Show that for a proit-maximizing firm producing at its optimal quantity, y, its average total cost is minimized when marginal cost is equal to average total cost. Some tips to get you started:

The equilbrium price and quantity of a good sold in a competitive market are determined by the forces of demand and supply. The equilbrium occurs at the point where the quantity demanded is equal to the quantity supplied.

A profit-maximizing firm will produce output upto the level at which the marginal revenue is equal to the marginal cost. Marginal revenue is the revenue from the sale of an additional unit of output. Marginal cost is the cost of producing one more unit of output.