Derive first order conditions that maximize firms objective

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Reference no: EM13687281

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?

Reference no: EM13687281

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