Apple
Users of the products of Apple tend to suffer from high maintenance costs. Therefore, Apple introduced a new product, Apple care, a kind of warranty for Apple’s hardware device. Let me explain using the example of my personal experience; I bought an iPhone12 pro at the OPS of £1299. I believe there is a probability that my phone may suffer from damages in the future and the repairing price for the screen is £266. For other damage such as batteries, the customers are likely to be charged a repairing fee of about £526. Therefore, purchasing Apple care becomes an excellent solution for iPhone users to hedge the risk of high repairing fees.
To decide whether buying the warranty is a rational choice, I need to understand how Apple care works. Briefly, Apple care for an iPhone12 pro in the UK cost £199 and can provide me with a two-year repairing service for the screen and other damage, only charging a small number of fees, which can get ignored following model. The first question was what the £199 stands for, as Apple care contains various services from screen repairing to Apple expert supporting. In my view, the £199 is the combination of premium warranty fee for different accidents that might happen. The only service I’m concerned about is the repairing service for screens or other damages. Therefore I’ll split the £199 into two parts, α199 for the premium of screen repairing only, and β199 for the premium of repairing other damage, and we assume the £199 warranty premium meet the independence assumption, and we have α+β=1.
Then, we let stand for the probability of the iPhone staying in excellent and perfect condition. No accident happens, representing the iPhone’s probability of suffering from screen broken only and for the iPhone suffering from other damages. Assuming the ordinal endowment wealth for me is the OSP for iPhone12 pro without Apple care, and I may pay for repairing the damages at a different price, my wealth suffering from screen broken should be; and my wealth suffering from other injury is. With the Apple care warranty service, screen and further damage will be repaired free of charge. Therefore, we can apply Apple care as full insurance, and the expected value for the iPhone with Apple care under all state of nature is =900.
As I recognize myself as risk-averse, I assume my utility function is that if I choose not to buy Apple care service, my expected utility could be. The expected utility for me purchasing the warranty could be. Let us have.
Let’s look back to the wealth of purchasing the warranty:
. As is the premium insurance for screen broken, we have, and in the same way, we have, and we knew that we could calculate the slope of the budget constraint =,=. For, we can calculate the marginal utility, and the warranty is full insurance, therefore if the loss occurs, then the marginal utility of an extra income needs to be equal to the marginal utility of an additional dollar of income if the loss doesn’t occur(Intermediate Microeconomics with Calculus, Hal R. Varian), therefore. As we assume that the insurance market is a fair market, under the standard tangency condition we have, we have, in a similar way, by combining the equation and ，we can get an approximate value for and, that is. Then we can have the cost. We need to understand what does represent under the fair market condition, where Apple can gain zero economic profit as it is not the specific probability for a particular individual but the expected probability for all customers. Therefore, I need to compare my probability for the different independent states of nature and become a critical value for me to decide whether to buy the warranty if I always take good care of my phone. There is a small probability of my phone suffering from damage. That is, my probability of no accidents is more significant than. I would not purchase the warranty, vice versa.
I have to admit the model still has some defects, as Apple care covers a lot more service, such as experts supporting. Therefore, which means, ，therefore, our simplification of the actual situation resulted in the inaccuracy values and may affect my judgment. I’m also concerned that high-tech products like iPhones have a significant depreciation rate, but this can be recognized as a positive affine transformation if we consider it a straight-line depreciation, therefore it would not affect our accuracy model.
I chose the example of Apple care, for I’ve been hesitating recently whether to buy the insurance for my phone and by solving the model, I find it could be a rational choice not to buy it. I recognize this as a good model because the insurance does change the probability distribution (Intermediate Microeconomics with Calculus, Hal R. Varian). And the warranty like Apple care is more complicated than the insurance we learned in our module, as it is the sum of all premium insurance of various kinds of damage. Therefore, to price the warranty like Apple care at the fair price, Apple should estimate the expected probability of all customers under a different state of nature, and then compare the probability with the insurance rate where, the fair price for the warranty could be the sum of all warranty premium, that is. To analyze whether it’s a wise option to buy the warranty, I can compare my probability for the different states with the expected probability for all consumers to make up my decision. Or I can reach my expected utility value for buying Apple care with the other situation, which would be a much easier way.
Appendix:
① in the insurance terms and conditions, screen repairing, and other damage, can not share the Apple care service of repairing at the same time. We assume that they are independent events.
https://www.apple.com/legal/sales-support/applecare/applecareplus/uk/
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