Key Terms and Concepts
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of output [i.e., p(Q) = TR(Q) - TC(Q)]. The objective is to maximize this unconstrained objective function with respect to output. The first- and second-order conditions for a maximum are dp/dQ = 0 and d2p/dQ2 < 0, respectively. The profit-maximizing condition is to produce at an output level at which MR = MC. Although profit maximization is the most commonly assumed organizational objective, firms that are not owner operated and firms that operate in an imperfectly competitive environment often adopt an organizational strategy of total revenue maximization. The first- and second-order conditions are dTR/dQ = 0 and d2TR/dQ2 < 0, respectively. Assuming that firms are price takers in resource markets (the price of labor and capital are fixed), because price and output are always positive, it can be easily demonstrated that the output level that maximizes total revenue will always be greater than the output level that maximizes total profit. This is because the law of diminishing marginal product guarantees that the rate of increase in marginal cost will be greater than the rate of increase in marginal revenue.
KEY TERMS AND CONCEPTS Expansion path The expansion path is given by the expression MPL/PL = MPK/PK. The expansion path is the locus of points for which the isocost and isoquant curves are tangent to each other. It represents the costminimizing (profit-maximizing) combinations of capital and labor for different operating budgets. First-order condition for total profit maximization Define total economic profit as the difference between total revenue and total cost, p(Q) = TR(Q) - TC(Q), where TR(Q) represents total revenue and TC(Q) represents total cost, both of which are assumed to be functions of output. The first-order condition for profit maximization is dp/dQ = 0; that is, the first derivative of the profit function with respect to output is zero. This yields dTR/dQ - dTC/dQ = 0, which may be solved to yield MR = MC. First-order condition for total revenue maximization Define total revenue as the product of total output (Q) times the selling price of the product (P), TR(Q) = PQ. The first-order condition for profit maximization is dTR/dQ = MR = 0; that is, the first derivative of the total revenue function with respect to output is zero. Isocost curve A diagrammatic representation of the isocost equation. Solving the isocost equation for capital yields K = C/PK ¥ (PL/PK)L. If we assume a given operating budget and fixed factor prices, the isocost curve is a straight line with a vertical intercept equal to C/PK and slope of PL/PK. Isocost equation The firm’s isocost equation is C = PLL + PKK, where C represents the firm’s operating budget (total cost), L represents physical
