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 described in the following equation: $Q_D = 25 - 0.25P_p$, 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 $P_L = \$100$. Assume a perfectly competitive market, such that the list price represents the marginal cost of producing each unit of the medical services. Answer the questions below, and show your work. (17 points total)
a. Write Natalia's demand equation without insurance with quantity demanded, $Q_D$, on the left side in terms of the list price, $P_L$. Graph Natalia's demand curve without insurance with demand, $Q_D$, on the horizontal axis and list price, $P_L$, on the vertical axis. What quantity of medical services does Natalia demand at the list price of $P_L = \$100$? (3 points)
b. Write Natalia's demand equation with full insurance with quantity demanded, $Q_D$, on the left side (hint: the demand equation is not a function of the list price, $P_L$). Graph Natalia's demand curve with full insurance with demand, $Q_D$, on the horizontal axis and list price, $P_L$, on the vertical axis. What quantity of medical services does Natalia demand at the list price of $P_L = \$100$? What is the numeric value of the social/welfare loss? Shading the social/welfare loss on your graph may help with finding the numeric value. (3 points)
c. Write Natalia's demand equation with a 50% coinsurance plan with quantity demanded, $Q_D$, on the left side in terms of the out-of-pocket price, $P_p$. Graph Natalia's demand curve for a 50% coinsurance plan with demand, $Q_D$, on the horizontal axis and list price, $P_L$, on the vertical axis. What quantity of medical services does Natalia demand at the list price of $P_L = \$100$? What is the numeric value of the social/welfare loss? Shading the social/welfare loss on your graph may help with finding the numeric value. (3 points)
