I believe household budgets (for poverty lines or cost of college) generally allow for greater costs for additional kids in a manner that is simply additive and less than the cost of the first kid.
For some child raising budget items, you can imagine that an additional kid requires more but is much less than the first (e.g., hand me down clothes, or the additional cost of putting a second kid in the car to drive to school).
For some other expenses, I can see that an additional kid can cost the same as the first (e.g., you may get no break for having to buy two trumpets, or you may need to drive one kid to band practice and one to dance lessons on opposite sides of town).
But are there any costs or dynamics (even if psychological, stress, time from work, etc.), where adding a second child is not simply additive? I’ve heard parents say, perhaps jokingly, that the “costs” to childrearing have an interaction effect that makes adding kids a non-linear impact, but not sure if that is just an impression from the unexpected additional chaos (which might be important to consider itself!).
I had three kids in four years. Some costs, as the OP clearly states are simply additive (private school food). Some are reduced or shared (clothes, common transportation, watching the same TV, using the same computer). In my case, we have one maid an we’d still have one if we only had 1 or 2 kid or none at all.
I don’t know if this is borne out by proper research, but many of the parents I know think that medical costs are more than additive. One kid gets sick and the whole family comes down with it. Then another gets sick and the whole family gets it. So a second kid doubles the amount of medication and also doubles the number of sicknesses that the medicine is needed for.
If the second child is the same sex as the first, then there are savings in terms of hand-me-downs, sharing rooms, etc.
If they’re different sexes, keeping things separate, and providing additional privacy, may incur additional costs (over and above the normal per-child expenses), I suppose.
Sometimes (and certainly in our case), the inverse is true. When we had Kid1 (she was a ‘surprise’!), we were totally unprepared. We weren’t completely broke, but we were far from financially secure. Kid1 got a lot of stuff that was handed down from other family members, bought at yard sales and flea markets, etc. By the time Kid2 came along (she was planned), we were more secure, plus the fact that almost 4 years had passed meant that a lot of Kid1’s stuff was ‘outdated’ by safety laws; the car seat was considered no more good; ditto the crib and the playpen. So Kid2 got a lot of new stuff. By the time we had Kid3, eight years after Kid2, hubby was well-employed, and I was helping to manage our investment properties, and really, Kid3 (now 11YO) is spoiled rotten. This is not to say she has the ‘best of everything’, but she has a Wii, an mp3 player, a Netbook, and a lot of stuff our older kids only wish they’d had (though I’ll grant you a lot of this stuff simply didn’t exist when they were that age, and now, at ages 23 and 19, they’re pretty well spoiled, too!)
I think it’s often the case that Kid1 is unplanned and the parents are unprepared, and therefore they don’t get the ‘best of everything’.
As to the OP, well, hand-me-downs work for certain things. But not everything. With clothes, not only is there the gender divide, but a ‘size divide’; if you have your first kid in the summer, and second in the winter, even if they are both girls, when Kid2 is 3mo old, the clothing from when Kid1 was 3mo old will be seasonally inappropriate, etc.
And child care is a biggie. If Kid1 is 3YO, she goes to day care at a ‘pre-schooler’ rate of charge, while Kid2 is still in diapers and much more expensive. Even if the day care gives a family rate discount, the baby still in diapers is going to cost more than the pre-schooler who is potty trained.
Housing certainly is a consideration. If you have a boy first, and a 2BR house, then have a girl a few years later, you may get away with having them share a bedroom for a couple of years, but eventually, you’re going to need a bigger house or apartment. Unless you move to a less desirable neighborhood (not out of the question), you’re talking considerably more money. I know around here, it’s easy to find 2BR apartments, much more difficult (therefore more costly) to find 3BR apartments.
If you have a 3rd kid, the easy-on-gas small 4-seater car you’ve been driving for a few years will no longer be adequate. Not only will you have to lay out money on a bigger car, but it will probably use considerably more gas.
It’s a good demonstration of the marginal utility principle. If you’ve got one kid, you wouldn’t take a million dollars for it. But most people wouldn’t pay a nickle to have another one just like it.
As mentioned above, the third child can be the expensive one. A larger residence, a different auto, and by that time the hand me downs are worn out and you’re starting all over with new. Plus you’ve got to switch from the man-to-man and adopt a zone defense.
Depending on the age of the first kid, an additional kid can be significantly higher for reasons I outlined above: children (preschoolers) who are out of diapers are much less expensive than infants/newborns; a lot of this has to do with laws that dictate how many care providers must be available for the different age groups. For instance (and I’m kind of pulling these numbers out of memory from when we lived in Maryland and my two oldest were very young), for preschoolers who are potty trained, it may be acceptable to have one day care provider for every four or five children; for newborns/infants, though, you need one provider for every two children. This means that day care centers charge a lot more for infants. So, even if you get a ‘family’ discount, that discount is more than eaten up by the fact that you have a baby in day care who is not potty trained/walking.
A lot of this depends on the age-spread of the kids, too, though; my MIL had six kids, but there was 24 years between the oldest and the youngest (!!)
I asked her once if it was tough having that many kids and she said that, basically, after the first couple, they kind of raised each other.
I didn’t have quite that experience, but I have three kids, and my oldest was 12 when I had my youngest. So it was pretty easy to take them all somewhere, because the older two were old enough, say, to go to the bathroom unaccompanied, or go grab me a few extra napkins or something.
Never had to worry about this - but isn’t there also a “family rate” issue for places like Disneyworld, etc.? 2 adults and X kids, where X is either 2 or 3; so that 3rd or 4th kid will cost you more than the others…
Of course the “infant in arms” problem of having to buy an airline seat for the baby is only a problem if you have triplets…
(Usually by the time you are flying with 2 or 3, only 1 is young enough to qualify for the “infant in arms” unless you wasted no time…)
Finally - there’s the leverage effect. Whatever you give in and allow for the first child, is the starting point for wheedling from the second one. “Johnny got his bike last year. Why can’t I have one this year? Can I have a 15-speed, Johnny has a 10-speed?” You certainly won’t get away with anything less than a 10-speed.
Not good at math here, and I realize everyone’s discussing it terms the OP suggests, i.e. whether the additional child would cost more than the average cost of the previous, but wouldn’t “more than additive” mean multiplicative (or whatever the word is) or exponential?