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

ID: 1176913 • Letter: 1

Question

1. Your market research group estimated the following demand curve for gadgets, the product your company produces and sells.

Qd = 4,000 %u2013 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?

a) Q = 4000 - 40*10 = 3600

Q(20) = 4000 - 40*20 = 3200

Q(30) = 4000 - 40*30 = 2800

b)Avg P = (10+20)/2 = 15

Avg Q = (3600+3200)/2 = 3400

dQ/dP = -40 ;

between 10 and 20 ; elasticity = (dQ/dP)*(P/Q) = -40*15/3400 = -0.1764 ;

between 20 and 30 ;

P = (20+30)/2 = 25

Q = (2800 + 3200)/2 = 3000 ;

Elasticity = -40*25/3000 = -0.3333

c)at 10 ;

e = -40*10/3600 = -0.111 ;

at 20 ;

e =-40*20/3200 = -0.25 ;

at 30 ;

e=-40*30/2800 = -0.4286;

d)3000 = 4000 - 40*P

P = 1000/40 = $25

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