Question

The following graph shows the daily demand curve for bikes in Dallas.
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 $20, $30, $40, $50, $60, $70, and $80 per bike.

Answer 1

The price elasticity of demand is how much a quantity changes, over its price.

• According to the midpoint method, the price elasticity of demand between points A and B is approximately 0.467.
• Suppose the price of bikes is currently $30 per bike, shown as point B on the initial graph. Because the demand between points A and B is inelastic, a $10-per-bike increase in price will lead to a decrease in total revenue per day.
• In general, in order for a price decrease to cause a decrease in total revenue, demand must be inelastic.

(a) Total Revenue

The total revenue (R) is the product of the price and the quantity demanded.

When Price = $20, the demand = 70.

So, we have:

$R_1 = 20 \times 70 = 1400$

When Price = $30, the demand = 50.

So, we have:

$R_2 = 30 \times 50 = 1500$

For other points, the total revenues are:

$R_3 = 40 \times 30 = 1200$

$R_4 = 50 \times 10 = 500$

$R_5 = 60 \times 0 = 0$

The graph does not show the demand of bikes at $70 and $80.

So, the total revenue cannot be calculated.

See attachment for the graph of total revenue.

(b) The price elasticity between points A and B

At point A, we have:

$(P_1,Q_1) = (40,35)$

At point B, we have:

$(P_2,Q_2) = (30,40)$

The price elasticity of demand using the midpoint formula is:

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

So, we have:

$E_d = \frac{(Q_2 - Q_1)/((Q_1 + Q_2)}{(P_2 - P_1)/((P_1 + P_2)}$

$E_d = \frac{(40 - 35)/((35 + 40)}{(30-40)/((40+30)}$

$E_d = \frac{5/75}{-10/70}$

$E_d = -0.467$

Hence, the price elasticity of demand is 0.467

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