What would be the cost of keeping BTC - USD exchange rate < 200 ?!

[NewLiberty]

With a constant influx of 10M per month (or really any number), and which is staying in BTC, no amount of money in the world is enough to keep the price below 200 (or another number).

Proof: with a constant influx of 10M/month a price of 200 is reached sooner or later. Then to keep the price down you need to buy at 200+x and sell at a loss for 200, losing x*50000 each month. x will be rising, because less and less sellers are available. Remember all the previous buyers stay in BTC, so supply is shrinking. x will skyrocket and likely cause bankruptcy of anyone trying this, but sooner or later you run out of sellers due to the limited amount of BTC even with infinite funds. As a hypothetical upper limit after 21000000*200/10000000/12 = 35 years there are no BTC left for you to buy and resell.

Not quite.

Not all transfers occur on exchanges (almost none of mine for example, as I primarily use bitcoin in commerce rather than as investment).
If one were only to buy (or trade to acquire) off exchange and only to sell on the exchange, this depresses the exchange pricing.  Additionally a large mining concern that sells all it mines and only sells via exchanges, can depress pricing (and also keep the cost to depress the price down if they are using the exchange price to set the price).

The point being, the answer is not knowable mathematically in the way you describe without accounting for all the off-exchange transactions.  

It does not matter where you buy. You will run out of people who can sell to you eventually, because there is a limited amount of bitcoin in existence. You can never* buy and resell more than this amount, regardless how high your subsidy.

*) Assuming rational people do not sell to you for less than they bought from you. If they sell to you for  equal or more than 200/ your proposed net influx is not maintainable.

Only if you assume that the exchange currency is failing, AND/OR that there is no bitcoin being used for commerce. 

When a transaction in bitcoin occurs, the price used is typically the price at the largest exchange, or a blended average based on volume.  These transactions are off-exchange but are based on the exchange price.  If the recipient of those coins then transfers the coins to the exchange and places a market sell order, the price falls to the bid price until it is filled.  This then lowers the exchange price for the next transaction that occurs in the economy.

The definitive math would only work if all transactions occur on the exchanges and bitcoin is never used as currency.

For an example.  I sell my silver for bitcoin, if I were to sell all the bitcoin I get on the exchanges the price falls.  If the buyer of those bitcoins uses them to buy my silver, and I again sell the bitcoin on the exchange, the price falls again.  This can happen a thousand times a month and even if 10M enter the exchange that month, the price can still fall.

For what its worth, I don't sell bitcoin on exchanges... 

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[Cyberdyne]

With a constant influx of 10M per month (or really any number), and which is staying in BTC, no amount of money in the world is enough to keep the price below 200 (or another number).

Proof: with a constant influx of 10M/month a price of 200 is reached sooner or later. Then to keep the price down you need to buy at 200+x and sell at a loss for 200, losing x*50000 each month. x will be rising, because less and less sellers are available. Remember all the previous buyers stay in BTC, so supply is shrinking. x will skyrocket and likely cause bankruptcy of anyone trying this, but sooner or later you run out of sellers due to the limited amount of BTC even with infinite funds. As a hypothetical upper limit after 21000000*200/10000000/12 = 35 years there are no BTC left for you to buy and resell.

Not quite.

Not all transfers occur on exchanges (almost none of mine for example, as I primarily use bitcoin in commerce rather than as investment).
If one were only to buy (or trade to acquire) off exchange and only to sell on the exchange, this depresses the exchange pricing.  Additionally a large mining concern that sells all it mines and only sells via exchanges, can depress pricing (and also keep the cost to depress the price down if they are using the exchange price to set the price).

The point being, the answer is not knowable mathematically in the way you describe without accounting for all the off-exchange transactions. 

It does not matter where you buy. You will run out of people who can sell to you eventually, because there is a limited amount of bitcoin in existence. You can never* buy and resell more than this amount, regardless how high your subsidy.

*) Assuming rational people do not sell to you for less than they bought from you. If they sell to you for  equal or more than 200/ your proposed net influx is not maintainable.

You'd have to also assume that the bitcoins being sold are *real* and not just un-backed entries in some fraudster's database.

[coinft]

It does not matter where you buy. You will run out of people who can sell to you eventually, because there is a limited amount of bitcoin in existence. You can never* buy and resell more than this amount, regardless how high your subsidy.

*) Assuming rational people do not sell to you for less than they bought from you. If they sell to you for  equal or more than 200/ your proposed net influx is not maintainable.

Only if you assume that the exchange currency is failing, AND/OR that there is no bitcoin being used for commerce. 

When a transaction in bitcoin occurs, the price used is typically the price at the largest exchange, or a blended average based on volume.  These transactions are off-exchange but are based on the exchange price.  If the recipient of those coins then transfers the coins to the exchange and places a market sell order, the price falls to the bid price until it is filled.  This then lowers the exchange price for the next transaction that occurs in the economy.

The definitive math would only work if all transactions occur on the exchanges and bitcoin is never used as currency.

For an example.  I sell my silver for bitcoin, if I were to sell all the bitcoin I get on the exchanges the price falls.  If the buyer of those bitcoins uses them to buy my silver, and I again sell the bitcoin on the exchange, the price falls again.  This can happen a thousand times a month and even if 10M enter the exchange that month, the price can still fall.

For what its worth, I don't sell bitcoin on exchanges... 

In your example you are trading silver and bitcoins back and forth, but there is no net money inflow since your buys and sells cancel out, so it does not match your proposed situation of 10M inflow.

The OP posits a 10M inflow on exchanges, and does not speak of any money outflow on or off exchanges. A constant 10M net inflow cannot be satisfied forever with by selling a limited resource at a constant price regardless of your subsidy.

If you meant your question to mean 10M enter exchanges but an arbitrary amount can leave by arbitrary means, having an undefined net change, then your question is very much ill specified and has no answer, and we are just wasting time.