Your post doesn't make any sense.
How exactly is the cost of entering the Bitcoin economy determined by the USD/BTC exchange rate? Eventually, merchants adjust prices to reflect the exchange rate, so the cost of buying a Big Mac is more or less the same, whether you pay for it in BTC, USD, EUR, or gold doesn't make any difference.
The costs of buying BTC are
a) Conversion costs - these are completely independent of exchange rate
b) Risks of your BTC losing value before you spend them - surely these are higher in an inflationary p2p currency??
How exactly would an inflationary p2p currency outcompete Bitcoin? Any sane person who has the choice to put some of their cash savings into InflaCoin or Bitcoin, will always chose Bitcoin over InflaCoin, provided the two are equal in all other respects.
On how the cost of entering the Bitcoin economy is determined by the exchange rateIn order to answer this, let's think instead of what it would cost now to adopt the gold standard. Adopting the gold standard would have a cost: There would be a requirement to back a certain amount of the money supply with gold. This would mean that the price of gold, of course, would go up, because government would have to buy gold in order to back the currency. There are about 5.3Bn ounces of mined gold (
http://en.wikipedia.org/wiki/Gold). US M2 is currently about USD9Tn (
http://en.wikipedia.org/wiki/File:Components_of_US_Money_supply.svg).
Let's say the clearing price to cover the US money supply is going to be $6k per ounce (just random numbers here). So if the US did not have any gold to begin with, they need to buy 1.5Bn ounces of gold. The economic output of the economy stays the same. Everything else stays the same, including the total assets and output of the economy, but $9Trn went to purchase gold (and the government taxed the people to get there). A massive wealth transfer just occurred from everyone else in the economy to those who originally owned that gold. Current US assets are ~$188Trn (
http://rutledgecapital.com/2009/05/24/total-assets-of-the-us-economy-188-trillion-134xgdp/). At a USD price of $1,500, those 1.5Bn ounces of gold represented 1.2% of economic assets. Suddenly, instead of having 1.2% of economic assets, the original holders of that gold have 4.8% of economic assets in USD terms. Total economic output remained the same, and yet there was a massive wealth transfer from one group to another because of the return to the gold standard.
Okay, so what was the point of that lesson? The point of that lesson is that one cost of adopting a currency (in the case above adopting a gold standard) is the wealth transfer that goes to the existing holders upon adoption. Why? Because total productive assets in the economy stayed the same and their share of those assets went up as a result of adoption.
Now, if I'm forced to adopt the gold standard because my country goes out and purchases all that gold on my behalf, transferring all that wealth to other citizens, I cannot do much about that. But if you ASKED me to voluntarily give up a few percent of my assets to other citizens merely because they held onto some shiny metal that wasn't going to produce anything and I did not actually want, there is no way I would do so.
We can think about Bitcoins in the same way. The cost of adoption for everyone is the amount of wealth that is transferred upon adoption, in terms of real productive assets, to those who participated in Bitcoin early. If I am not going to be coerced into paying that, then I must do so voluntarily. So I must believe that the value of doing so exceeds this cost. There is supposedly someone who has 340k Bitcoins or so. And yet the actual output of the economy stays the same. His spending power must have come from somewhere (someone).
So the costs of buying BTC are:
a. Conversion costs;
b. Risk of losing your purchasing power; and
c. The wealth transfer embedded in the conversion to another currency.
Those must be weighed against the benefits, which I noted before. The issue is, there is a way to get those benefits WITHOUT using BTC itself, because the only barrier to entry is the first mover advantage (acceptance of the currency). So if the third cost becomes too high, someone can just abandon the system and create a competing system with similar properties. And if that system provides all the same benefits WITHOUT the massive wealth transfer to early adopters, then people will use that instead.
How would an inflationary currency outcompete a deflationary one?To a certain extent, you answered the question yourself.
First, if you want to HOLD cash, you would rather HOLD it in a deflationary currency. But what if you want to spend it? I don't want to SPEND my deflationary cash... I can buy more goods in the future if I just hold onto that cash now! If everyone has the incentive to hoard, that leads to deflation and a decline in spending. This limits economic growth; we know this from the real world. Too much hoarding; not enough purchasing. What will it do to Bitcoins? Well, the real value of Bitcoins is not in the coin itself (it's just data), but rather in the fact that you can use them to buy real goods and services. And if you don't want to use them because you would rather hoard them, then there isn't much value to them, is there? Seems like a conundrum, but then you add competition to the mix. Someone else comes out and offers the same concept of a digital currency that is untraceable, that cannot be seized, that crosses borders, but there is no deflation! People spend their coins freely. They don't have to worry about losing out because they are not long the currency. And so everyone who wants to use an untraceable, seizure-proof, transnational currency switches to that one. And no one wants your Bitcoins anymore. And suddenly Bitcoin inflation is infinite, because there is no market for them.
Second, this new currency avoids the massive wealth transfer to early adopters (let's just say they have a solution for it; I don't know what the solution is). So there is no cost of adoption of the currency? And people will spend it freely? And I don't have to worry about speculating when holding it because prices are relatively stable? Count me in!
Third, it's tough to make loans in a deflationary currency, and as a result the money supply cannot grow through the fractional reserve process (it can theoretically, but I am saying in practice it will not). Why is it tough to make loans? Because you will only make loans that are risky enough to still require someone to pay you for lending. If the currency is appreciating relative to goods (there is deflation) of 20% per year, then someone has to be a risk of greater than 20% in order for me to charge them interest. Otherwise I'd rather just get my currency appreciation (deflation) earnings.
Price stability is not a valid goal. Prices should go down as an economy grows and goods/services become more abundant. If they didn't, and prices were artificially kept constant, then population would instead grow to match supply until some supply falters and there is no longer enough room on the petri dish for everyone. And I think you know what happens then.
Price stability, excluding changes in productivity, is a valid goal. I don't think that price stability affects population growth or total world output. Price stability, when excluding changes in productivity, is a monetary policy and currency issue.