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# Finding optimal output and price levels

Tyvex LLC produces professional quality color laser printers. The market for professional color laser printers is monopolistically competitive. Assume that the inverse demand curve faced by Tyvex (given its competitors' prices) can be expressed as
P = 5,000 - .2Q
and Tyvex's total costs can be expressed as

TC = 20,000,000 + .05Q2.

a) What price and quantity will Tyvex choose?

b) Is this likely to be a long-run equilibrium for Tyvex LLC? Why or why not?

c) If not, what is likely to happen in the market for professional color laser printers, and how will it affect Tyvex?

#### Solution Preview

a) What price and quantity will Tyvex choose?

P=5000-0.2Q
Total revenue=P*Q=(5000-0.2Q)*Q=5000Q-0.2Q^2
Marginal Revenue=MR=dTR/dQ=5000-0.4Q

TC=20,000,000+0.05Q^2
Marginal Cost=MC=dTC/dQ=0.1Q

Firm will choose output level such that MR=MC to maximize its profits.
Put ...

#### Solution Summary

Solution depicts the steps to find optimal output and price level. It also discusses the likely behavior in long run.

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