This question is asking us "what causes authoritarian to institute democratic reforms?"
Prephrase: The answer is found in the first paragraph. It talks about how they recognize that changes in society necessitate democratic reforms by authoritarian rulers. Their motivation is out of necessity and not any commitment to higher ideals.
(A) "if the health of a nation requires it." They are not undertaking reforms for the health of the nation, but because they are required to undertake reforms because of changing societal forces.
(B) "offer the greatest amount of personal freedoms to citizens." This answer choice is similar to A. Once again the authoritarian ruler is motivated for selfish reasons, and not out of a concern for the citizens of the country.
(C) "speed the transition from authoritarian rule to democracy." They are not looking to speed up the transition. They are just instituting democratic reforms, because their hand is being forced by changes in society.
(D) "ensure the long term health of the nations economy." This is not mentioned at all in the passage. Remember it is purely because they are forced to undertake changes as a result of societal changes.
(E) This is what we want. Check out lines 1-7 and 56-60 for more information on the support for this answer.