Question

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 _______ .

Answer 1

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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Answer 2

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)