A sporting goods store has estimated the demand curve for a popular brand of running shoes as a function of price. Use the diagram to answer the question that follow.
A. Calculate demand elasticity using the midpoint formula between points A and B, between points C and D, and between points E and F
b. If the store currently charges a price of $50, then increases that price to $60, what happens to total revenue from shoe sales (calculate P Q before and after the price change)? Repeat the exercise for initial prices being decreased to $40 and $20, respectively
Ans: A.
Percent change in quantity=Q2?Q1(Q2+Q1)÷2×100
Percent change in price=P2?P1(P2+P1)÷2×100
200-100 50-60
X 100% X100%
200+100/2 50+60/2
=100/150 X 100% = -10/55 X 100%
=0.67 = -0.18
A and B = 0.67/-0.18
= -3.72
30-40 400-300
X 100% X100%
30+40/2 400+300/2
=-10/35 X 100% = 100/350 X 100%
= -0.28 = 0.28
C and D= -0.28/0.28
= -1
E and F= (20-10) (500-600)= -0.27
10 -20 600-500
X 100% X100%
10+20/2 600+500/2
=10/20X 100% =-100/550 X 100%
=-0.5 = 0.18
A and B = 0.4/-0.18
= -0.27
Ans: B
If the store charges $50 but then increases the price to $60 the total revenue falls from $10,000 to $6,000.
P Q before 200*50 =$10,000 100*60 =$6,000
P Q after 300*40 = $12,000 500*20 =$10,000
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