Since the beginning of 2014, the price of iron ore has dropped around 20% as concern over China's slowing economy grows while output of iron ore continues to rise. However, the world's three largest publicly traded iron ore miners, BHP Billiton (NYSE:BHP), Rio Tinto (NYSE:RIO), and Vale (NYSE:VALE) aren't worried just yet.

The lowest costs around
These three mining behemoths are currently producing such vast quantities of iron ore that their cost of production per tonne is far below the key $100 per tonne level. Actually, Rio, BHP and Vale are all producing iron ore for less than $60 per tonne; with the spot price of iron ore currently sitting at $112, there is plenty of headroom for all three to keep churning out profits.

Specifically, Rio's management told investors earlier this year that the company's cash cost of production per tonne of ore was $20.80. Analysts at UBS estimate that Rio's all-in sustaining cash cost of production is $43 a tonne and that BHP's cost is slightly higher at $45 per tonne, indicating a profit margin of 150% per tonne at the current iron ore spot price. Vale's costs come in below $50 per tonne of production as well. -- with even more capacity coming online in the near future, the cost of production is expect to fall further.

Ramping up production
It's not just a low cost of production that makes BHP, Rio and Value unconcerned about falling iron ore prices, all three companies are also working hard to slash costs and drive up output, driving profit growth.

In particular, BHP's iron ore production was up 16% for the three months ending December, and the company's production of metallurgical coal used in steelmaking also hit record levels in the second half of last year. Elsewhere, the company is increasing its oil and gas production from shale oil assets within the United States; it expects these assets alone to generate $3 billion in cash annually for the company by 2020. These record production figures come at a time when BHP is slashing spending. In particular, BHP is planning on cutting capex for 2014 to only $16.1 billion, down from $22 billion in fiscal 2013.

In addition, Rio announced record production of iron ore, bauxite (used in the production of aluminum), and thermal coal during 2013. Meanwhile, the company is planning on cutting its capex spending by 20%, to only $11 billion for 2014, and then a further 20% for the year after, to only $8 billion for fiscal 2015.

Sadly, Vale has not reported similar output increases, but the company is planning on cutting capex, to $14.8 billion for 2014, the third year of declining spending for the company after reaching a high of $18 billion during 2011.

All in all, these cuts are designed to increase cash flow and, over the long term, improve shareholder returns. For example, if BHP sticks to its capital spending budget, and generates the same value of cash from operations as it did during fiscal 2013, the company's free cash flow will be in the region of $2 billion during 2014. This will be the first time that BHP will report positive free cash flow in two years. In addition, if Vale sticks to its capital expenditure forecast for 2014, the company should be set to generate nearly $2 billion in free cash flow for fiscal 2014.

Not just low costs
Aside from a low cost of production, there is another reason why these miners are in a great position to ride out the weakness in iron ore price.

You see, to combat a devastating smog currently engulfing much of China, the Chinese authorities have imposed strict emission limits on many industrial companies. This includes steel producers. As a result, there has been a rise in the demand for 'lump,' a higher quality iron ore that doesn't require sintering before being used in steel production. Sintering is essentially turning lower quality iron ore into lump, but the process is energy-intensive and a major contributor to pollution. The demand for lump has meant that the lump market has seen somewhat of a bubble recently, with prices, in comparison to standard ore, almost doubling. Further, some analysts believe that this is only the start of a bull market for lump as more sintering plants close down in China's drive to combat pollution.

Foolish summary
So in conclusion, over the last few years, BHP, Rio and Vale have been struggling with rising levels of debt and sliding commodity prices. However, as these miners cut costs and capital spending and ramp up output, the future looks bright for them despite the sliding price of iron ore.