Question

Suppose a doctor’s visit actually costs $75. Bob has demand for doctor’s visits given by the following equation where ?? _is the quantity demanded and P is the price of a doctor’s visit: Qd = 20-.1P

a. Draw Bob’s demand curve

b. How many times will Bob go to the doctor (i.e. what is his quantity demanded) if he has no insurance and must pay full price?

c. How many times will Bob go to the doctor with full insurance (i.e. no cost sharing, so he gets to go for free)?

d. What is the dollar value of the social loss due to moral hazard with full insurance? Illustrate with a diagram and calculate, and then give a brief, intuitive explanation as to why this is a loss to society.

e. Suppose Bob’s insurance plan calls for a $50 co-pay. How many times will Bob go to the doctor? What is the dollar value of the moral hazard with the co-pay? Illustrate with a diagram and calculate.

f. Compare and contrast your analysis in part e. to the situation where the insurance company required a 20% coinsurance rate instead of a co-pay.

g. Is it possible that the co-pay or coinsurance cold actually reduce social wellbeing? Explain.

Answer 1

1. Demand curve is given by Q_d = 20 - 0.1P

Now when P = 0, Q_d = 20 and when Q = 0, P = 200

Hence, plotting price on vertical axis , its intercept is 200 and quantity demanded on horizontal axis, its intercept is 20.

Equilibrium is attained at price $75 such that Q_d = 20-0.1*75 = 12.5

The demand is drawn below:

2. If he has to pay $75 , number of visits = 12.5.

3. With full insurance , he will visit the exact horizontal intercept of the demand curve i.e, 20.

4. The loss due to full insurance is denoted by the area a .

The, loss = 1/2*base*height = 1/2 * (20-12.5) * 75 = $281.25

The loss is due to the excess visit even not required under full insurance. Full insurance is also unwanted because it drives away consumers from leading a healthy and conscious lifestyle unlike under no insurance or coinsurance.