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Finding optimal output and price levels

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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?

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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

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

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Finding optimal output and price levels problem

Please help with the following economics problem. Provide step by step calculations.

You are the manager of a firm that sells its product in a competitive market at a price of 50. Your firms cost structure is c=40 + 5Q2.

The profit maximizing output for your firm is one of the following:

4/5
10
5
45

Suppose a monopolistic knows the own-price elasticity of demand for its product is -3 and its marginal cost of production is constant MC(Q) = 10. To maximize its profits, the monopoly price is

1.50 per unit
6.67 per unit
10.00 per unit
15.00 per unit

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