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Finding the Optimal Output Price Combination

Consider an industry dominated by one firm that acts as a price leader. The industry also has a large number of smaller price followers that can sell as much as they want at the price set by the dominant firm. The demand curve for the output of all firms in the industry is:

QT = - 42,500 + 70P

The total cost curve for the dominant firm and the aggregate cost curve for the price followers are:

TCD = 50,000 + 150Q + 0.005Q2

ΣMCf = 250 + 0.05Q

Determine the price and output combination that the dominant firm would need to maximize profit for itself.

Solution Preview

Consider an industry dominated by one firm that acts as a price leader. The industry also has a large number of smaller price followers that can sell as much as they want at the price set by the dominant firm. The demand curve for the output of all firms in the industry is:

QT = - 42,500 + 70P

The total cost curve for the dominant firm and the aggregate cost curve for the price followers are:

TCD = 50,000 + 150Q + 0.005Q2

ΣMCf = 250 + 0.05Q

Determine the price and output combination that ...

Solution Summary

Solution describes the steps to find the optimal price and output level in the given case.

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