Many parts of life have gone cheaper - while feeding and clothing your family used to take a full time job, now you can buy (that level+amount) of food and clothing for just a few hours of work at minimuma wage.
However, major parts of our current expense, like housing at desirable areas, are "competitive" in that if everybody earns ten times as much then the good would also cost ten times as much.
"Housing" in the sense as shelter somewhere is very cheap to make, only "housing" in an area where you (and everyone else) would want to work and raise your kids is expensive.
"Education" in the sense of simply obtaining knowledge and information is very cheap now, only "education" in the meaning of degree=certification that you're "better than average" is expensive.
I once calculated that I literally could live in semi-abandoned areas with the 1916 level of goods&services (+ a PC and internet) for 5-10 hours of work/week even if that was at minimum wage, and remote contracting often does much better. Including paying for the home - they're dirt cheap in places that people are leaving for the expensive places. However, the trouble is that I don't really want to and can afford to "do better" - and everyone else does as well.
Yes, it seems that life has generally gotten cheaper if you don't require health care, childcare, or education. The one thing that hasn't gone down in price that everyone needs is food.
When we consider that "life has gotten cheaper" then looking at 2005-2014 is rather counterproductive, since the big changes there were before 2000; at least I was talking more on the scale of 100 years than 10 years which has rather different trends.
Also, the healthcare price increase is mostly by changing the "basket" of what we mean by "healthcare" - if we compare current healthcare with e.g. 1916 or 1966, then it's much more expensive but mostly because healthcare now includes expensive procedures for ailments that simply would not be treated back then other than painkillers to ease the death.
The true answer involves looking at the basic inputs of an economy and seeing which are being regulated heavily, and how that flows through as price increases.
Land, labour and energy are the basic inputs. You could argue capital as well. Technology is a productivity multiplier. Some things are getting cheaper - much cheaper. But other things are getting heavily regulated, which drives flow-on price increases.
The problem is those flow on increases have swamped the price reductions from automation. Technology price reductions are gradual and incremental, whereas regulation can be applied on thickly at the stroke of a pen.
Where I live, heavy regulation on land use causes shortages, which drives up the price of everything. To sell tech in a shop requires silly rent, and paying someone to mind the cash register has been regulated to be high. So while the price of a 8Gb isn stick has crashed, the shop and the employee have rocketed up.
I'd add time to that, and raw materials. Knowledge is a nonconsumable input, but education, training, and skills maintenance are also factors.
Adam Smith's Wealth of Nations has an interesting breakdown of factors contributing to wages, though he also maintains that a wage must always be sufficient to sustain not only the labourer himself (hey, this was 1776), but his wife and children, and their education so as to provide for the next generation of workers.
There are some other points I'll address directly to your parent's question.
Because technology also leads to better "things" that cost more but overall provide more value for the money.
Think of it this way: if you wanted to replicate the average life of someone who lives in the 1950's, it would be cheaper than today (I know housing kinda screws that up). No internet, a basic car without all the electronics and safety gear, no computer, smaller house, rarely flying anywhere, etc.
The trade off with improved productivity is this: you can either work less and make the same amount or you can work the same amount and make more. Most people choose the later.
It has gotten cheaper in terms of physical resources (reality), but not in terms of money.
Two of the three main goals of the money system, as stated in the Federal Reserve Act of 1913, are to maintain stable prices and maximize employment.
So, not only does technological ephemeralization run counter to these explicit goals, it also cedes power from the super administrators who dictate the money supply which ultimately determines monetary prices across the globe.
The value from all of this technology/automation is being captured by a smaller and smaller number of people. When your employer introduces technology that makes you 50% more productive, they are not going to pay you 50% more or let you work 50% less for the same pay. They're going to pocket the surplus as profit.
It mostly has, but that's hard to show. Land rents/housing , education and medical care all have been subsidized, so there is more of it ( expect land - they're not making any more of it) and it costs more.
First of: compared to when? If your baseline is, say, 1870 or 1770, life is far cheaper in terms of hours of work required to purchase basic goods. There's a long literature of basic worker incomes and expenditures, reading of which is fascinating.
If the question shifts to, say, 1950 - 2000, and your focus is the US or Western Europe (and we're considering a majority ethnicity male), I'd argue that life may or may not have gotten more expensive (though I think it has), but it's become tremendously less stable.
Lifetime employment means not having to worry about losing your current job, finding a new one, and supporting yourself and dependents in the meantime. Doing all of that on a barely-sufficient income (e.g., minimum savings), or worse, an insufficient income, becomes quite challenging.
Emma Rotshchild (yes, one of those Rothschilds), a Smith scholar, notes that his liberal philosophy isn't just philosophically liberal but materially liberal. Having income surplus to needs allows making choices. Or, as Eric Ravenscraft put it at Lifehacker: "When you’re broke, the only freedom you have is to make bad decisions."
He explains that:
Paying rent isn’t really a “good decision” so much as a responsibility. You don’t get a pat on the back for paying your rent. It’s great when you’re able to do it—you can’t always be sure you can when you’re poor—but it’s just treading water. You can’t choose to invest wisely or save for emergencies.
Putting yet another spin on this: a life in which you've optimised every decision and every action is one in which your only freedom, your only option, your only inconsistency, in any way, is something which will make your situation worse.
I can't think of a better argument for why a fully-optimised, fully-efficient life or existence would be hell.
Back to your question.
There are multiple elements of this:
1. What are market dynamics, and who has negotiating or bargaining advantage? Adam Smith notes that the upper hand lies with "masters" (employers), not labour.
2. What is price, and how does it relate to cost and value (and what's value, while we're at it) as well? To what extent are these givens, and to what extent are they fictions of market, ideology, or political strengths?
3. The Jevons Paradox. Another dilemma of efficiency is that making something more efficient is the same as reducing its cost, all else constant. Which means you'll increase demand, either individually or in aggregate. The things which have become cheaper (e.g., clothes) we now buy far more of (a closet full, rather than your work-day wear, and a suit for religious service).
4. Social signalling. Thorstein Veblen's contribution -- expensive information costs (both sending and receiving) make social signalling through appearance and consumption critical.
5. Price dynamics of wages, products, extractive materials, and rents. In particular, whilst some prices are drivers (higher-cost raw materials increase market prices), others follow general market prices (higher wages create higher rents). Unless supply of rented goods or services is fungible (e.g., Bay Area housing), well, you know what happens.
However, major parts of our current expense, like housing at desirable areas, are "competitive" in that if everybody earns ten times as much then the good would also cost ten times as much.
"Housing" in the sense as shelter somewhere is very cheap to make, only "housing" in an area where you (and everyone else) would want to work and raise your kids is expensive.
"Education" in the sense of simply obtaining knowledge and information is very cheap now, only "education" in the meaning of degree=certification that you're "better than average" is expensive.
I once calculated that I literally could live in semi-abandoned areas with the 1916 level of goods&services (+ a PC and internet) for 5-10 hours of work/week even if that was at minimum wage, and remote contracting often does much better. Including paying for the home - they're dirt cheap in places that people are leaving for the expensive places. However, the trouble is that I don't really want to and can afford to "do better" - and everyone else does as well.