Question

In: Economics

In the following table, the profits from a duopoly model of competition are shown. Firms 1...

In the following table, the profits from a duopoly model of competition are shown. Firms 1 and 2 simultaneously choose the quantity of outputs to produce. Each firm is restricted to producing 25, 35, 50 or 100 units of output. Is there a Nash equilibrium? What is it? Briefly explain.

Firm 2

Q2 = 25

35

50

100

Q1 = 25

125, 125

100, 140

63, 125

-63, -250

Firm 1

35

140, 100

105, 105

53, 75

-123, -350

50

125, 63

75, 53

0, 0

-250, -500

100

-250, -63

-350, -130

-500,-250

-900, -900

Solutions

Expert Solution

First look at the strategy of firm 1. When firm 2 selects 25 units, firm 1 selects 35 units as its profit are 140 at highest. When firm 2 selects 35 units, firm 1 selects 35 units as its profit are 105 at highest. When firm 2 selects 50 units, firm 1 selects 25 units as its profit are 63 at highest. When firm 2 selects 100 units, firm 1 selects 100 units as its losses are lowest at 63.

Now look at the strategy of firm 2. When firm 1 selects 25 units, firm 2 selects 35 units as its profit are 140 at highest. When firm 1 selects 35 units, firm 2 selects 35 units as its profit are 105 at highest. When firm 1 selects 50 units, firm 2 selects 25 units as its profit are 63 at highest. When firm 1 selects 100 units, firm 2 selects 100 units as its losses are lowest at 63.

There is a single Nash equilibrium where both firms produce 35 units.


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