91影视

The consumer surplus of the academic customer is calculated below:

$$\begin{gathered} CS=0.5脳6脳\left(8-2\right) \\ =0.5脳6脳6 \\ =18millioncentspermonth \\ =\$180,000permonth \end{gathered}$$

The rental fee will be $180,000 per month, and the usage fee will be 2 cents per month. The total profit will be $1,800,000 per month.

The consumer surplus of the business customer is calculated below:

$$\begin{gathered} CS=0.5脳8脳\left(10-2\right) \\ =0.5脳8脳8 \\ =32millioncentspermonth \\ =\$320,000permonth \end{gathered}$$

The rental fee will be $320,000 per month, and the usage fee will be 2 cents per month. The total profit will be $3,200,000 per month.

The total profit 5 million per month (= 3,200,000 + 1,800,000).

The total demand function will be the summation of the demand function of the total of both the customers. The total demand function will be:

$$\begin{gathered} \text{Q = 10}\left(\text{10 - P}\right)\text{+ 10}\left(\text{8 - P}\right) \\ \text{= 100 - 10P + 80 - 10P} \\ \text{= 180 - 20P} \\ \text{P = 9 - 0.05Q} \end{gathered}$$

The profit-maximizing condition will be at the level where the marginal revenue is equal to the marginal cost.

$$\begin{gathered} \text{MR = 9 - 0.1Q} \\ \text{MC = 2} \\ \text{MR = MC} \\ \text{9 - 0.1Q = 2} \\ \text{0.1Q = 7} \\ \text{Q = 70}\text{million}\text{second} \\ \text{P = 9 - 0.05}\left(\text{70}\right) \\ \text{= 9 - 3.5} \\ \text{= 5.5}\text{cents}\text{per}\text{second} \end{gathered}$$

The profit is calculated below:

$$\begin{gathered} \mathrm{蟺}=\left(5.5-\right)2脳70 \\ =245\mathrm{million}\mathrm{cents}\mathrm{per}\mathrm{month} \\ =\$2.45\mathrm{million}\mathrm{per}\mathrm{month} \end{gathered}$$

The profit will be $2.45 million per month.

Under a two-part tariff and no price discrimination, the rental fee is set equal to the consumer surplus of the academic institution. The rental fee will be:

$$\begin{gathered} {\text{Rent = CS}}_{\text{A}}\text{= 0.5}\left({\text{8 -P}}^{\text{*}}\right)\left({\text{8 -P}}^{\text{*}}\right) \\ \text{= 0.5}{\left({\text{8 -P}}^{\text{*}}\right)}^{\text{2}} \end{gathered}$$

P* is the usage fee, Q_A is the total computer time used by ten academic customers, and Q_B is the total computer time used by ten business customers.

The total revenue and total cost curves will be:

$$\begin{gathered} \text{TR =}\left(\text{20}\right)\left(\text{Rent}\right)\text{+}\left({\text{Q}}_{\text{A}}{\text{+Q}}_{\text{B}}\right){\text{P}}^{\text{*}} \\ \text{TC = 2}\left({\text{Q}}_{\text{A}}{\text{+Q}}_{\text{B}}\right) \end{gathered}$$

The profit function will be:

$$\begin{gathered} \mathrm{蟺}=20\left(\mathrm{Rent}\right)+\left({\mathrm{Q}}_{\mathrm{A}}+{\mathrm{Q}}_{\mathrm{B}}\right)\mathrm{P}*-2\left({\mathrm{Q}}_{\mathrm{A}}+{\mathrm{Q}}_{\mathrm{B}}\right) \\ =10{\left(8-\mathrm{P}*\right)}^2+\left(\mathrm{P}*-2\right)\left(180-20\mathrm{P}*\right) \\ \frac{\mathrm{诲蟺}}{\mathrm{dP}*}=20\mathrm{p}*-160+180-40\mathrm{p}*+40=0 \\ -20\mathrm{p}*+60=0 \\ 20\mathrm{p}*=60 \\ \mathrm{p}*=3\mathrm{cents}\mathrm{per}\mathrm{second} \end{gathered}$$

The usage fee will be 3 cents per second; the rental fee will be $0.5{\left(8-3\right)}^2=0.5{\left(5\right)}^2=12.5millioncents=\$125,000permonth$.

The Q_A and Q_B will be:

$$\begin{gathered} Q_A=10\left(8-3\right) \\ =10脳5 \\ =50millionseconds \\ {Q}_b=10\left(10-3\right) \\ =10脳7 \\ =70millionseconds \\ Q=50+70 \\ =120millionseconds \end{gathered}$$

The profit will be,

$$\begin{gathered} \mathrm{蟺}=20\left(12.5\right)+\left(120\right)3-2\left(120\right) \\ =250+360-240 \\ =370\mathrm{million}\mathrm{cents} \\ =\$3.7\mathrm{million}\mathrm{per}\mathrm{month} \end{gathered}$$

The profit is greater when the rental price is not zero; thus, the price cannot equal marginal cost, reducing the profit.