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. Elasticity and total revenue
The following graph shows the daily demand curve for bikes in Detroit.
Use the green rectangle (triangle symbols) to compute total revenue at various prices along the demand curve.
Note: You will not be graded on any changes made to this graph.
Total Revenue
0
5
10
15
20
25
30
35
40
45
50
55
60
300
275
250
225
200
175
150
125
100
75
50
25
0
PRICE (Dollars per bike)
QUANTITY (Bikes)
Demand
A
B
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.
Total Revenue
0
25
50
75
100
125
150
175
200
225
250
275
300
5300
4900
4500
4100
3700
3300
2900
2500
2100
1700
TOTAL REVENUE (Dollars)
PRICE (Dollars per bike)
50, 2937.5
According to the midpoint method, the price elasticity of demand between points A and B is approximately0.6 .
Suppose the price of bikes is currently $100 per bike, shown as point B on the initial graph. Because the demand between points A and B isinelastic , a $25-per-bike increase in price will lead toa decrease in total revenue per day.
In general, in order for a price decrease to cause a decrease in total revenue, demand must beinelastic .
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MrRoyal

The price elasticity of demand is the change in quantity demanded relative to the change in price.

  • The second figure in the attached image represents the revenue graph
  • The price elasticity of demand is 0.143
  • The demand must be inelastic

Let:

[tex]P \to Price\\Q \to Quantity[/tex]

(a) The total revenue

From the first graph (see attachment), we have:

[tex](P_1,Q_1) = (50,90)[/tex]

[tex](P_2,Q_2) = (75,81)[/tex]

[tex](P_3,Q_3) = (100,72)[/tex]

[tex](P_4,Q_4) = (125,63)[/tex]

[tex](P_5,Q_5) = (150,54)[/tex]

[tex](P_6,Q_6) = (175,45)[/tex]

[tex](P_7,Q_7) = (200,36)[/tex]

The total revenue (T) is calculated using:

[tex]T = P \times Q[/tex]

So, we have:

[tex]T_1 = 50 \times 90 = 4500[/tex]

[tex]T_2 = 75 \times 81 = 6075[/tex]

[tex]T_3 = 100 \times 72 = 7200[/tex]

[tex]T_4 = 125 \times 63 = 7875[/tex]

[tex]T_5 = 150 \times 54 = 8100[/tex]

[tex]T_6 = 175 \times 45 = 7875[/tex]

[tex]T_7 = 200 \times 36 = 7200[/tex]

The second figure in the attached image represents the revenue graph

(b) Price elasticity of demand

Between points A and B, we have:

[tex](P_1,Q_1) = (50,90)[/tex]

[tex](P_2,Q_2) = (25,99)[/tex]

The price elasticity of demand is:

[tex]E_d = \frac{(Q_2 - Q_1)/(Q_1 + Q_2)/2}{(P_2 - P_1)/(P_1 + P_2)/2}[/tex]

So, we have:

[tex]E_d = \frac{(Q_2 - Q_1)/(Q_1 + Q_2)}{(P_2 - P_1)/(P_1 + P_2)}[/tex]

[tex]E_d = \frac{(99 - 90)/(90 + 99)}{(25 - 50)/(50 + 25)}[/tex]

[tex]E_d = \frac{9/189}{-25/75}[/tex]

[tex]E_d = -0.143[/tex]

The price elasticity of demand between points A and B is 0.143, and the demand must be inelastic because an increase in price of the bike leads to a decrease in the total revenue

Read more about price elasticity of demand at:

https://brainly.com/question/13380594

Ver imagen MrRoyal