Question

There are 2 firms that sell a certain software, Microsoft and Oracle. Microsoft invented the software and so they act as a market leader by first deciding how much of the software they are going to produce each month. Oracle observes this decision by Microsoft and then chooses how much they are going to produce. The marginal cost of producing the software is constant at $2 for both companies. The total market demand for the software is P = 84 - 0.2Q. According to the Stackelberg model, what price will both companies sell the software at? (Write answer without the dollar sign.)

Answer 1

Let the quantity produced by leader firm is Q1

Now we estimate the reaction function of firm 2

Total Revenue of firm 2=TR2=(84-0.2Q1-0.2Q2)*Q2=84Q2-0.2Q1Q2-0.2Q2^2

Marginal Revenue of firm 2=MR2=dTR2/dQ2=84-0.2Q1-0.4Q2

Set MR2=MC for profit maximization

84-0.2Q1-0.4Q2=2

0.4Q2=82-0.2Q1

Q2=205-0.5Q1

Now take the second firm

Total Revenue for firm 1=TR1=P*Q1=(84-0.2Q1-0.2Q2)*Q1

Total Revenue for firm 1=TR1=(84-0.2Q1-0.2*(205-0.5Q1)*Q1

Total Revenue for firm 1=TR1=(84-0.2Q1-41+0.1Q1)*Q1=(43-0.1Q1)*Q1=43Q1-0.1Q1^2

Marginal Revenue=MR1=dTR1/dQ1=43-0.2Q1

Set MR1=MC for profit maximization

43-0.2Q1=2

Q1=205

Q2=205-0.5Q1=205-0.5*205=102.50

Total Output=Q=Q1+Q2=205+102.50=307.50

P=84-0.2Q=84-0.2*307.5=$22.50 or say 22.50