Question

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.

Answer 1

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.