70 60 A 10 0 100 200 300 400 500 600 Shoe sales per week a C

70 60 A 10- 0 100 200 300 400 500 600 Shoe sales per week 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. c. Explain why the answers to a. can be used to predict the answers to b.

Solution

a. Elasticity = (% change in quantity) / (% change in price)

Mid point % change = (Xnew - Xold) / Xaverage

Percentage change in quantity from A to B calculated by mid-point formula is = (200-100)/150 * 100 = 66.67%

Percentage change in price from A to B, by mid-point formula = (50-60)/55 * 100 = -18.18%

Elasticity = 66.67/-18.18 = -3.66

Now, looking at points C and D

% change in quantity between C and D by mid-point formula = (400-300)/350 * 100 = 28.57%

% change in price between C and D by mid-point formula = (30-40)/35 * 100 = -28.57

Elasticity = 28.57/ - 28.57 = - 1

Elasticity between E and F

% change in quantity by mid-point formula = (600-500)/550 * 100 = 18.18%

% change in price by mid-point formula = (10-20)/10 * 100 = - 100%

Elasticity = 18.18/100 = 0.1818

b. If the store charges $50, then the revenue = 50 * 200 = $10,000

If the store charges $60, then the revenue = 60 * 100 = $6000

The total revenue decreases in this case

Now, when the price decreases to $40, then the total revenue is = 40 * 300 = $12000

Further reducing the price to $20, the total revenue is = 20 * 500 = $10000

The answer to a can be used to predict the answer to b because there is an \"elastic\" relation between points A and B, thus the total revenue increase as price reduces. Whereas there is an \"inelastic\" relation between points E and F, and thus a decrease in total revenue as price reduces.