# Calculating optimal output and market price

Propylene is used to make plastic. The propylene industry is perfectly competitive and each producer has a long run total cost function given by

LTC= 1/3 Q^3 -6Q^(2 )+40Q

Where Q denotes the output of the individual firm.

The market demand for propylene is

X =2200 -100P

Where X and P denote the market output and price respectively.

1. Calculate the optimal output produced by each firm at the long run competitive equilibrium (LRCE).

2. Calculate the market price and market output at the LRCE.

3. Calculate the number of firms at the LRCE.

Suppose the demand curve shifts to

X =A -100P

Where A is a positive number.

Calculate how large A would have to be so that in the new LRCE, the number of firms is twice what it was in the initial equilibrium.

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#### Solution Preview

1. Calculate the optimal output produced by each firm at the long run competitive equilibrium (LRCE).

At LRCE, long run marginal Cost is equal to long run average cost.

Given, LTC= 1/3 Q^3 -6Q^(2 )+40Q

Long run marginal cost (LRMC) is given by

LRMC=d(LTC)/dQ=Q^2-12Q+40

Long run average cost (LRAC) is given by

LRAC=LTC/Q=1/3 ...

#### Solution Summary

Solution describes the steps to calculate optimal output and market price. It also calculates number of firms present in the market in the given scenario.