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Reaction function, equilibrium output and market price

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VisiCalc, the first computer spreadsheet program, was released to the public in 1979. A year later, introduction of the DIF format made spreadsheets much more popular because they could now be imported into word processing and other software programs. By 1983, Mitch Kapor used his previous programming experience with VisiCalc to found Lotus Corp. and introduce the widely popular Lotus 1-2-3 spreadsheet program. Despite enormous initial success, Lotus 1-2-3 stumbled when Microsoft Corp. introduced Excel with a much more user-friendly graphical interface in 1987. Today, Excel dominates the market for spreadsheet applications software, and Lotus represents a small part of IBM's suite of instant messaging tools.

To illustrate the competitive process in markets dominated by few firms, assume that a two-firm duopoly (Firm A and Firm B) dominates the market for spreadsheet application software, and that the firms face a linear market demand curve
P = 1,250 - Q
where P is price and Q is total output in the market (in thousands). Thus Q = QA + QB.

For simplicity, also assume that both firms produce an identical product, have no fixed costs, and marginal costs MCA = MCB = $50.

a. Given this Cournot oligopoly market,
i. Determine the reaction function of each firm.
ii. Determine the equilibrium output level for each firm, and total market output (Qo).
iii. Determine the equilibrium market price.

b. Instead of the market above being an oligopoly, it could be monopolized, perfectly competitive, or monopolistically competitive. Assume that the equilibrium market output and market price under each of the market structure are as follows:

Qo = Total market output if the market is an oligopoly
Po = Market price if the market is an oligopoly

QM = Total market output if the market is a monopoly
PM = Market price if the market is a monopoly

QPC = Total market output if the market is perfectly competitive
PPC = Market price if the market is perfectly competitive

QMC = Total market output if the market is monopolistically competition
PMC = Market price if the market is monopolistically competition

Questions:

i. Rank the market output (Qo, QM , QPC, QMC ) from the lowest to the highest.
ii. Rank the market prices (Po, PM , PPC, PMC ) from the lowest to the highest.

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A. To determine the reaction function of each firm we must first recall the formula for total revenue in a Cournot duopoly

For Firm A it would be:
TRA = $1,250QA - QA2 - QAQB
Therefore marginal revenue for Firm A is:
MRA = TRA/QA = $1,250 - $2QA - QB

Similar total revenue and marginal revenue curves would hold for Firm B.

Because MCA = 50, Firm A's profit-maximizing output level is found by setting MRA= MCA = 50:

MRA = MCA
$1,250 - $2QA - QB = 50
$2QA = $1,200 - QB
QA = 600 - 0.5QB

From this we see that the profit-maximizing level of output for Firm A depends upon the level of output produced by both firms. ...

Solution Summary

Illustration of oligopoly using spreadsheet market; comparison of oligopolies, monopolies, and monopolistic competition.

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Sample problem set

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1. Consider the following market demand and asymmetric cost functions for the airplane production industry.

Market Demand is: P=200- (qA + qB)
Cost Function for Boeing: C(qB) = 40 qB
Cost Function for Airbus: C(qA) = 30 qA

a.) Assume that the two act according to the Cournot model, i.e. they set quantities. Derive the optimal output for each firm and the resulting market price. Be careful with the algebra, as the firms are no longer symmetric.
b.) Suppose now Boeing is the Stackelberg leader. What are the optimal outputs for the two firms and the market price under this assumption?
c.) Suppose now Airbus is the Stackkelberg leader. What are the optimal outputs for the two firms and the market price under this assumption?
d.) Comment on the differences in your answers to (a.)(b.) and (c.). What are the implications of having the higher cost firm as the Stackelberg leader when compared to the Cournot equilibrium? What are the implications of having the lower cost firm as the leader when compared to the Cournot equilibrium?
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