<P> Generally, a firm must have revenue R ≥ TC, total costs, in order to avoid losses . However, in the short run, all fixed costs are sunk costs . Netting out fixed costs, a firm then faces the requirement that R ≥ VC, variable costs, in order to continue operating . Thus, a firm will find it more profitable to operate so long as the market price p ≥ AVC, average variable cost . Conventionally stated the shutdown rule is: "in the short run a firm should continue to operate if price exceeds average variable costs ." Restated, the rule is that to produce in the short run a firm must earn sufficient revenue to cover its variable costs . The rationale for the rule is straightforward . By shutting down a firm avoids all variable costs . However, the firm must still pay fixed costs . Because fixed cost must be paid regardless of whether a firm operates they should not be considered in deciding whether to produce or shut down . </P> <P> Thus in determining whether to shut down a firm should compare total revenue to total variable costs (VC) rather than total costs (FC (fixed costs) + VC). If the revenue the firm is receiving is greater than its variable cost (R> VC) then the firm is covering all variable cost plus there is additional revenue which partially or entirely offsets fixed costs . (The size of the fixed costs is irrelevant as it is a sunk cost . The same consideration is used whether fixed costs are one dollar or one million dollars .) On the other hand if VC> R then the firm is not even covering its production costs and it should immediately shut down . The rule is conventionally stated in terms of price (average revenue) and average variable costs . The rules are equivalent--if one divides both sides of inequality TR> VC (total revenue exceeds variable costs) by the output quantity Q one obtains P> AVC (price exceeds average variable cost)). If the firm decides to operate it will produce where marginal revenue equals marginal costs because these conditions insure profit maximization (or equivalently, when profit is negative, loss minimization). </P> <P> Another way to state the rule is that a firm should compare the profits from operating to those realized if it shut down, and select the option that produces the greater profit (positive or negative). A firm that is shut down is generating zero revenue and incurring no variable costs . However the firm still incurs fixed cost . So the firm's profit equals the negative of fixed costs or (- FC). An operating firm is generating revenue, incurring variable costs and paying fixed costs . The operating firm's profit is R - VC - FC . The firm should continue to operate if R - VC - FC ≥ - FC which simplified is R ≥ VC . The difference between revenue, R, and variable costs, VC, is the contribution toward offsetting fixed costs, and any positive contribution is better than none . Thus, if R ≥ VC then the firm should operate . If R <VC the firm should shut down . </P> <P> An implicit assumption of the above rules is that all fixed costs are sunk costs . When some costs are sunk and some are not sunk, total fixed costs (TFC) equal sunk fixed costs (SFC) plus non-sunk fixed costs (NSFC) or TFC = SFC + NSFC . When some fixed costs are non-sunk, the shutdown rule must be modified . As Besanko notes, to illustrate the new rule it is necessary to define a new cost curve, the average non-sunk cost curve, or ANSC . The ANSC equals the average variable costs plus the average non-sunk fixed cost or ANSC = AVC + ANFC . The new rule then becomes: if the price is greater than the minimum average costs, produce; if the price is between minimum average costs and minimum ANSC produce, and if the price is less than minimum ANSC for all levels of production, shut down . If all fixed costs are non-sunk, then (a competitive) firm would shut down if the price were below average total costs . </P>

When will a profit-maximizing firm shut down in the short run