Question

For questions 14: Market demand for widgets is Q = 100 - p. Whether there is just one firm 10- selling widgets or many firms selling widgets, the marginal cost and average cost is 10. 10 2 Assume there is one firm selling widgets. What is the equilibrium price (p) and quantity sold (Q)? 2 Assume there are two firms selling widgets acting as Cournot duopolists (Firm 1 and Firm 2). What is the quantity sold for each firm? 122 Assume there are two firms selling widgets acting as Stackelberg duopolists, with Firm 2 moving first and Firm 1 following. Further assume that Firm 2's marginal profit function at its maximum is Ma(q) = 45 - 4/2, where q is the amount of widgets sold by Firm 2. What is the quantity sold for each firm? 2 From question 11 (Cournot duopolists), what is the price of widgets? 14 2 From question 12 (Stackelberg duopolists), what is the price of widgets?

Answer 1

10) monopoly equilibrium condition,

MR=MC

Q=100-p

P=100-q

MR=100-2q

100-2q=10

Q=90/2=45

11)p=100-q1-q2

MR1=100-2q1-q2

MC1=10

MR1=MC1

100-2q1-q2=10

Q1=45-0.5q2{ best response function of firm 1)

By symmetry ( having same MC=10 and facing same demand),we can derive best response function of firm 2

Q2=45-0.5q1

Putting q2 into q1

Q1=45-0.5(45-0.5q1)=45-22.5+0.25q1

Q1=22.5/0.75=30

Q2=45-0.5*30=30

12) putting firm 1 best response into demand

P=100-45+0.5q2-q2

P=55-0.5q2{ residual demand of firm 2}

MR2=55-q2

MR2=MC

55-q2=10

Q2=45

Q1=45-0.5*45=45-22.5=22.5

13) cournot equilibrium,.q1=q2=30

P=100-30-30=100-60=40

14) stackelberg equilibrium,q1=45

Q2=22.5

P=100-22.5-45=100-67.5

P=32.5