Industry Total Cost Functions and the Status of the Core

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The industry total cost function gives the least total cost to an industry of producing a prescribed total output. For standard demand schedules where price and quantity vary inversely, a nonempty core requires nondecreasing returns to scale. Because a nonempty core is necessary for a neoclassical competitive equilibrium, this means an industry can be in a competitive equilibrium only if it has nondecreasing returns to scale. Thus industries in which the firms have identical U-shaped average cost (Viner industries) or flat-bottomed average cost do not satisfy this condition so they cannot have a competitive equilibrium for arbitrary standard demand schedules.