Most mining companies are highly diversified, but Antofagasta and Kazakhmys are pretty much single-country, single commodity miners.Both companies mine for copper, Antofagasta in Chile, Kazakhmys in Kazakhstan. As such, investors in these firms are pretty much betting that prices for the red metal will continue rising. Both companies also send large amounts of copper to Europe. In the half year to 30 June, of Antofagasta's £3bn in revenues, some $630m came from shipments to the continent, while Kazakhmys, which sends copper by rail to the Russian ports of St Petersburg on the Baltic and Novorossiysk on the Black Sea, made $746m from sales to Europe (from continuing operations).But Kazakhmys's fortunes are more closely tied to continuing economic growth in its eastern neighbour China, which accounted for $844m of revenues. Antofagasta, whose biggest customer is Japan, made only $476m from sales to China. Of course, the world copper price is largely dictated by the rise of China no matter who the customer. But transportation costs are also an issue, so if China really is destined to become the world's biggest economy, Kazakhstan's geographical position is a decided advantage. China recently lent Kazakhmys £1bn - apparently on very generous terms - to develop mines near the border between the two countries.Perhaps a more significant difference between the two companies is the amount it costs them to pull the copper out of the ground. Antofagasta said cash costs totalled $1.06 a pound during the first half (with the copper price averaging $426.3 a pound) against $0.93 for Kazakhmys. That said, Antofagasta estimates costs will come in at $1.10 for the year, while Kazakhmys maintains a previous estimate of between $1 and $1.30 a pound.The costs both companies report include "by-product" credits. Their mines also contain large amounts of gold and the amount they earn from sales of the precious metal is subtracted from the total mining costs. If there is a global downturn and a fall in copper prices, Antofagasta and Kazakhmys will be partly sheltered if gold prices stay strong.Antofagasta's latest big copper project Esperanza is also a large gold producer and as production grows, the company will be further shielded against copper price fluctuations.Kazakhmys is also looking to expand. The Bozshakol project is expected to come into production in 2015.An interesting difference between the two companies is the political climate in their home countries. Post-Pinochet Chile is a democracy. Kazakhstan has been ruled by the same president, Nursultan Nazarbayev, since it became independent in 1991.In its interim results last year, Kazakhmys unveiled a $130m charge for "major social projects." The company is building the space age Presidential Library, presumably in honour of Mr Nazarbayev, in Kazakhstan's capital Astana.No such charges appeared in this year's interim results, but "social costs", which include investment in sports, educational and health facilities, rose to $69m from $45m. Investors may wonder whether they will have to cough up for another "major social project" once the library is built next year. What the Chinese giveth Kazakhmys, the Kazakh government taketh away.This difference between Kazakhstan and Chile may help to explain why on a price-to-earnings basis Kazakhmys's shares are considerably cheaper than Antofagasta's.