A monopolist has a demand curve given by D: P = 100 - Q and a marginal cost curve given by S: P = 2Q.
How would you solve this?
Step 1: Graph the Market
Step 2: Derive Marginal Revenue
Step 3: Finding P and Q
In other words, the monopolist chooses Q to maximize TR, and charges "as much as he can get away with"--the highest price consumers will pay for that profit-maximizing Q.
Step 4: Comparing Efficiency
The orange area represents consumer surplus under monopoly, the purple area represents producer surplus under monopoly, and the light green area represents deadweight loss. You can easily see that at the socially efficient point, some of producer surplus and DWL would be allocated to consumers, and the rest of DWL would be allocated to producers.
Step 5: Calculating DWL Precisely
You could also calculate this as the change in total surplus, calculating the sum of producer and consumer surplus under monopoly and competition.
**Note that the 104.16 is calculated using 33.33333 (repeating) rather than 33.3. If you use 33.3, you will get 103.75, which is also acceptable.