Question

A smartphone giant wants to evaluate wireless charging. The conjoint analysis yields the following results. How much are consumers willing to pay for wireless charging (compared with the lightning port)?

Charging Method: Wireless vs. Lightning Port
Price: $300 vs. $400
Coefficients: 2.0 vs. -10.0

a) $100
b) $20
c) $2
d) $10

Answer 1

Consumers are willing to pay approximately $16.67 more for wireless charging on a smartphone compared to a lightning port, based on the coefficients given in a conjoint analysis.

Step-by-step explanation:

The student's question pertains to assessing how much more consumers are willing to pay for a smartphone with wireless charging compared to one with a lightning port based on conjoint analysis results. The key data points provided are the coefficients for Charging Method (2.0 for wireless and -10.0 for lightning port) and the Price points ($300 vs. $400).

To determine the value of wireless charging, we calculate the difference in utility between the wireless charging and the lightning port options based on the coefficients. The wireless charging has a positive coefficient, indicating that consumers prefer it over the lightning port, which has a negative coefficient. This preference leads to a willingness to pay more for wireless charging.

By adding the absolute values of both coefficients (2.0 for wireless and 10.0 for lightning), we get a total utility difference of 12.0 units. Now, considering that the price difference given is $100 (from $300 to $400), we allocate this $100 difference over the 12.0 utility units. Dividing $100 by 12 gives us approximately $8.33 per utility unit. Since the difference in coefficients is 12 units and the wireless has a 2.0 advantage over the lightning port, the wireless charging feature is worth 2/12 of the $100 price difference, which is approximately $16.67.

Therefore, consumers are willing to pay approximately $16.67 more for a smartphone with wireless charging compared to a smartphone with a lightning port.

Answer 2

Using conjoint analysis coefficients, we find that the value consumers are willing to pay for wireless charging over a lightning port is an additional $10, making option d) the correct choice.

Step-by-step explanation:

The question deals with determining how much consumers are willing to pay for wireless charging compared to a lightning port on a smartphone using the principles of conjoint analysis.

The coefficients derived from the conjoint analysis are 2.0 for the wireless charging method and -10.0 for the price factor of $400 compared to $300. To determine the value of wireless charging, one must balance the positive coefficient of the charging method against the negative coefficient of the higher price. Specifically, the coefficient for wireless charging (2.0) must counterbalance the price coefficient of increasing the price from $300 to $400, which has a coefficient of -10.0.

Using algebra to set the coefficients to each other gives us the equation 2.0 * x = 10.0, where x represents the consumer's willingness to pay for wireless charging in dollars. Solving for x gives us x = 10.0 / 2.0, which means x = $5. However, since the question presents options in increments of 10, the closest correct option would be $10, indicating that consumers are likely willing to pay an additional $10 for wireless charging over the lightning port. Therefore, option d) $10 is the correct answer.