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Category: Microeconomics

Sunk Costs

Sunk Costs are costs that were incurred in the past.  One basic principle of economics is that sunk costs are irrelevant to decision making.  Since economics is a social science and, as such, aimed at explaining what actually happens, it is argued that sunk costs don’t influence the “supply” or “demand” and so do not influence prices and quantities in the market.    From the point of view of managerial economics, the emphasis is on explaining to managers that it makes no sense to worry about sunk costs since it will not influence the profitability.

Think of the old sayings like “it’s water under the bridge,” or “let bygones be bygones.”  Sacrifices already made have already been made, and so what was sacrificed is irrelevant to deciding what to do now.

For example, suppose a business spent $10 million on a machine.  It will last 5 years and produce 1000 units per year.  Suppose materials and labor needed to produce each unit cost $3000.   If the cost of the machine is divided over the 5000 units of output it helps produce, that is a cost of $2000 per unit.  Given the cost of the materials and labor, that comes out to be $5000 per unit.  Naturally, one should consider this figure in pricing the product.  Right?  Wrong.  The $2000 per unit attributed to the cost of the machine is a sunk cost and irrelevant.   It is something to consider when deciding whether or not to purchase the machine.  And once the machine is purchased, it does influence the ability of the firm to produce output.  But the amount that was paid for the machine is a sunk cost and irrelevant to deciding how much to produce and how much to charge.

Another example regards purchasing stocks.  Suppose one purchased stock for $30,000.  Its price has fallen to $25,000.  It is a mistake to sell the stock because that would impose a loss of $5000.  Right?  Wrong.  The amount paid for the stock is irrelevant.  All that is relevant is the likely future changes in the price of the stock.  Holding onto the stock may be sensible if the price is going to rise.  Holding on to the stock if the price is likely to fall doesn’t make sense.

Opportunity Costs

Another way of making the point about sunk costs is that only opportunity costs matter.  When one is deciding to buy a machine, the $10 million must be given up and that involves the sacrifice of alternative purchases.  That is an opportunity cost and that matters.  After the $10 million has been spent, then that is no longer an opportunity cost.  It is a sunk cost.  An opportunity cost would be the resale value of the machine.  Suppose you could sell it for $4 million.  Then the cost of using the machine is $4 million, not the $10 million that had been paid.

Another interesting consideration regarding opportunity costs is that one should always consider the opportunity costs of inputs provided by owners.  Firms typically purchase inputs like labor and materials.  They also finance some of their capital purchases, and have interest costs as well as the depreciation of the capital goods.  These expenditures of funds are quite naturally described as costs.  But the owners of firms often provide some inputs themselves.  Almost always, some of the investment funds are provided in this manner–equity.   The amount that could have been earned by the owners in other employments is the opportunity cost of the funds.  For a sole proprietor, this might be possible to determine.  In the situations of corporations or partnerships, it becomes quite complex since different owners might have done different things with the funds.  Still, even in that situation, some interest rate should be applied to those funds to determine the opportunity cost and that amount needs to be added to all the explicit expenses to determine the total cost of production.

In some small firms, especially in the past, the owner would contribute labor to production without paying himself or herself a salary.  It is probably best to pay a salary based on the opportunity cost of the owner’s labor.  But if that isn’t done, the opportunity cost of the owner’s labor should be counted as part of the cost of producing the product.

marginal product or marginal physical product is the extra output produced by one more unit of an input (for instance, the difference in output when a firm’s labour is increased from five to six units).

Assuming that no other inputs to production change, the marginal product of a given input X can be expressed as

\mathrm{MP} =  \frac{\Delta \mathrm{Y}}{\Delta \mathrm{X}}

where ΔX is the change in a firm’s production inputs and ΔY is the change in quantity of production output.

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