Presume that a firm has its policies determined by a manager whose objective function is to maximize sales, i.e. revenues, without letting profit drop below some fixed level, m. Let R(y,a) denote firm's revenue when the level of production is y and the advertising level is a. Let C(y) denote cost of manufacturing y units of output and p is the per unit price of advertising. We assume dC/dy>0, dR/da>0.
1. Setup constrained optimization problem of the firm. a can be positive or 0.
2. Derive the first order conditions that maximize the firm's objective considering that a can be positive or 0. Assume now that a>0. Derive 2nd order conditions that ensure max profit.
3. Will the output chosen by the firm be equal to, less than or greater than output chosen under profit max?