Maybe, my question is a little chaotic. I want a mathematical model to describe the arbitrage of a single commodity.
As I know , if I have much money, I can buy out or buy most of some commodity, such as apple. Then, the price of apple will go up. Next, I sell my apple at high price. Seemly, I can make profit by this method. But, in fact, there are some question. When I bulk sell my apple, the price will decline quickly, so, I make profit a little or loss. But if I slowly sell my apple, the new apple will be produced, the price decline too, although decline slow, but I need more time to sell my apple, as time go on, the price will return to normal, so I still make profit little.
Obviously, this process has not a clear expression by language. So, I guess there must be a mathematical model to describe this process. What is the relation of supply, demand, price, and what is the best method of arbitrage ? What paper or book I should read ?