91Ó°ÊÓ

During weekdays, Uber faces the following demand function:

P = 50 - Q.

The total and marginal revenue during the weekdays will be:

$$\begin{gathered} \text{TR =}\left(\text{50 - Q}\right)\text{Q} \\ {\text{= 50Q -Q}}^{\text{2}} \\ \text{MR =}\frac{\text{d}}{\text{dQ}}\left({\text{50Q -Q}}^{\text{2}}\right) \\ \text{= 50 - 2Q} \end{gathered}$$

During surge hours, Uber faces the following demand function:

P = 100 - Q.

Thus, the total and marginal revenue during the weekdays will be:

TR = 100Q - Q²

MR = 100 - 2Q

The marginal cost is MC = 0.

Uber’s profit-maximizing quantity and price during weekdays are as follows:

$$\begin{gathered} \text{MR = MC} \\ \text{50 - 2Q =}0 \\ \text{2Q = 50} \\ \text{Q = 25} \\ \text{P = 50 - Q} \\ \text{= 50 - 25} \\ \text{= \$ 25} \end{gathered}$$

Uber can maximize its profit during weekdays by providing 25 rides at $25 per ride.

Uber’s profit-maximizing quantity and price during surge hours are as follows:

$$\begin{gathered} \text{MR = MC} \\ \text{100 - 2Q =}0 \\ \text{2Q = 100} \\ \text{Q = 50} \\ \text{P = 100 - Q} \\ \text{= 100 - 50} \\ \text{= \$ 50} \end{gathered}$$

Uber can maximize its profit during weekend nights or surge hours by providing 50 rides at $50 per ride.

In this part, the marginal cost is MC = 10.

Now, Uber’s profit-maximizing quantity and price during weekdays are as follows:

$$\begin{gathered} \text{MR = MC} \\ \text{50 - 2Q = 1}0 \\ \text{2Q = 40} \\ \text{Q = 20} \\ P=50-20 \\ =\$30 \end{gathered}$$

Uber can now maximize its profit during weekdays by providing 20 rides at $30 per ride.

Uber’s profit-maximizing quantity and price during surge hours when MC = 10 are as follows:

$$\begin{gathered} \text{MR = MC} \\ \text{100 - 2Q = 1}0 \\ \text{2Q = 90} \\ \text{Q = 45} \\ \text{P = 100 - 45} \\ \text{= \$ 55} \end{gathered}$$

Uber can now maximize its profit during surge hours by providing 45 rides at $55 per ride.

The following diagram contains the market conditions for Uber during surge hours when the marginal cost is constant at $10:

P* and Q* represent the profit-maximizing price and quantity, respectively. Area A and B represent the profits earned by Uber, and area C represents the deadweight loss.

From the diagram, you can compute the profit as the area of the rectangle shown by A and B as follows:

$$\begin{gathered} \mathrm{π}\text{= 45}\left(\text{55 - 10}\right) \\ \text{= 45}×\text{45} \\ \text{= \$ 2025} \end{gathered}$$

You can compute the deadweight loss by the area of triangle C as follows:

$$\begin{gathered} \text{DWL = 0.5}\left(\text{90 - 45}\right)\left(\text{55 - 10}\right) \\ \text{= 0.5}×\text{45}×\text{45} \\ \text{= \$ 1012.5} \end{gathered}$$

Uber earns a profit of $2025 and generates deadweight loss worth $1012.50 during surge hours when the marginal cost is $10.