Andropov's relations with Gorbachev shifted over time, just like Fyodor Kulakov's had. Since Gorbachev was not able to improve the outlook for Soviet agricultural production during his period in charge, there is some question whether continuing inability to do so would have reduced his standing with Andropov.
I'm not sure about what kinds of reforms Andropov would have initiated, but I doubt he would put liberals in positions of power, dismantle socialist institutions like the Supreme Soviet (not to mention the Party itself), or subject the entire economy to poorly thought out reforms. The extent of his political reforms probably would be just to get rid of Brezhnev holdovers and to intensify the fight against corruption, which would put more faith among the people in the Party and state leadership, end some of the worst hypocrisies and injustices, at least at the highest levels, and improve labour discipline. In the economic sphere, Andropov would be very cautious, considering elements of Hungarian goulash socialism (although that had run into problems in the early 1980s due to the international debt crisis), localized experiments -such as agricultural cooperatives, individual factory initiatives, etc., or the Chinese variant. Though the latter is the favourite among contemporary Russian analysts discussing the 'what ifs' of Andropov, I personally doubt it, on the basis of the fact that Andropov came from the same cadre of leaders who had rejected and severely criticized the Chinese economic reforms from the 1970s on. To posit my own wishful thinking 'what if', perhaps Andropov would have received more consultation on the work of Viktor Glushkov and the other cyberneticists who had sought to implement an information gathering and planning mechanism using a vast network of computers. In the 1980s there were more and more of them, and many in fact thought that Gorbachev's uskorenie was in fact the limited implementation of a Glushkov-like program (the 1986 Party Congress confirmed the need for massive computerization of the workplace).
Couple other points, related to global geopolitical trends:
1) From the early 1980s, while Brezhnev was still alive, the USSR was working to improve relations with China. Andropov continued this trend (so incidentally, did Gorbachev). The longer the USSR had survived, the more relations were likely to improve, given the technocratic and rational/stability-seeking leadership in China. Thus, the USSR could eventually build up economic relations to receive an array of cheap consumer goods made in China in exchange for durable machine building, transport, and other equipment, along with raw materials and energy supplies. Theoretically, the stronger the Soviet-Chinese economic partnership (regardless of politics, since China would doubtless seek to remain neutral), the better for global socialism overall. If this relationship began to bear fruit in the early 1990s, Gorbachev would have had even less incentive or acceptance among the conservative Party apparat to begin his reforms.
2) Whether or not the Soviets withdrew from Angola, Mozambique, and elsewhere in southern Africa, the Apartheid regime would have eventually crumbled, and in a situation where it was the result of conflict or a truly revolutionary situation, the ANC would see no reason to make a deal with the old regime as they had in existing reality. Hence, the political and economic system instituted in South Africa may have become more radically oriented toward socialism, and toward the Soviet Union, since the latter was an active supporter of the black liberation struggle while most of the West covertly supported the Apartheid regime. In this situation, a potential ally of the USSR would control the Cape of Good Hope, along with a great deal of the rare materials in the world (together with the USSR, the two countries comprised up to 80% of certain rare materials). This situation again would require merely that the USSR survive and continue to act rationally to promote close relations with the ANC, thus securing a major strategic victory in Africa and in the Cold War overall.
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EdvardK: Not nearly enough variables on the RYAN checklist had been ticked off to cause for mass alarm on the part of the Soviet leadership. Also, you'll have to take the wikipedia cited source by Andrew and Mitrokhin (a defector) with a grain of salt. If you read their two books you'll notice the degree of anti-communist bias in the book, which sometimes affects presentation of their evidence.