Question

1. The Dolan Corporation, a maker of small engines, determines that in 2011 the demand curve for its products was

                                       P = 2,000 – 50 Q,

where P is the price (in dollars) of an engine and Q is the number of engines sold per month.

a. To sell 20 engines per month, what price would Dolan have to charge?

b. If managers set the price at $500, how many engines will Dolan sell per month?

c. What is the price elasticity of demand when the price is $500?

d. At what price, if any, will the demand for Dolan’s engines be unitary elastic?

  

Answer 1

a)Substitute the quantity (20) for Q in the demand equation and solve for P. P = 2,000 –50 (20) = $1,000.

b)Substitute the price ($500) for P in the demand equation and solve for Q.

500 = 2,000 –50 Q =50 Q = 2,000 –500 =Q = 30

C)

Demand elasticity

substitute for the slope and for the price and quantity combination as follows: 1/η = (-50) (30/500) = - 1500/500 = -3

Therefore, the price elasticity of demand

(η) is –1/3

d)

As we discussed above, price elasticity of demand is -1 at the midpoint of the demand curve. This point is also the midpoint of the intercept. Since the intercept in the demand equation is 2,000, half of that is 1,000. Now we simply need to find the quantity on the demand curve when the price is $1,000. Substitute 1,000 in the demand equation and you will get: 1000 = 2,000 –50 Q =50 Q = 2,000 –1000 =Q = 20 Therefore, the price elasticity of demand is -1 at price of $1,000 and quantity of 20.