Question

Suppose patient demand for blood tests at a local hospital to screen for various illnesses is given by Q = 10,000 - 20P, where Q is the number of tests and P is the price of each test in dollars. It costs the hospital a constant $250 to run each test. Assume that patients have insurance that covers 90% of the cost of a blood test. Suppose that, because it helps to detect communicable diseases, each blood test that is administered has a positive externality that can be valued at $50. The deadweight loss resulting from the hospital administering blood tests in this case will be_____ in size relative to if there were no positive externality associated with the tests (enter just the word larger, smaller, or identical in the blank).

Answer 1

Consider the given problem here the demand for “blood test” at local hospital to screen is given by,

“Q = 10,000 – 20*P, => P = 500 – (1/20)*Q”. Now, there is a constant cost of “$250” for each test and patients have insurance t6hat cover 90% of the cost of blood test, => MC = 0.1*250 = 25.

So, at the equilibrium, “P = MC”, => 500 – (1/20)*Q = 25, => (1/20)*Q = 475*20 = 9,500.

So, at the equilibrium, “P=25” and “Q=9,500”.

Now, suppose there has a positive externality of value, “$50”, => the new demand curve is given below.

=> P = 550 – (1/20)*Q, => at the equilibrium, “P=MC”, => 550 – (1/20)*Q = 25.

=> (1/20)*Q = 550 – 25 = 525, => Q = 525*20 = 10,500.

Now, at the old quantity “Q=9,500” the corresponding price from the new demand curve is, “P=550 – (9,500/20) = 550 – 475 = 75.

So, the “DWL” is given by, “(1/2)*(75-25)*(10,500 – 9,500) = 0.5*50*1000 = 25000.