Question

In: Economics

Please show and explain you work. Firm 2 Don’t Expand Small Expansion Large Expansion Firm 1...

Please show and explain you work.

Firm 2

Don’t Expand

Small Expansion

Large Expansion

Firm 1

Don’t Expand

18,18

15,20

9,18

Small Expansion

20,15

16,16

8,12

Large Expansion

18,9

12,8

0,0

There are two firms that are considering the effect on their profits of expanding their capacity. Their choices are no expansion, a small capacity expansion, and a large capacity expansion. Expansion of capacity would allow a firm to obtain a larger market share, but it would also put downward pressure on prices, depressing profits, especially is the other firm also expands capacity. The decisions are made simultaneously.

  1. Explain the payoff to each firm if Firm 1 pursues a large expansion and Firm 2 doesn’t expand.
  2. Does either firm have a dominant strategy? Explain. Be specific.
  3. Is there a Nash equilibrium? Explain. Be specific
  4. What is the optimal outcome if the firms coordinated their actions? Be specific
  5. Explain why the optimal outcome is not a stable equilibrium. Be specific.

Solutions

Expert Solution

If there are two firms that are considering the effect on their profits of expanding their capacity. Their choices are no expansion(DE), a small capacity expansion(SE), and a large capacity expansion(LE). From the given payoff matrix table.

  • If Firm 1 pursues a large expansion and Firm 2 doesn’t expand. The payoff will be that firm 1 will get a higher payoff of 18 and firm 2's payoff will be smaller i.e. 9
  • From the above circled preferred stretegies we can see that non of the firms have a dominant stretegy.
  • We can see from the table that Nash equilibrium is small expansion, small expansion (16,16) where both values are circled.
  • If the firms coordinated their actions, the optimal outcome would have been do not expand for both firms where both the firms would get a higher payoff(18,18). This is because at low level of production price is higher and hence profit is also higher.
  • The Optimal outcome is not a stable equilibrium because the firms will not follow the low output agreement as expanding output may give higher payoff to one firm if only it expands and not other, but thinking this both will expand and hence will get lower payoff.

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