these two firms?

b.(2 points) What are the equilibrium price (P∗), production quantities (q∗1,q∗2), and profits(π∗1,π∗2), if these firms are rivals – what is the outcome in the perfectly competitive model?

c. (2 points) What are the equilibrium price (P∗), production quantities (q∗1,q∗2), and profits(π∗1,π∗2), if these firms collude – what is the outcome in the monopoly model?

Answer #1

Answer for a

MC for Firm 1

MC1=20+2q1

MC for Firm 2

MC1=20+2q2

Both firms are identical and change in cost for each additional output depends on quantity and MC is non zero even if no production happens at all.

Answer for 2

When both the firms are rivals of each other they observe other firm's output level and gives the best response to maximise the profit.

Consider two identical firms competing in a market described
by:
• (Inverse) Demand: P = 50 − Q , where Q = q1 + q2
• Cost Firm 1: C1 = 20q1 +q1^2
• Cost Firm 2: C2 = 20q2 + q2^2
a. (1 point) What is firm 1’s marginal cost? Firm 2’s marginal
cost? What can you observe about these two firms?
b.(2 points) What are the equilibrium price (P∗), production
quantities (q∗1,q∗2), and profits(π∗1,π∗2), if these firms are...

Consider three firms that face market demand P = 101 - Q. The
cost functions are C1(q1)=6(q1^2) for firm 1, C2(q2)=4(q2^2) for
firm 2, and C3(q3)=4q(3^2) for firm 3. Firm 1 is the Stackelberg
leader and firms 2 and 3 are the followers. What is firm 1's
equilibrium output q1^*?

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 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...

Consider a market with two firms whose products are identical.
The market demand curve is p = a − bq where a > 0 and b > 0,
and where q = q1 + q2. Firm i’s profits are πi(q1, q2) = pqi − cqi
. Assume that the firms move in sequence, with firm 1 choosing q1
first, and then firm 2 choosing q2; however, assume firm 2 observes
q1 before choosing q2.
(a) What is a Nash equilibrium...

Suppose that two firms compete in the same market producing
homogenous products with the following inverse demand function:
P=1,000-(Q1+Q2)
The cost function of each firm is given by:
C1=4Q1
C2=4Q2
Suppose that the two firms engage in Bertrand price
competition. What price should firm 1 set in equilibrium? What
price should firm 2 set? What are the profits for each firm in
equilibrium? What is the total market output?
Suppose that the two firms collude in quantity, i.e.,
acting together...

Consider the Cournot duopoly model where the inverse demand is
P(Q) = a – Q but firms have asymmetric marginal costs:
c1 for firm 1 and c2 for firm 2.
What is the Nash equilibrium if 0 < ci < a/2
for each firm?
What if c1 < c2 < a, but
2c2 > a + c1?

Consider a market with only two firms. Demand on this market is
given by D(p)= 90 - 3p. Initially both firms have the same constant
per-unit cost, specifically c1 = c2 = 20 .
(a) What is the Nash equilibrium in this market if firms behave
as Bertrand competitors? How much does each firm produce, what
price do the firms charge, and what are their profits?
(b) Now suppose that firm 1 acquires a new production technique
that lowers its...

Consider a market in which the demand function is
P=50-2Q,
where Q is total demand and P is the price. In the market, there
are two firms whose cost function is
TCi=10qi+qi^2+25,
where qi1 is the quantity produced by firm i and
Q=q1+q2
Compute the marginal cost and the average cost.
Compute the equilibrium (quantities, price, and profits)
assuming that the firms choose simultaneously the output.

Three oligopolists operate in a market with inverse demand given
by p (Q ) = a −Q , where Q = q1 + q2 + q3, and qi is the quantity
produced by firm i. Each firm has a constant marginal cost of
production, c and no fixed cost. The firms choose their quantities
dy- namically as follows: (1) Firm 1, who is the industry leader,
chooses q1 ≥ 0; (2) Firms 2 and 3 observe q1 and then
simultaneously...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 14 minutes ago

asked 30 minutes ago

asked 34 minutes ago

asked 39 minutes ago

asked 49 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago