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. Now suppose that all patients that visit the hospital have insurance that covers 90% of the cost of a blood test. In that case, the number of blood tests that will be run at the hospital is____. The deadweight loss that results from the hospital administering blood tests in this case is $____ (enter only numbers in the blank, and please round to the second decimal place if necessary).

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”, => here MC=250. So, at the equilibrium “P=MC”.

=> 500 – (1/20)*Q = 250, => (1/20)*Q = 250, = > Q = 250*20 = 5,000. So at P=250 the corresponding Q=5,000.

Now, for each test and patients have insurance that cover 90% of the cost of blood test, => new “MC” is given by MC1 = 0.1*250 = 25.

So, at the equilibrium, “P = MC1”, => 500 – (1/20)*Q = 25, => (1/20)*Q = 475*20 = 9,500.

So, now the DWL is given by, “(1/2)*(9,500-5,000)*(250 – 25) = 0.5*4500*225 = 506,250.