91影视

The optimum level for each market will be when the marginal revenue is equal to Marginal cost.

The price and quantity in the East Coast (Q₁) are calculated below:

$$\begin{gathered} {\text{MR}}_{\text{1}}{\text{= 15 - 2Q}}_{\text{1}} \\ \text{MC = 3} \\ {\text{MR}}_{\text{1}}\text{= MC} \\ {\text{15 - 2Q}}_{\text{1}}\text{= 3} \\ {\text{2Q}}_{\text{1}}\text{= 12} \\ {\text{Q}}_{\text{1}}\text{= 6} \\ \text{P = 15 - 6} \\ \text{= \$ 9} \end{gathered}$$

In the East Coast, the quantity will be 6 units at $9.

The price and quantity in the Midwest (Q₂) are calculated below:

$$\begin{gathered} {\text{MR}}_{\text{2}}{\text{= 25 - 4Q}}_{\text{2}} \\ \text{MC = 3} \\ {\text{MR}}_{\text{2}}\text{= MC} \\ {\text{25 - 4Q}}_{\text{2}}\text{= 3} \\ {\text{4Q}}_{\text{2}}\text{= 22} \\ {\text{Q}}_{\text{2}}\text{= 5.5} \\ \text{P = 25 - 2}\left(\text{5.5}\right) \\ \text{= 25 - 11} \\ \text{= \$ 14} \end{gathered}$$

In the Midwest, the quantity will be 5.5 units at $14.

The marginal revenue in both the market is calculated below:

$$\begin{gathered} \text{M}{{\text{R}}_{\text{1}}}_{{\text{Q}}_{\text{1}}\text{= 6}}\text{= 15 - 2}\left(\text{6}\right) \\ \text{= 15 - 12} \\ \text{= \$ 3} \\ \text{M}{{\text{R}}_{\text{2}}}_{{\text{Q}}_{\text{2}}\text{= 5.5}}\text{= 25 - 4}\left(\text{5.5}\right) \\ \text{= 25 - 22} \\ \text{= \$ 3} \end{gathered}$$

The marginal revenue in both markets will be $3.

The total profit is calculated below:

$$\begin{gathered} \mathrm{蟺}=\left(9脳6\right)+\left(14脳5.5\right)-\left[5+3\left(11.5\right)\right] \\ =54+77-5-34.5 \\ =\$91.5 \end{gathered}$$

The total profit will be $91.5.

The deadweight loss will be DWL = 0.5 (Q_C-Q_M)(P_M- P_C). The Q_C and P_C represent quantity and price of competitive market; Q_M and P_M represent quantity and price of monopoly market. In the competitive market, the P_C = MC is optimal; thus, the price will be $3 in a competitive market, and the quantity at this price in market 1 will be 12 units, and in market 2 will be 11 units.

The total deadweight loss is calculated below:

role="math" localid="1644382519200" $$\begin{gathered} DW{L}_1=0.5\left(12-6\right)\left(9-3\right) \\ =0.5脳6脳6 \\ =\$18 \\ DW{L}_2=0.5\left(11-5.5\right)\left(14-3\right) \\ =0.5脳5.5脳11 \\ =\$30.25 \\ TotalDWL=18+30.25 \\ =\$48.25 \end{gathered}$$

The total deadweight loss will be $48.25.

The total demand curve will be:

$$\begin{gathered} {\text{Q}}_{\text{1}}{\text{= 15 -P}}_{\text{1}} \\ {\text{Q}}_{\text{2}}{\text{= 12.5 - 0.5P}}_{\text{2}} \\ {\text{Q =Q}}_{\text{1}}{\text{+Q}}_{\text{2}} \\ {\text{= 15 -P}}_{\text{1}}{\text{+ 12.5 - 0.5P}}_{\text{2}} \\ \text{Q = 27.5 - 1.5P} \\ \text{P = 18.33 - 0.67Q} \end{gathered}$$

The quantity and price at the optimum level are calculated below:

$$\begin{gathered} {\text{TR = 18.33Q - 0.67Q}}^{\text{2}} \\ \text{MR = 18.33 - 1.33Q} \\ \text{MC = 3} \\ \text{MR = MC} \\ \text{18.33 - 1.33Q = 3} \\ \text{1.33Q = 15.33} \\ \text{Q = 11.5} \\ \text{P = 18.33 - 0.67}\left(\text{11.5}\right) \\ \text{= 18.33 - 7.7} \\ \text{= \$ 10.6} \end{gathered}$$

At $10.6, the quantity in each market will be:

$$\begin{gathered} {\text{Q}}_{\text{1}}\text{= 15 - 10.6} \\ \text{= 4.4} \\ {\text{Q}}_{\text{2}}\text{= 12.5 - 0.5}\left(\text{10.6}\right) \\ \text{= 12.5 - 5.3} \\ \text{= 7.2} \end{gathered}$$

Output in market 1 will be 4.4 units, and in market 2 will be 7.2 units.

The total profit is calculated below:

$$\begin{gathered} \mathrm{蟺}=\left(10.6脳11.5\right)-5-3\left(11.5\right) \\ =121.9-5-34.5 \\ =\$82.4 \end{gathered}$$

The total profit will be $82.4.

The total deadweight loss is calculated below:

$$\begin{gathered} DW{L}_1=0.5\left(10.6-3\right)\left(12-4.3\right) \\ =0.5脳7.6脳7.7 \\ =\$29.26 \\ DW{L}_2=0.5\left(10.6-3\right)\left(11-7.2\right) \\ =0.5脳7.6脳3.8 \\ =\$14.44 \\ TotalDWL=29.26+14.44 \\ =\$43.7 \end{gathered}$$

The total deadweight loss will be $43.7.