Final answer:
To identify a firm's supply curve, solve the supply function for price, graph with quantity on the horizontal axis and price on the vertical axis, and use the intersection with a chosen quantity to find the supply price. Graphing is a helpful alternative for those who are not comfortable with algebra.
Step-by-step explanation:
To identify the supply curve for a firm, you can use graphing techniques. If the formula of a supply curve is given, such as S = 500 + 10Q - 0.9Q² + 0.4Q³, it represents the relationship between the quantity supplied (Q) and the supply price (P). Although the formula provided in the question seems misformatted (as it lacks P), we can infer that S corresponds to the supply price here.
First, solve the equation for P if necessary, and then graph the supply curve on a set of axes, with Q on the horizontal axis and P on the vertical axis. Pick a quantity value (Qo) and draw a vertical line up from Qo to the supply curve to find the corresponding price at which the firm is willing to supply that quantity, as illustrated in our example.
Additionally, when graphing the supply curve along with a demand curve P = 8 - 0.5Qd, where the two curves intersect, you can determine the market equilibrium where quantity supplied equals quantity demanded, and find the equilibrium price and quantity.