Question

You are the manager of an organization in America that distributes blood to hospitals in all states and the District of Columbia. A recent report indicates that nearlyAmericans contract HIV each year through blood transfusions. Although every pint of blood donated in the United States undergoes a battery of nine different tests, existing screening methods can detect only the antibodies produced by the body’s immune system—not foreign agents in the blood. Since it takes weeks or even months for these antibodies to build up in the blood, newly infected HIV donors can pass along the virus through blood that has passed existing screening tests. Happily, researchers have developed a series of new tests aimed at detecting and removing infections from donated blood before it is used in transfusions. The obvious benefit of these tests is the reduced incidence of infection through blood transfusions. The report indicates that the current price of decontaminated blood isper pint. However, if the new screening methods are adopted, the demand and supply for decontaminated blood will change to$Q^d=210-1.5Pand{Q}^s=2.5P-150$. What price do you expect to prevail if the new screening methods are adopted? How many units of blood will be used in the United States? What is the level of consumer and producer surplus? Illustrate your findings in a graph.

Short answer

The price expected to prevail is $90 and 75 units of blood will be used.

The consumer surplus is $1875 and the producer surplus is $1125.

Step-by-step solution

Given Information

$$\begin{gathered} Q^d=210-1.5P \\ {Q}^s=2.5P-150 \end{gathered}$$

Price prevailing due to the adoption of new screening methods and the quantity of blood:

.To equate the demand function is equal to the demand functions are

$Q^d=Q^s$

Given the supply and demand equations ate$Q^d=210-1.5Pand{Q}^s=2.5P-150$

$Q^d=Q^s$

Substituting in the equation:

$\begin{array}{rcl}210-1.5P& =& 2.5P-150\\ 210+150& =& 2.5P+1.5P\\ 360& =& 4P\\ P& =& \frac{360}{4}\\ P& =& 90\\ & & \end{array}$

Thus, the equilibrium price will be $90.

To find the equilibrium quantity, Substitute the equilibrium price into the supply function and calculate

$\begin{array}{rcl}{Q}^s& =& 2.5P-150\\ & =& 2.5\times 90-150\\ & =& 225-150\\ Q^s& =& 75\\ & & \end{array}$

The equilibrium quantity is 75 units, if the new screening methods will be adopted. Thus, the quantity of blood will be used in 75 units

Calculation of consumer and producer surplus in the graph :

At Qs = 0,

$\begin{array}{rcl}{Q}^s& =& 2.5P-150\\ 0& =& 2.5P-150\\ 2.5P& =& 150\\ P& =& 60\\ & & \end{array}$

At Qd = 0,

$\begin{array}{rcl}{Q}^d& =& 210-1.5P\\ 0& =& 210-1.5P\\ 1.5P& =& 210\\ P& =& 140\\ & & \end{array}$

The consumer surplus is:

$\begin{array}{rcl}CS& =& 0.5\times \left(140-90\right)\times 75\\ & =& 1875\\ & & \end{array}$

Thus, the consumer surplus is $1875.

The producer surplus is:

$\begin{array}{rcl}PS& =& 0.5\times \left(90-60\right)\times 75\\ & =& 1125\\ & & \end{array}$

The producer surplus is $1125.