Two firms compete in a homogeneous product market where the inverse demand funct

Question

Two firms compete in a homogeneous product market where the inverse demand function is P = 20 -5Q (quantity is measured in millions). Firm 1 has been in business for one year, while Firm 2 just recently entered the market. Each firm has a legal obligation to pay one year’s rent of $1.2 million regardless of its production decision. Firm 1’s marginal cost is $2, and Firm 2’s marginal cost is $10. The current market price is $15 and was set optimally last year when Firm 1 was the only firm in the market. At present, each firm has a 50 percent share of the market.

a. Based on the information above, what is the likely reason that Firm 1’s marginal cost is lower than Firm 2’s marginal cost?

b. Determine the current profits of the two firms

Firm 1's profits: $

Firm 2's profits: $

c. What would each firm’s current profits be if Firm 1 reduced its price to $10 while Firm 2 continued to charge $15?

Firm 1's profits: $

Firm 2's profits: $

Explanation / Answer

Ans
a)Firms 1's marginal cost is lower than that of firm 2 because of
Learning curve effects.

b)P=20-5Q
P=15
15=20-5Q
Q=1
Each firm has 50% of mrket share then each produce
0.5 quantity.
Q1=Q2
TR for firm 1= p.Q1=15*0.5=7500000
TC for firm 1=Q.MC + 1200000=1000000+1200000=2200000
profit for firm 1=TR-TC
=7500000-2200000
=5300000

TR for firm 2=p.Q2=15*0.5=7500000
TC for firm 2=Q.MC + 1200000=5000000+1200000=6200000
profit for firm 2=TR-TC
=1300000

c)TR for firm 1= p.Q1=10*0.5=5000000
TC for firm 1=Q.MC + 1200000=1000000+1200000=2200000
profit for firm 1=TR-TC
=5000000-2200000
=2800000

Since firm 2 does not change his price his profits will
remain at 1300000

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