Key Terms and Concepts

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

units of labor input, K represents physical units of capital input,is PL is the rental price of labor (wage rate),and PK is the rental price of capital (or the interest rate).The isocost equation defines all the possible combinations of labor and capital input that firm can purchase with a given operating budget and fixed factor prices. Marginal resource cost of capital The increase in the firm’s total cost arising from an incremental increase in capital input.Sometimes referred to as the rental price of capital,the marginal resource cost of capital is the return to the owner of capital services used in the production process.

The marginal resource cost of capital is sometimes referred to as the interest rate. Marginal resource cost of labor The increase in the firm’s total cost arising from an incremental increase in labor input.Sometimes referred to as the rental price of labor,in a perfectly competitive labor market,the marginal resource cost of capital is the return to the owner of labor services used in the production process.The marginal resource cost of labor is sometimes referred to as the wage rate. Marginal revenue product of capital The product of the selling price of a good or service and the marginal product of capital.The marginal revenue product of capital is given by the expression P ¥ MPK,where P is the selling price of the product and MPK is the marginal product of capital.It is the incremental increase in a firm’s total revenues arising from the incremental increase in capital input,which results in an incremental increase in total output (the amount of labor input is constant). Marginal revenue product of labor The product of the selling price of a good or service and the marginal product of labor.The marginal revenue product of labor is given by the expression P ¥ MPL,where P is the selling price of the product and MPL is the marginal product of labor.It is the incremental increase in a firm’s total revenues arising from the incremental increase in labor input,which results in an incremental increase in total output (the amount of capital input is constant). MPL/PL = MPK/PK The expansion path.This expression represents the cost-minimizing (profit-maximizing) combinations of capital and labor for different operating budgets. MR = MC The first-order condition for profit maximization.Profit is maximized at the output level at which marginal revenue is equal to rising marginal cost. P ¥ MPL = PL To maximize profit,a firm will hire resources up to the point at which the marginal revenue product of the labor (P ¥ MPL) is equal to the marginal resource cost of labor (PL).In other words,a firm will hire additional incremental units of labor until the additional revenue generated from the sale of the extra output resulting from the application of an incremental unit of labor to the production process is precisely equal to the cost of hiring an incremental unit of labor.