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# What is the inverse demand function and profit maximizing price and level of production for a monopolistically competitive firm?

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You are a manager of a monopolistically competitive firm, and your demand and cost functions are given by Q=20-2P and C(Q) = 104 - 14Q + Q^2

a) find the inverse demand function for your firms product
b) determine the profit maximizing price and level of production
c) calculate your firms profits
d) what long run adjustments should you expect.

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https://brainmass.com/economics/price-levels/determining-price-level-production-profits-229960

#### Solution Preview

a) Inverse Demand Function would be
P= (20-Q)/2
=> P = 10 - 0.5Q

b) Profit maximization happens when Marginal Revenue equals Marginal Cost
First we determine Marginal Revenue
Total Revenue = PxQ = 10Q - 0.5Q^2
Therefore Marginal Revenue (MR) = 10 - Q ...

#### Solution Summary

This solution provides step by step calculations for determining price, level of production, and profits. It briefly discusses expected long run adjustments.

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