Question

Scans of internal organs using magnetic resonance imaging (MRI) devices are often covered by subsidized health insurance programs such as Medicare. Consider the following table illustrating hypothetical quantities of individual MRI testing procedures demanded and supplied at various prices, and then answer the questions that follow.

Price	Quantity Demanded	Quantity Supplied
\(100	100,000	40,000
\)300	90,000	60,000
\(500	80,000	80,000
\)700	70,000	100,000
\(900	60,000	120,000

(a) In the absence of a government-subsidized health plan, what is the equilibrium price of MRI tests? What is the amount of society’s total spending on MRI tests?

(b) Suppose that the government establishes a health plan guaranteeing that all qualified participants can purchase MRI tests at an effective price (that is, out-of-pocket cost) to the individual of \)100 per test. How many MRI tests will people consume?

(c) What is the per-unit price that induces producers to provide the amount of MRI tests demanded at the government-guaranteed price of $100? What is society’s total spending on MRI tests?

(d) Under the government’s coverage of MRI tests, what is the per-unit subsidy it provides? What is the total subsidy that the government pays to support MRI testing at its guaranteed price?

Short answer

(a) The equilibrium price is $500. Society's total spending on MRI tests is $ 40 billion.

(b) People will consume 100,000 MRI tests.

(c) Society's total spending on MRI tests is $10 billion.

(d) The total subsidy paid by the government is $60 billion.

Step-by-step solution

Step 1. Given Information.

The data showing the quantity demanded and quantity supplied at a particular price for MRI is as follows:

Price	Quantity Demanded	Quantity Supplied
$100	100,00	40,000
$300	90,000	60,000
$500	80,000	80,000
$700	70,000	100,000
$900	60,000	120,000

Part (a). The equilibrium price of MRI.

The quantity demanded and quantity supplied for MRI is equal to 80,00 at which the price is $ 500. The equilibrium price of MRI tests is $500.

The total amount of spending on MRI tests is equal to:

$$\begin{gathered} =Price\times Quantity \\ =\$500\times 80,000 \\ =\$40million \end{gathered}$$

Part (b). The number of MRIs consumed for $100.

According to the data given, for $100 per test the quantity demanded is 100,000 while the quantity supplied 100,000 would cost $700 per test.

Part (c). The per-unit price induces consumers.

The consumer would be paying $ 100 per teest while the government is willing to supply the required quantity at $700. The remaining amount will be subsidized by the government.

The total spending on MRI tests is,

$$\begin{gathered} =\$100\times 100,000 \\ =\$10billion \end{gathered}$$

Part (d). The Government's Subsidy.

The price for the supplier is $700 and the price the consumer will be willing to pay is $100.

The subsidy per unit for the government is,

$$\begin{gathered} =\$(700-100) \\ =\$600 \end{gathered}$$

Total Government Subsidy is,

$$\begin{gathered} =\$600\times 100,000 \\ =\$60billion \end{gathered}$$