Question

The market demand for primary care visits is given by the inverse demand curve ?? = 400 – 8? and the inverse market supply is ?? = 40 + 4?

. a. Graph the market supply and demand and indicate the market equilibrium values for price and quantity

. b. Suppose that the consumers in this market are then provided health insurance that pays for all services after consumers pay a 40% coinsurance rate for every visit. On the same graph, graph the demand for primary care visits generated by this insurance plan. What is the market equilibrium price and quantity with a 40% coinsurance rate?

c. What is the dead weight loss of moral hazard under dental insurance?

d. Explain briefly whether insurance makes the demand for health care visits more or less elastic and why.

Answer 1

Solution:

.

a) P_d = 400-8Q . Ps  = 40+4Q

Q_d = (400-P)/8 . Q_s = (P-40)/4

Q_s=Q_d

(P-40)/4 = (400-P)/8

8P-320 = 1600-4P

4P = 1280

P = 320 and Q=70

  

b)   After Insurance Plan demand curve becomes

Q_d = (400-40%P)/8 = (400-.40P)/8

At equilibrium Q_d=Q_s

(400-.04P)/3 = (P-40)/4

16000 - 0.16P = 3P - 120

3.16 P = 16120

P = 5101.266

Q = 1265.317 ie, 1265

  

Co insurance Rate = .40*5101.266

= 2040.5064

c) Dead Weight Loss =   1/2 * (1265 - 70) * (5101.266 - 2040.5064)

= 1/2 * 1195 * 3060

= 18,28,350

.

d) Insurance make the demand less elastic because when consumer are provided with a cover of insurance they become less responsive to change in price because they are now paying only a small fraction of price. Hence demand becomes inelastic or less elastic.