Question

1. (30 points) There are two firms considering introducing a new product to the market. Each firm carn either set a high price or low price for its product. If both set a low price the market will be shared between the two firms. In this case, each firm expects to make a profit of $2m. If one firm sets a high price while the other sets a low price, the former is expected to make $1m and the latter is expected to make $5m. When both set a high price, again, the market will be shared and each firm expects to make a profit of $4m. If both firms know all this information and will choose their prices simultaneously, without knowing what the other chooses, what will be the outcome? What price would each firm pick?

Answer 1

Payoff matrix is as follows (values in $m).

		FIRM 2
		High Price	Low Price
FIRM 1	High Price	(4, 4)	(1, 5)
	Low Price	(5, 1)	(2, 2)

When Firm 2 chooses high price, Firm 1's best strategy is Low price since payoff is higher (5 > 4).

When Firm 2 chooses Low price, Firm 1's best strategy is Low price since payoff is higher (2 > 1).

When Firm 1 chooses high price, Firm 2's best strategy is Low price since payoff is higher (5 > 4).

When Firm 1 chooses Low price, Firm 2's best strategy is Low price since payoff is higher (2 > 1).

Therefore Nash equilibrium (optimal strategy) is: (Low price, Low price) [see below].

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