Question

 6. Elasticity and total revenue

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

 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 $30, $45, $60, $75, $90, $105, and $120 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 $45 per bike, shown as point B on the initial graph. Because the demand between points A and B is _______ , a $15-per-bike increase in price will lead to _______  in total revenue per day.

 In general, in order for a price decrease to cause a decrease in total revenue, demand must be _______ .

Answer 1

Revenue at point A (price = $60) is the sum of rectangle equal to AEOC whose area is (24 - 0) * (60 - 0) = 1,440

Revenue at point B (price = $45) is the sum of rectangle equal to FBOD whose area is (28 - 0) * (45 - 0) = 1,260

When price of bike rises from point B to A, its revenue rises.

Revenue at price $30 is the sum of rectangle equal to HIGO whose area is (32 - 0) * (30 - 0) = 960

Revenue at price $75 is the sum of rectangle equal to JKLO whose area is (20 - 0) * (75 - 0) = 1,500

Revenue at price $90 is the sum of rectangle equal to NOMO whose area is (16 - 0) * (90 - 0) = 1,440

Revenue at price $105 is the sum of rectangle equal to QRPO whose area is (12 - 0) * (105 - 0) = 1,260

Revenue at price $120 is the sum of rectangle equal to TUSO whose area is (8 - 0) * (120 - 0) = 1960

• Price at point A = 60(P1) and quantity consumed is 24(Q1).

Price at point B = 45 (P2) and quantity consumed is 28 (Q2).

Elasticity using mid point method = {(Q2 - Q1) / [(Q2 + Q1) / 2]} / {(P2 - P1) / [(P2 + P1) / 2]}

= {(28 - 24) / [(28 + 24) / 2]} / {(45 - 60) / [(45 + 60) / 2]} = [0.15 / (-0.28)] = -0.53

Price elasticity of demand will have negative sign due to negative relationship between price and quantity demanded thus we can ignore negative sign here. Price elasticity of demand = 0.53

When Price elasticity of demand is between 0 and 1, good have inelastic demand. As the demand between point A and B is inelastic, a rise in price of $15 will cause rise in total revenue.

In general, in order for a price decrease to cause a decrease in total revenue, demand must be inelastic.

Answer 2

30	32	960
45	28	1,260
60	24	1,440
75	20	1,500
90	16	1,440
105	12	1,260
120	8	960

 This would be the accurate table to help plot points on the second graph.