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Market Researchers at XYZ Corp. estimate that the demand function for the firm's product is

Q=50P ^-1.5 I ^0.5

Q= Quantity Demanded P= Product's Price I= Per Capita Disposable Income

Marginal Cost of the firm's product is estimated to be $10. Population is constant.

XYZ's price for the product is $20. Is this the optimal price? Why or why not? If not what would be the optimal price?

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Solution Summary

This job figures optimal price.

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We can re-write the demand curve into:
P ^1.5 = 50 I ^0.5 / Q
(P^1.5)^(2/3) = (50 I ^0.5 / Q)^(2/3)

The firm's total revenue is
TR = Q*P = Q * (50 I ^0.5 / Q)^(2/3) = (50 I ^0.5)^(2/3) * ...

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