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?

Answer #1

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^*?

SCENARIO 3: Consider an industry consisting of two firms
producing an identical product. The inverse market demand equation
is P = 100 − 2Q. The total cost equations for firms 1 and 2 are TC1
= 4Q1 and TC2 = 4Q2, respectively.
9. Refer to SCENARIO 3. Suppose that the two firms are Cournot
rivals. Firm 1’s reaction function is:
a. Q1 = 12 − Q2.
b. Q1 = 12 − 0.25Q2.
c. Q1 = 24 − 0.5Q2.
d. Q1...

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...

Consider a two-firm oligopoly facing a market inverse demand
curve of P = 100 – 2Q, where Q is the sum of q1 and q2. q1 is the
output of Firm 1 and q2 is the output of Firm 2. Firm 1's marginal
cost is constant at $12, while Firm 2's marginal cost is constant
at $20. Answer the following questions, assuming that the firms are
Cournot competitors.
a. How much output does each firm produce? (answer is 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 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 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 duopolists face the market inverse demand curve P = 100
- Q, Q = q1 + q2, and both firms have a constant marginal cost of
10 and no fixed costs. If firm 1 is a Stackelberg leader and firm
2's best response function is q2 = (100 - q1)/2, at the
Nash-Stackelberg equilibrium firm 1's profit is $Answer

Consider a duopoly with two firms with the cost functions:
Firm 1: C1(q1)=5q1
Firm 2: C2(q2)=5q2
The firms compete in a market with inverse demand
p = 300 - 8Q
where Q=q1+q2. The firms compete in a
Cournot fashion by choosing output simultaneously.
What is the Nash-Cournot equilibrium output of firm 1? Round to
nearest .1

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