Question

6. Elasticity and total revenue

The following graph shows the daily demand curve for bikes in San Francisco.

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.

On the following graph, use the green point (triangle symbol) to plot the annual total revenue when the market price is $ 50,575, $ 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 $ 125 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 an increase in total revenue, demand must be _______ .

Answer 1

Total Revenue(TR) = Quantity x Price

The demand curve given is P = 300 - (25/6)Q ==> Q = 72 - (6/25)P.

Thus, TR = (72 - (6/25)P)P = 72P - (6/25)P^2. Following table gives the value of TR for various P for the plot.

Price, P	Quantity, Q	Total Revenue, TR
50	60	3000
75	54	4050
100	48	4800
125	42	5250
150	36	5400
175	30	5250
200	24	4800

The price elasticity of demand = % change in Quantity/% change in price.

Using the midpoint method,

% change in Quantity = (Q2-Q1)/((Q1+Q2)/2) = (48-42)/(45) = 2/15

% change in Quantity = (P2-P1)/((P1+P2)/2) = (125-100)/112.5 = 25/112.5 = 1/4.5 = 2/9.

The price elasticity of demand = (2/15)/(2/9) = 9/15 = 0.6.

THE REST OF THE ANSWERS ARE CORRECTLY MARKED