An important distinction in health insurance is between the list price (P_L) and out-of-pocket price (P_P) of a medical good or service. The list price is the official price that the provider charges the insurance company, while the out-of-pocket price is the price that the insurance customer faces. Sometimes, the out-of-pocket price depends on the list price.

Natalia has demand for medical services as follows: Q = 100 2P_P, where P_P is the out-of-pocket price she actually faces. She is considering four different insurance options: No insurance, full insurance, a coinsurance plan, and a copayment plan. The medical services each have a list price of P_L = $30.

1. Graph Natalia's demand curve under the assumption of no insurance.

2. Graph Natalia's demand curve under the assumption of full insurance. Calculate the quantity demanded and the social loss.

3. Graph Natalia's demand curve for a 50% coinsurance plan. Calculate the quantity demanded and the social loss.

4. Graph Natalia's demand curve for a $20 copayment plan. Calculate the quantity demanded and the social loss.

5. Would the coinsurance plan or the copayment plan be better at mitigating moral hazard? Why?