It's amazing that with water shortages and the arid climate, farming is still a very important part of the American Southwest economy. That being said, it is not the most important part.
Industry has grown exponentially since World War II, and many huge corporate monoliths call the American Southwest home.
Tourism is a big thing in this area, as there are abundant natural wonders all over the region. Oh, and Las Vegas pumps up those tourism numbers as well. Don't forget about New Mexico; Santa Fe and Old Town Albuquerque have a great cultural feel to it. There is a great homage paid to Native Americans, the Albuquerque Balloon Festival is the largest in the country. White Sands National Monument is a very cool tourist attraction.
While mining is not as big as it used to be, over 70 percent of copper is mined in the American Southwest.