I've had a few years of economics courses already but still there are some basic things in the field that I just can not wrap my head around... (let's say economics is not my favorite field of study)
The problem that I'm having is about an algebraic representation of a demand curve in a perfectly competitive market.
Say that there is a set of N suppliers (with |N| possible tending towards infinity, hence a perfectly competitive market; let's just assume free entrance to the market too), consider a supplier i. The market demand function in terms of the output of supplier i can now be written as:
Here what is in the curly brackets is just the total market output. Now here's my problem, if you take the derivative of this function wrt. q_i, then you find that this derivative equals beta. However, I've also heard that the derivative of market demand with respect to a firm's output, in a perfectly competitive environment, is 0; as in perfect competition, a firm cannot control the price through its output this effect is very very small because of the many other suppliers.
Where in my reasoning did I go wrong?