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 ...

...Calculating variable cost (VC), average variable cost (AVC... For each level of output, calculate this manufacturer's ... ATC, calculated as TC/Q AVC, calculated as VC ...

...Calculate the coefficient of variation of each project. ... a. What is the optimal number of steaks served ... b. What is the price that the manager charges for a steak ...

... As calculated in part b, slope of isocost curve is ... What is your total profit at the optimal output? ... difference between Marginal Revenue and Marginal cost is at ...

... A. Calculate the incremental profit that McFarlancl-Adler would earn by ... E. If the price of output is S2 per unit ... is employment of 3 units of X optimal for a ...

... dQ=4000-10Q+0.006Q^2 For profit maximization, put MC=Price 4000-10Q ... Solution describes the steps to calculate minimum value of AVC, optimal output and ...