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# Calculating optimal price and minimum AVC

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1. After a 10% price discount, a firm found that its weekly sales increased by 30%. If the marginal cost (MC) of this product is \$40 each, what is the optimal price for this product?

2. Suppose the total cost equation for a competitive firm is given by:
TC=1,000+ 10Q -2Q^2 + 0.5Q^3
(A) At what output is the average variable cost (AVC) at a minimum?

(B) If the market price of the firm's output is \$7.5 per unit, should the firm produce or shut down?

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#### Solution Preview

1. After a 10% price discount, a firm found that its weekly sales increased by 30%. If the marginal cost (MC) of this product is \$40 each, what is the optimal price for this product?

Change in quantity demanded=+30%
Change in price=-10%
Marginal Cost, MC=\$40
Price elasticity of demand, Ep=Change in quantity demanded/Change ...

#### Solution Summary

There are two problems. Solution to first problem depicts the steps to calculate optimal price in the given case. Solution to second problem calculates the output level at which AVC is minimum. It also determines if a firm should continue its operations at the given price level.

\$2.49