Your market research group estimated the following demand curve for gadgets, the

Question

Your market research group estimated the following demand curve for gadgets, the product your company produces and sells.
Qd = 4,000 – 40P
If this relationship between quantity demanded and prices continues to hold true in the future,
a. How many gadgets will be demanded at $10, $20, and $30?
b. What is the arc price elasticity between $10 and $20; between $20 and $30?
c. What is the point price elasticity at each of the three prices?
d. If your company sold 3,000 gadgets last year, what is the price it charged?

Explanation / Answer

a)
Qd = 4,000 – 40P
At P=$10
Qd = 4,000 – 40*10 = 3600
At P=$20
Qd = 4,000 – 40*20 = 3200
At P=$30
Qd = 4,000 – 40*30 = 2800

b) Arc Elasticity

PEoD = (% Change in Quantity Demanded)/(% Change in Price)

(% Change in Quantity Demanded) = [[QDemand(NEW) - QDemand(OLD)] / [QDemand(OLD) + QDemand(NEW)]] *2]

(% Change in Price) = [[Price(NEW) - Price(OLD)] / [Price(OLD) + Price(NEW)]] *2]

For Price between $10 and $20
QDemand(NEW) = 4,000 – 40*20 = 3200
QDemand(OLD) = 4,000 – 40*10 = 3600


(% Change in Quantity Demanded) = [[3200 - 3600] / [3600 + 3200]] *2] = =-0.117647059

(% Change in Price) = [[20 - 10] / [10 + 20]] *2] = 0.666666667

arc price elasticity = -0.118/0.667 = -0.176

For Price between $20 and $30
QDemand(NEW) = 4,000 – 40*30 = 2800
QDemand(OLD) = 4,000 – 40*20 = 3200


(% Change in Quantity Demanded) = [[2800 - 3200] / [3200 + 2800]] *2] = -0.133

(% Change in Price) = [[30 - 20] / [20 + 30]] *2] = 0.4

arc price elasticity = -0.133/0.4 =-0.3333

d) 3,000 = 4000-40P

40P = 1000

P= $25

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