New currencies that supply similar features to Bitcoins can increase the effective supply to the extent the coins are interchangeable in the market. Even if the other coin is worth, say, one tenth as much as a Bitcoin, ten of that coin can still be used as a market substitute for one Bitcoin.

Depending on the currency's properties, however, it can also increase the demand for Bitcoins, which can drive the price up. If it brings in new users, new merchants, or even new speculative interest, that can be an upward force.

But I think your question about competition, following the question about market price, just assumes that higher prices are good for currencies. I have to disagree with this for several reasons. First, Bitcoin is still in the early stages. It needs to be adopted as a means of exchange to survive long term. Increase in prices can discourage adoption because high prices can increase the fear of a "bubble burst" leading to a sudden drop. Currency risk drives down adoption.

The value of a Bitcoin can be a good measure of adoption because use as a means of exchange drives up demand which drives up price. But the converse doesn't follow. The absolute price of Bitcoin has no effect on its suitability for use as a means of exchange. If it's worth half as much, you just use twice as much.

The currency in a country changes hands (the velocity) about 4 times per year (1%/day) and this gives the value of the currency. The only way a new currency can (partially) replace another currency is by being better in some sense (e. g. lower transaction costs, backed by a proof-of-work protocol, more resistant to malicious attacks). If this happens the old currency will depreciate in value until the two currencies together change hands 4 times/year with the depreciation factor being dependent on the velocity of each currency which depends on market factors (e. g. BTC is used for drugs, USD is used for taxes). However a new currency has to be much better than the incumbent to even have a chance to succeed. BTC is much better than USD in many respects and thus has a good chance to take market share from the fiat currencies.

Bitcoin is a spec in USD's ocean.

Litecoin is a tiny fraction of Bitcoin's pond.

Bitcoin promises non-reversible transactions. This promise is backed by 30 Thash/s of SHA hashing capacity.

Litecoin claims to promise non-reversible transactions. That promise is backed by a variable number of MHash/s of Scrypt hashing capacity. That capacity can be matched by an attacker with less than $1 million USD. There are many millions of USDs worth of GPUs looking for a new home. These may come to Litecoin's benefit or they may be the demise of Litecoins. Who knows. But Litecoin is not Bitcoin Lite.