What are sunk costs?

This note addresses the ambiguities in contemporary treatments of sunk and fixed costs. Sunk costs of contestable market literature identify cost differences between established firms and potential entrants. Sunk costs decline through time as do fixed costs in traditional theory. However, the nature of the time periods involved differs substantively.

Like traditional fixed costs, sunk costs are a barrier to entry. Fixed costs are the would-be (not actual) costs of inputs which cannot be varied because the time period under consideration is too short for either their procurement and assimilation into production or their disposition at normal prices. However, sunk costs are revealed by a difference between the price per unit of capital services of an entrant and that of an established firm during the contract period of the output price of the entrant upon which the profitability of entry is being calculated.

Specifically, if the effective rental rate or per unit cost of capital during the contract period is greater for the entrant than for the incumbent firm, the entrant could not profitably enter. For example, if capital services are homogeneous and purchased competitively, if their costs are fixed over the contract period after entry, and if the amortization period of their costs is shorter for the entrant than for the established firm (due to late entry), then a barrier would exist which would be attributable to sunk costs [Baumol et al., "On the Theory of Contestable Markets," in J. E. Stiglitz; G. F. Mathewson, eds., New Developments in the Analysis of Market Structure, ch. 12, Cambridge, MA: MIT Press, 1986, pp. 339-65].

Let the effective rental cost of capital to the entrant, [[Rho].sub.e], be:

[[Rho].sub.e] = r[Beta] + ([Beta] - [Alpha])r[[Epsilon].sup.-r[Tau]]/(1 - [[Epsilon].sup.-r]), (1)

where: [Beta] is the price and [Alpha] is the salvage price of a unit of capital; r is the discount rate; and [Tau] is the length of the contract period. The necessary condition for an entrant to be barred from entry is:

[p.sub.e][y.sub.e] - C([y.sub.e], [[Rho].sub.e]) [less than or equal to] 0 [for every] [p.sub.e] [less than or equal to] [p.sub.i], [y.sub.e] [less than or equal to] Q([p.sub.e]), (2)

where: [P.sub.e] is the offer price for the contract period; [y.sub.e] is the output of the entrant during the period; C([y.sub.e], [[Rho].sub.e]) is the entrant's variable and sunk costs over the period; [p.sub.i] is the incumbent's posted price during the period; and Q([p.sub.e]) is the entrant's demand [Baumol et al., 1986, pp. 341-51].

If the contract period is sufficiently long, i.e., if [Tau] [approaches] [infinity], sunk costs go to zero as the contract period becomes equivalent to a traditional long run when all costs are variable. Alternatively, if the inputs in inventory can be resold at their purchase prices plus interest less depreciation, i.e., if [Beta] = [Alpha], then investment (entry) is reversible, the costs of capital inputs are variable, the rental price of capital does not represent either sunk costs or a potential barrier, and the market is perfectly contestable.

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