I can't answer your question on the economic rationale but I can touch some of the politcal reasons.

We actually just talked about this in my U.S. in the 1970s course. Basically to understand why the U.S initially opened relations with China you need to take a look at China's relationship with the USSR at the time and how Nixon and his staff viewed this from the outside. Since 1956 the Soviets and Chinese had diverged on their ideologocal views of Marxism and in 1961, Mao denounces the Soviet version of communism, diplomatic relations fall apart, and a border conflict in 1969. Now think of how this diplomatic deterioration of the two biggest communist countries in the world looks to Nixon. Looks like a good oppurtunity to reopen relations with the most populace communist country in the world and gain some political pull on the Soviets, "the enemy of my enemy is my friend." As well Nixon would be looking into working out an agreement over the issue of Vietnam (unsuccessfully). I hope this somewhat helps you out I'll try to provide sources in the morning. I know there is no way I covered everything but most likely someone will come around and provide all the information your looking for.

Edit: Sources: lecture notes (not sure if these are credible enough but it's where i got the bulk of my info, if they aren't let me know), Chambers Dictionary of World History, B.P. Lenman, T. Anderson editors, Chambers: Edinburgh:2000. p. 769.

This policy was put forward by Henry Kissinger, in one of his best examples of realpolitik, by addressing foreign policy through a practical standpoint rather than an ideological one. At the time, our greatest geopolitical enemy was the Soviet Union. China's relationship with the Soviets was bad, to put it lightly. The Sino-Soviet split occurred in 1961 with Mao denouncing the Soviets as not being sufficiently communist, and Khrushchev responded by withdrawing Soviet scientists and technicians from China, resulting in the cancellation of multiple projects.

Kissinger proposed an anti-Soviet alliance with China, and they accepted, resulting in trade. Cuba and North Korea were strictly under the Soviet realm of control, and so we were opposed. That is not to say that we were opposed to better relations. Kissinger also led an easing of relations with the Soviets, better known as detente. This was accomplished by strategic arms treaties. I can only assume that trade would have opened up between the Soviets and America, but we never got to that point.

The use of realpolitik during this era also explains why the US supported various authoritarian regimes, regardless of political ideology.