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A significant number of Video Cards (significant investment) are required to reduce the possibility of 51% attacks. What would happen to the price of a Bitcoin if the prices of Video Cards suddenly plummeted, or (easier to imagine) their capacity quickly increase 20-fold.

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If hardware cost or efficiency rises, the new mining power will enter the network, and the difficulty will rise, keeping the rate of bitcoin production stable - this is one of the key design elements of bitcoin. So, arguably nothing should happen to the price of bitcoins due to cheaper/better mining hardware.

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Price comes from ratio of supply and demand. Bitcoin supply rate doesn't change, about 300 bitcoin per hour. So the price changes only when demand changes, and the difficulty to mine bitcoins adjusts to the new price, in another words price change would affect network difficulty, but not the other way around. Therefore video card price would affect difficulty, but it wouldn't change bitcoin market price.

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Price drives difficulty and not the other way around (or at least not as much). The price/performance of hardware affects difficulty so you can't predict the Bitcoin price based on the cost to run the Bitcoin network.
For example, during the last 6 months the Bitcoin price fell 90% while the hardware costs remained exactly the same.

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The change of price in Bitcoins would probably be temporary. Once the difficulty would adjust itself and coins would be generated slower. After that, the market would probably go back to normal levels, after people would figure out that the cost of electricity are bigger than the worth of Bitcoins. It is pretty much what is happening right now.

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Because of difficulty adjustments price wouldn't be affected. Regardless of how much hashing power the network has the number of coins produced will remain relatively static. More efficient (in terms of $/MH and MH/W) video cards will drive up hashing power of the network.

The performance per watt will likely be more important than performance per dollar as purchased video cards are a sunk cost however they need to compete in an ongoing basis against newer more efficient cards in power consumption.

A video card with half the power consumption for the same performance (MH/s) will have a lower cost of production. This means it can be profitable at a higher ratio of difficulty:price. If a sufficient portion of the network is using more efficient hardware we would expect the difficulty relative to price to rise. This will eventually force out users with inefficient hardware. We have already seen that in the demise of CPU mining.

Eventually this will be seen with the rise of FPGA mining. FPGA don't need to achieve a price parity with GPU (and likely never will) but as their price becomes more competitive, more will be adopted and that will increase the efficiency of the network significantly. The ratio between difficult : price will rise accordingly.

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