Suppose there is a number of identical firms producing diamonds. Let the total cost function for each firm be given by $C(q, w)$, where q is the firm’s output level and w is the wage rate of diamond cutters.
I'm supposed to solve for a firm's (short-run) supply curve, given a wage rate $w$, and the industry's (total) supply curve).
I'm very confused with the relationship between the cost function and the supply curve. For part a this question, I get the marginal cost from taking the derivative of the cost function -- is the marginal cost also the supply curve? We know the cost function of the firm, but how can I arrive at the industry's supply curve?