Let's say a company which does not pay dividend's has a positive shareholder's equity of $100,000.

What benefit do the shareholder's here have if they are not receiving dividend's? Furthermore, lets say the company does really well in 2008 and the total shareholder's equity is now $200,000. What has changed for shareholder's in this situation.

How does this relate to retained earnings?
How does this relate to the value/price of stock if this is a publicly traded company, and how would it relate to the value of the company if it was a private company?

Sorry if these are basic/trivial.

using my basic understanding, a shareholder could sell his share at x% * $100,000

now the amount he would receive by selling has doubled, x% * $100,000

retained earnings are the amount of profit the company keeps in savings. e.g. it had made $100,000 profit and kept it all, so the equity went up from $100,000 to $200,000.

if it had paid a dividend of $20,000, the retained earnings would only be $80,000. so shareholder equity would only be $180,000.

i do not study share prices, but i assume the share price increase doubles as the shareholders now own the worth of net assets. however, future expectations etc are built into the share price.

it wouldnt matter if it was a private company i believe, that only matters for who can own, tax reasons etc.

i may be completely wrong with the above though, i just saw accounting question and felt obliged to answer!

Ultimately the shareholders are the owners of a company, with the outstanding shares representing a claim on the shareholders' equity (net of assets less liabilities).

Because the company had a good year, shareholders will realize that their shares are intrinsically more valuable then they were the year prior, as will be reflected in the trading price. Assuming no more shares were issued during the current year, one would expect the share price to increase commensurately with the increase in shareholders' equity.

To further answer your question, retained earnings will be the account that reflects the increase in equity, as the net income from the current year will flow through to this account at year end. Although no dividends are issued in your example, they would be subtracted from retained earnings (the company is paying out some of the equity) if they were.

To reiterate, for a publicly traded stock, the shareholder benefits by being able to command a higher price for his shares. If it were a private company, then the owners would have more assets (such as cash) which they directly own (and could pay out in dividends to themselves should they so desire).