Microeconomic Theory
12th Edition
ISBN: 9781337517942
Author: NICHOLSON
Publisher: Cengage
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Chapter 15, Problem 15.3P
b)
To determine
Graphical representation of Nash equilibrium and isoprofit.
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Let ci be the constant marginal and average cost for firm i (so that firms may have different marginal costs). Suppose demand is given by P=1-Q.
Calculate the Nash equilibrium quantities assuming there are two firms in a Cournot market. Also compute market output, market price, firm profits, industry prof- its, consumer surplus, and total welfare.
Represent the Nash equilibrium on a best-response function diagram. Show how a reduction in firm 1’s cost would change the equilibrium. Draw a representative isoprofit for firm 1.
Three firms compete in the style of Cournot. All firms have a constant returns to scale technology: There are no fixed cost and each firm's marginal cost is constant. The market demand is given by Q(P) = 9 - P. Firm 1's marginal cost is MC1 = 1, firm 2's marginal cost is MC2 = 2. Let MC3 be the marginal cost of Firm 3. Which of the below is a necessary condition so that q > 0 for all three firms in a Nash equilibrium?
a. MC3 < 1
b. MC3 < 4
c. MC3 < 3
d. MC3 > 1
e. MC3 < 2
The market demand function is Q=10,000-1,000p.
Each firm has a marginal cost of m=$0.28. Firm 1, the leader, acts before Firm 2, the follower. Solve for the Stackelberg-Nash equilibrium quantities, prices, and profits. Compare your solution to the Cournot-Nash equilibrium.
The Stackelberg-Nash equilibrium quantities are:
q1=___________ units
and q2=____________units
The Stackelberg-Nash equilibrium price is:
p=$_____________
Profits for the firms are
profit1=$_______________
and profit2=$_______________
The Cournot-Nash equilibrium quantities are:
q1=______________units
and q2=______________units
The Cournot-Nash equilibrium price is:
p=$______________
Profits for the firms are
profit1=$_____________
and profit2=$_______________
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