Each individual faces a 10% chance of contracting muscular back pain. Assume that back pain can only be treated by aggressive physical therapy. Physical therapists will provide as many visits as demanded for $120 per visit.

(a) Once an individual is diagnosed with the problem, his demand curve for back pain treatment (physical therapy session) is represented by the following formula:
Q = 40 - ¼ * P

where P is the price of an office visit and Q is the quantity of office visits
demanded. Draw the demand and supply curves for back pain treatment. Clearly
label your axis. What is the equilibrium quantity and price of physical therapy visits? How much will he/she spend on treatment for back pain?

(b) Now assume that individuals can buy an insurance policy at the beginning of the year before they know whether they will have muscular back pain. The insurer will pay for physical therapy sessions (without copayments or deductibles) for people who are diagnosed with the problem. How many physical therapy visits will the insured people have when they have back pain? How much will the insurance company have to pay for each person with back pain?

(c) What is the dead weight loss associated with full health insurance? Show it on your graph in part (a).

(d) Assume economy of risk-averse individuals with demand functions similar to the one described in part

(a). Will insurance, which provides full coverage, arise in this market? describe your answer (if yes, then quote the actuarially fair premium; if not, describe why not)