Question

A risk-neutral consumer is deciding whether to purchase a homogeneous product from one of two firms. One firm produces an unreliable product and the other a reliable product. At the time of the sale, the consumer is unable to distinguish between the two firms’ products. From the consumer’s perspective, there is an equal chance that a given firm’s product is reliable or unreliable. The maximum amount this consumer will pay for an unreliable product is $\cancel{S}0$, while she will pay $\cancel{S}100$for a reliable product.

a. Given this uncertainty, what is the most this consumer will pay to purchase one unit of this product?

b. How much will this consumer be willing to pay for the product if the firm offering the reliable product includes a warranty that will protect the consumer? Explain.

Short answer

a.The consumer will pay maximum $50 per product in the presence of uncertainty.

b. The consumer might wish to pay maximum $100 per product in the presence warranty.

Step-by-step solution

Concept Introduction

In presence of uncertainty, it is possible to know the price the consumer’s price to buy a unit of a product. The consumer might be indifferent to buying it in one store or another since the risk is neutral.

Amount consumer will pay

a.

The equation to find out expected value is –

$E\left(x\right)=q_1{x}_1+q_2{x}_2+......q_n{x}_n.....\left(1\right)$

Where, q = The probability that occur each event.

x = the possible outcomes of the random variable.

The consumer is risk-neutral, so the probability that the consumer will pay$\cancel{S}0$for an unreliable product is $50\%\left(1/2\right)$, while the probability that of paying$\cancel{S}100$for a reliable product is also$50\%\left(1/2\right)$.

Thus, substituting these values in the above equation –

$E\left(x\right)=\frac{1}{2}\times 0+\frac{1}{2}\times 100\times 50$

Therefore, the value for amount is obtained as $\cancel{S}50$.

Amount consumer will pay with warranty

b.

Being risk-neutral, the consumer cannot distinguish between the two firms' products. If one firm offers a reliable product with some extent of guarantee or warranty, the consumer will buy that product. Thus, the consumer will pay the maximum amount for the reliable product, which is $100

Therefore, the value for amount is obtained as $\cancel{S}100$.