# equation for the point elasticity as a function of quantity

3. The demand equation for a product is given by P =30 - 0.1Q²

a. Write an equation for the point elasticity as a function of quantity.

b. At what price is demand unitary elastic?

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#### Solution Preview

a. since P =30 - 0.1Q²

the differential of P is

dP/dQ = -0.2Q

The formula of point elasticity is

E = ...

#### Solution Summary

Point Elasticity is featured.

Arc Elasticity, Demand Curve, Total Revenue

The Jaimison Company produces steel. Its demand curve is linear. Its current price and quantity are $237.50 and 1,050 tons, respectively. Management determines that if they lower the price to $200, the will sell 1,200 tons of steel.

a. Calculate the arc price elasticity between these two points on the demand curve.

b. Should management lower the price? Explain

C. Use the information in the problem to derive the equation for Jamison's demand curve equation (i.e., the "inverse" demand curve).

d. Find the price that maximizes total revenue. What is the elasticity of demand at this point? What is the total revenue?

e. Jamison's marginal costs are $100 per ton. Find Jamison's profit maximizing output and price.

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