Firms Alpha and Beta serve the same market. They have constant average costs of $2 per unit. The firms can choose either a high price ($10) or a low price ($5) for their output. When both firms set a high price, total demand is 10,000 units which is split evenly between the two firms. When both set a low price, total demand is 18,000, which is again split evenly. If one firm sets a low price and the second a high price, the low priced firm sells 15,000 units, the high priced firm only 2,000 units. Analyze the pricing decisions of the two firms as a non-cooperative game.

Question

Business

Ralph

25 July, 13:06

Firms Alpha and Beta serve the same market. They have constant average costs of $2 per unit. The firms can choose either a high price ($10) or a low price ($5) for their output. When both firms set a high price, total demand is 10,000 units which is split evenly between the two firms. When both set a low price, total demand is 18,000, which is again split evenly. If one firm sets a low price and the second a high price, the low priced firm sells 15,000 units, the high priced firm only 2,000 units. Analyze the pricing decisions of the two firms as a non-cooperative game.

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Answers (1)

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Rodrigo Taylor · Answer 1

A Nash equilibrium exists when both firms offer a low price.

Explanation:

Firm A

profit w / high price profit w / low price

$40,000 / $45,000 /

profit w/high price $40,000 $16,000

Firm

B $16,000 / $27,000 /

profit w/low price $45,000 $27,000

contribution margin with high price = $10 - $2 = $8

contribution margin with low price = $5 - $2 = $3

Both firms' dominant strategy is to offer a low price since the expected profits = $45,000 + $27,000 = $72,000 is higher than the expected profits with a high price ($40,000 + $16,000 = $56,000). Therefore, a Nash equilibrium exists when both firms offer a low price.