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?

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.

... Put d(AVC)/dQ=0 to find optimal point. ... Solution describes the steps to calculate price and minimum value of average cost in the given scenario. ...

... variable cost, total variable cost, total cost and minimum AVC. Solution to second problem explains the steps to calculate minimum AVC, optimal level of output ...

... the corresponding Q, calculate TR then calculate MR by ... given marginal revenue the optimal level of output for ... structure of competition and to the price in this ...

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