# One-time consumer equipment purchase vs ongoing monthly service fees: which is better?

## Question:

What area of economics addresses questions about the price of a one-time consumer equipment purchase vs ongoing monthly service fees? For example, to analyze when it makes sense to purchase an upgraded smartphone for its greater capacity/utility, considering fixed ongoing cellular service costs. Or when it makes sense to upgrade your home wifi system to provide greater coverage and speed, given fixed monthly internet service costs.

I am assuming you have to keep the cell or wifi plan and you are just upgrading the fixed cost of a new router or cell phone. Let’s take the smartphone/cellular plan case.

Suppose you currently pay \$100 per month for your cellular plan and the cost of your current phone was \$500 when you bought it.  The fact you bought this phone+plan means it was worth it to you when you entered into the contract, right?  So, how much was it worth it to you? Well, ask what else could you have done with the money if you had stayed on a landline?

Could you have invested your money somewhere else each month?  A savings account might get you 1% per year and stocks (until March 2020!!) might have given you, say, 6% per year.  Let’s say you could put the money somewhere in between, say at 3% per year or 3%/12 = 0.25% per month.

OK, then that original plan (whether you thought about it at the time or not) was giving you an implied benefit of at least \$101.25 per month? How do I know this?

Assume you had it in your mind to pay the \$100/month forever (it makes the calculation simpler). In that case, the price of the phone+plan should have been no more (to you) than the price tag on the phone (\$500) plus the monthly costs at the opportunity cost of 3% per year, and the benefits would be the stream of monthly benefits also at that opportunity cost. The cost to you was \$500+\$100/(0.0025) and the benefit per month was \$B/(0.0025).

The benefit has to be greater or equal to the cost.  Setting the benefit equal to the cost and solving for B, gives B=\$101.25 per month.  Likely you feel your benefit of cell phone service is much higher than this, but this is the lowest benefit you revealed you would accept when you bought the original contract.

Suppose the new phone is \$1,000.  Then assuming the \$100/month service plan hasn’t changed, \$1000=(B-\$100)/0.0025 or B=\$102.50. If the new phone is worth more to you than \$102.50 per month then you should buy it.

In terms of revealed benefits, the difference between your current phone and your new phone is the difference in these benefits AT LEAST \$1.25 per month.  If the new gadgets on the new phone are at least worth this much, then it is worth it to you. Notice, like most deals that come with monthly service or financing plans, the upfront cost is not where the big difference lies.  You still have to shell out \$100 per month so you need to compare your benefits mostly against that price. The phone price being double is in the long run fairly insignificant when you think about it compared to a difference of only \$1.25 a month.

But wouldn’t everyone find a difference of \$1.25/month worth it?  Clearly not if some people don’t upgrade. I have the same cell phone I bought in 2012 despite my teenager’s chagrin that I don’t have enough memory on it to use tik-tok or snapchat. Some folks’ costs are other folks’ benefits.