On the following graph, use the green point (triangle symbol) to plot the annual total revenue when the market price is $50, $75, $100, $125, $150, $175, and $200 per bike.
According to the midpoint method, the price elasticity of demand between points A and B is approximately _______ .
Suppose the price of bikes is currently $200 per bike, shown as point A on the initial graph. Because the demand between points A and B is _______ ,a $25-per-bike decrease in price will lead to _______ in total revenue per day.
In general, in order for a price increase to cause a decrease in total revenue, demand must be _______ .
Ans.
Total revenue table -
Price | Quantity | TR ( Price x Quantity ) |
50 | 100 | 5000 |
75 | 90 | 6750 |
100 | 80 | 8000 |
125 | 70 | 8750 |
150 | 60 | 9000 |
175 | 50 | 8750 |
200 | 40 | 8000 |
Graph according to the above table will be -
Point A ,
P1 = 200 and , Q1 = 40
Point B ,
P2 = 175 and , Q2 = 50
Price Elasticity (mid point method) = Q2 - Q1 / ( Q2 + Q1 / 2 ) x ( P2+ P1 / 2 ) / P2 - P1
= 50 - 40 / ( 50 + 40 / 2 ) x ( 175 + 200 / 2 ) / 175 - 200
= 10 / ( 90 / 2 ) x ( 375 / 2 ) / - 25
= 10/45 x 187.5/-25
= 0.2222 x -7.5 = 1.67 ( approx. ) > 1 , hence it is elastic.
Blank 1 - price elasticity = 1.67
Blank 2 - demand is elastic
Blank 3 - increase in TR
Blank 4 - elastic
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Annual Total Revenue(in dollars) for bikes sold per each price: $50,$75,$100,$125,$150,$175,$200 is as per below
It shows points A,B,C,D,E,F,G,H which are the combination of price(dollars) per bike and corresponding annual total revenue(dollars)
According to mid point method, the price elasticity of demand between points A and B is approximately 242.19
Explanation: Midpoint(average of prices) of $175 and $200 is 200+175/2= 375/2= 187.5
Quantity demanded at $200= 4200/200= 21
Quantity demanded at $175= 5000/175= 28.57
Midpoint(average of quantities demanded) of 21 and 28.57 is 28.57+21/2= 24.78
Percentage change in price= 200-175/187.5x100= 13.33
Percentage change in quantity demanded= 5000-4200/24.78x100= 3228.41
ep(Price elasticity of demand)= Percentage change in quantity demanded/Percentage change in price
= 3228.41/13.33
ep= 242.19
Suppose the price of bikes is $200 per bike, shown as point A on the initial graph. Because the demand between points A and B is elastic(ep>1), a $25-per bike decrease in price will lead to $13.698 in total revenue per day
Explanation: with $25 decrease in price of bikes, new price is $175 and new annual total revenue is 5000, so total revenue per day is 5000/365 days= $13.698 per day
In general, in order for a price increase to cause a decrease in total revenue, demand must be elastic(ep>1=elasticity more than one)
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