Do I put the author and page number in brackets and then fully MLA it in Works Citation?
Yes, if you are supposed to be using MLA citation.
What if there are more than two articles written by the same author?
Consult the MLA guide you picked up at your university bookstore, or ask Google, great god of students and people too lazy to go bookstores. I believe it involves some sort of indented list, but I can't remember off hand, and as this isn't something *I* need to know at present, I see no reason to look it up.
However, Harrison/Lipset argue that the cause of poverty in the third world are blamed on their cultures and values; tradition.
First, "the cause . . . are" violates standard subject verb agreement. And do they argue that the causes are blamed on their culture, or that they should be blamed, which is different and which sounds like what you mean?
They defined capitalism as a market in which sellers and buyers come together on a voluntary basis to exchange goods and services in return for money, at a price. Because of this, workers in developing countries were and still are getting pennies a day for their work. They were exploited.
If they were exchanging goods and services voluntarily, how were they being exploited? These two sentences contradict each other. The first would be the obvious rebuttal to the second.
In conclusion, the modernization theory is only optimistic and full of contradictions. It is important to understand the history of a situation so a more realist approach can be taken to solve it.
You haven't shown this. You have given a fairly good summary of the dependency theory, and a pretty poor one of the modernization theory. However, your inability to summarize the latter well is not a refutation of it. It is perfectly fine to come down on the side of dependency theory, but you need to explain in more detail what is wrong and contradictory with the modernization theory if you want that to work. For instance, you say that
The only problem, they say, is that their methods have not really been tried in the third world.
Can you provide evidence of a third world country that has implemented democratic capitalism (or even totalitarian capitalism) and yet that still remains a third world country? That would be a strong argument in favor of the dependency theory.