B)
There are various reasons why Stalin and not Trotsky emerged as Lenin's successor. Firstly were Stalin's sly tactics, and his determination. Stalin took a boring yet powerful job within the Bolshevik party, so that he could basically remove his opponents and add his supporters. Also he publicly idolised Lenin, and tried at every opportunity to appear close to him. He doctored photographs to make him and Lenin appear together, and he would always speak of leading a 'Leninist' way. He was the chief mourner at Lenin's funeral also. Stalin had told Trotsky the wrong date for Lenin's funeral, and being in the south of Russia, Trotsky believed he couldn't get back for the funeral in time, and so he missed it. Although it was not his fault, it looked to many people that he couldn't be bothered, and he didn't honour Lenin. Stalin constantly posed as a more moderate calming influence against the wild excesses of Trotsky. He chose the policies that would get him plenty of supporters, and turned the opposition against each other. He cunningly built up his base of supporters, which was not something Trotsky was trying to do.
Lenin's testament had stated that he didn't think that Stalin would use the power with sufficient caution. When it was read out, Stalin went pale, but he was saved by Zinoviev, who said that Lenin had been very ill in his final days.
Trotsky underestimated Stalin hugely. He did not think that Stalin would possibly become party leader, and he concentrated on his other opponents such as Kamanev. Trotsky was also arrogant and often offended senior party members. People were worried that Trotsky would lead Russia into more bitter wars, and would cause more suffering. Trotsky wanted to make the whole world communist, and to take over industrial nations to make Russia more industrialised. Another major blow to Trotsky is that at the time he shouldn't have been most active, when Lenin was dying in 1923, he had fallen ill, and so was not very involved with party affairs. The final straw was that Trotsky resigned as Commissar for War, to which no one really knows why.
In the end Stalin's image as Lenin's disciple and his more moderate policies gained him more supporters than the eccentric Trotsky. Stalin one by one manipulated his possible opponents and removed them. Trotsky was too careless and arrogant, and underestimated Stalin.
C)
The purges and show trials caused a huge amount of fear from the Russian people. The purges started in 1928, when some engineers were accused of sabotaged. Following this many show trials took place, and anyone suspected of being even slightly anti communist would be arrested, and many were killed. This caused people to even turn in their own families, and no one would dare speak out against Stalin. This reign of fear made sure that people tried to be as communist as possible, and everyone would pretend they were strong Stalin supporters. Many innocents were killed just to enforce this fear, and everyone lost someone they knew in the purges.
The secret police, called the Cheka, would arrest anyone who was seen as a threat to Stalin. This would include political activists, and people who did not share the Communist point of view. By the Cheka any plots against Stalin could be caught, and he could maintain his totalatarianist position as dictator of Russia.
By propaganda he made it seem that Russia was extremely successful. The ordinary Russian people bizarrely seemed to love Stalin. They seemed to think that Russia was very successful, and would deny Stalin's evils. Propaganda would be supporting communist policies, and criticising his opponents. This changed the way that people thought, and so more people would support his cause. The cult of personality was where everyone loved Stalin, and believed him to be a great leader. They had virtually been brainwashed by propaganda, and no one ever spoke against Stalin because they feared him. If everyone loves him, it isn't going to be hard to maintain power.
Stalin's economic policies did help him to keep control to a certain extent. He was not too firm about his thoughts on the economic policies. He used them as an argument against his opponents, and used them as an excuse for removing them. He changed his policy when he wanted an argument against other opponents, and successfully eliminated most opposition within the party. The economic policies he was choosing were pretty mild, and so it would not be strongly opposed.
Overall I think they are not equally as important. I believe that the economic policies were not as effective as the others, as they were not solid, didn't guarantee support and kept changing. I think however that the propaganda, cult of personality, purges and show trials were the most important factors that helped him to maintain control, because it caused fear, yet at the same time they admired him and loved him for what he had done for Russia. The Cheka were also a major factor, however they weren't as feared as the purges.
Without any one of these factors however, it would have been difficult for Stalin to gain and maintain control.