Using commars in long sentences

Hi all,

I am having trouble knowing in which instances I should use a comma.

For example, have I correctly used a comma in the two sentences below? In the first I have separated a phrase describing the noun; in the second I have separated bits of quite a long sentence. If I have done this correctly, which "rule" have I followed? I would like to know so I can continue to do this correctly in future. If I have not done this correctly, how could I construct the sentence in a better way? Thank you.

(1) Clearly cabinet, the core body of Ministers making high-level policy decisions, is the centrepiece of the executive.

(2) This approach implies that whenever the government decides to abdicate control in relation to some service, thinking that it would be adequately supplied in the market domain, all those responsible for providing the service have different responsibilities.