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Calculating expected price and optimal output level

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?

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.

$2.19