Question

Consumers know that some fraction x of all new cars produced and sold in the market are defective. The defective ones cannot be identified except by those who own them. Cars do not depreciate with use. Consumers are risk-neutral and value nondefective cars at $10,000 each. New cars sell for $5,000 and used ones for $2,500. What is the fraction x

Answer 1

x = 2/3

Step-by-step explanation:

From the question, we have:

Probability of a defective car = x

Probability of a nondefective car = 1 - x

Value of defective car = Price of used cars = $2,500

Value of a nondefective car = $10,000

Expected value = Price of a new car = $5,000

The formula for calculating the expected value is given as follows:

Expected value = (Probability of a defective car * Value of defective car) + (Probability of a nondefective car * Value of a nondefective car) .......... (1)

Substituting all the relevant values into equation (1) and solve for x, we have:

$5,000 = (x * $2500) + (1 - x)$10,000

5,000 = 2500x + 10,000 - 10,000x

5000 - 10000 = 2500x - 10000x

-5000 = - 7500x

x = -5000 / - 7500

x = 2/3