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Calculating expected price and optimal output level

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You are the manager that sells a commodity in a market that is, for all intents and purposes, a perfectly competitive market. Your cost function is TC = C(Q) = 50+0.01*Q^2. Your marginal cost function is MC(Q) = 0.02*Q. Unfortunately, due to production lags, you must make your output decision prior to knowing for certain what price will prevail in the market. You believe that there is a 20% chance that the market price will be $500 otherwise, the other possible value for the market price is $600.

1. Calculate the expected market price.
2. What output should you produce in order to maximize expected profits?

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Solution Preview

1. Calculate the expected market price.

Probability of price being $500 is 20% i.e. 0.20
Probability of price being $600 is ...

Solution Summary

Solution describes the steps to calculate expected price and optimal output level.

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Determine the profit-maximizing output and price under 3 scenarios.

Using the function C(Q) = 400+50Q+5Q^2 determine the profit-maximizing output and price and discuss its long-run implications under 3 scenarios.

1) The firm is a perfect substitute with a similar product offered by Firm B, Firm C that have similar cost functions and that currently sell for $200 each.

2) The firm firm has NO substitutes and so is a monopolist, and the demand for the Firm is expected to be forever Q=30-(1/5)P (note use earlier listed cost function)

3) The firm has no substitutes and currently the demand for the firms product is Q = 80-(1/5)P but the firm anticipates that other firms can develop close substitutes in the future.

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