Shutdown (economics)

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In economics, a firm will shutdown production when the revenue received from the sale of the goods or services produced cannot even cover the variable costs of production. In that situation, the firm will experience a higher loss when it produces, compared to not producing at all.

Technically, shutdown occurs if marginal revenue is below average variable cost at the profit-maximizing output. Producing anything would not generate returns significant enough to offset any fixed cost and part of the variable cost. By not producing, the firm loses only the fixed cost.

Contents

[edit] Explaining

The goal of a firm is to maximize profits or minimize losses. The firm can achieve this goal by following two rules. First, the firm should operate where MR = MC. Second, the firm should shutdown rather than operate if it can reduce losses by doing so.[1] [2]

[edit] The shutdown rule

In the short run, a firm operating at a loss [R < TC (revenue less than total cost) or P < ATC (price less than unit cost)] must decide whether to continue to operate or temporarily shutdown.[3] Conventionally stated the shutdown rule is “in the short run a firm should continue to operate if price exceeds average variable costs.”[4] Restated the rule is to produce in the short run a firm must earn sufficient revenue to cover its variable costs.[5] The rationale for the rule is straightforward. By shutting down a firm avoids all variable costs.[6] However, the firm must still pay fixed costs.[7] Because fixed cost must be paid regardless of whether a firm operates they should not be considered in deciding whether to produce or shutdown.[8]

Thus in determining whether to shut down a firm should compare total revenue to total variable costs (VC) rather than total costs (FC + VC). If the revenue the firm is receiving is greater than its total variable cost (R > VC) then the firm is covering all variable cost plus there is additional revenue (“contribution”), which can be applied to fixed costs.[9] (The size of the fixed costs is irrelevant as it is a sunk cost.[10] 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 you divide both sides of inequality TR > TVC by Q gives P > AVC). If the firms decides to operate firm will continue to produce where marginal revenue equals marginal costs because these conditions insure not only profit maximization (loss minimization) but also maximum contribution.[11]

Another way to state the rule is that a firm should compare the profits from operating to those realized if it shutdown and select the option that produces the greater profit.[12][13] A firm that is shutdown is generating zero revenue and incurring no variable costs. However the firm still incurs fixed cost.[14] So the firm’s profit equals fixed costs or (- FC).[15] 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.[16][17] The difference between revenue, R, and variable costs, VC, is the contribution to fixed costs and any contribution is better than none. Thus, if R ≥ VC then firm should operate. If R < VC the firm should shut down.

The break even point is minimum average cost.[18] The shut down point is at the minimum of the average variable cost curve.[19]

[edit] Short run Shutdown rules

  1. If price is greater than minimum average cost - produce.
  2. If price is between minimum average cost and minimum average variable cost - produce or shut down.
  3. If price is less than minimum average variable cost for all levels of production - shut down.[20]

What if price equals minimum average variable cost? The firm would be indifferent. Economists adopted a tie-breaker - produce.

[edit] Sunk costs

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 price is between minimum average costs and minimum ANSC produce, and if price is less than minimum ANFC for all levels of production, shut down.[21] If all fixed costs are non-sunk, then (a competitive) firm would shut down if the price were below average total costs.[22]

[edit] Long-run consequences

A decision to shut down means that the firm is temporarily suspending production.[23] It does not mean that the firm is going out of business (exiting the industry).[24] If market conditions improve, prices increase or production costs fall, the firm can resume production. Shutting down is a short-run decision.[25] A firm that has shut down is not producing. The firm still retains its capital assets; however, the firm cannot leave the industry or avoid its fixed costs in the short run. Exit is a long-term decision. A firm that has exited an industry has avoided all commitments and freed all capital for use in more profitable enterprises.[26] A firm that exits an industry earns no revenue but it incurs no cost fixed or variable. The firm has zero revenue and no costs.[27]

However, a firm cannot continue to incur losses indefinitely. In the long run, the firm will have to decide whether to continue in business or to leave the industry and pursue profits elsewhere. The long-run decision is based on the relationship of the price and long-run average costs.[28] If P ≥ AC then the firm will not exit the industry. If P < AC, then the firm will exit the industry. These comparisons will be made after the firm has made the necessary and feasible long-term adjustments.[29] In the long run a firm operates where marginal revenue equals long-run marginal costs.[30] Thus the firm's long run supply curve is the long run marginal cost curve above the minimum long run average cost curve.[31]

[edit] Long Run Exit Rule

Exit if

  • TR < TC
  • P < AC[32]

Conversely a firm will enter the market in the long run if P > AC.[33]

[edit] Example

Assume that a firm has fixed costs of $20,000, variable costs of 45,000 and revenue of 35,000.[34] The firm is operating at a loss since total costs exceed total revenue. Nonetheless a manager may be tempted to continue to produce because he is earning sufficient revenue to pay his fixed costs and a portion of his variable costs. However, the proper course is to shut down. The shutdown loss is 20,000 while the operating loss is 30,000. The shutdown decision is a short-run decision. A firm that has shut down must decide whether to remain in the industry or exit the industry and seek profits elsewhere. The firm in the example will leave the industry unless it can reduce variable costs or increase revenue. Note that the level of fixed costs is irrelevant to the shutdown decision. If fixed costs were to be reduced to 10,000, the firm would still shut down because variable costs exceed revenue.

[edit] Monopolist Shutdown Rule

A monopolist should shut down when price is less than average variable cost for every output level;[35] in other words, where the demand curve is entirely below the average variable cost curve.[36] Under these circumstances at the profit maximum level of output (MR = MC) average revenue would be lower than average variable costs and the monopolists would be better off shutting down in the short run.[37] The shutdown rule can also be stated as the monopolist should shut down if average revenue is less than average variable costs at all levels of production.[38]

[edit] Calculating the shutdown point

The short run shutdown point is the minimum of the average variable cost curve. Assume that firms total cost function is TC = Q3 -5Q2 +60Q +125. Variable cost = Q3 -5Q2 +60Q Average variable costs = (Q3 -5Q2 +60Q)/Q= Q2 -5Q + 60

  • AVC' = 2Q - 5
  • AVC' = 0
  • 2Q - 5 = 0
  • 2Q = 5
  • Q = 2.5

[edit] Universal shutdown rule

The firm shuts down "only if its revenue is less than its avoidable costs."[39]

[edit] Notes

  1. ^ Perloff, J. (2009) p.231.
  2. ^ Lovell (2004) p.243.
  3. ^ Revenue, R, equals price, P, times quantity, Q.
  4. ^ Samuelson, W & Marks, S (2003) p. 227.
  5. ^ Melvin & Boyes, (2002) p. 222.
  6. ^ Pindyck, R & Rubinfeld, D:(2001) p.259.
  7. ^ Pindyck, R & Rubinfeld, D: (2001) p.259.
  8. ^ This version of the rule implicitly assumes that the firm has incurred sunk costs which are being amortized and treated as fixed costs. Or that fixed costs equal sunk costs. This assumption does not always hold. Sunk costs may have been incurred and paid for or the cost of fixed inputs may be partially recoverable through sale and salvage. If all fixed are recoverable then the firm should shut down if price drops below average total costs rather than average variable costs.Pindyck, R & Rubinfeld, D: (2001)
  9. ^ Samuelson, W & Marks, S (2003) p. 296.
  10. ^ Perloff, J. (2009) p.237.
  11. ^ Samuelson, W & Marks, S (2006) p.286.
  12. ^ Png, I: 1999. p. 102
  13. ^ Landsburg, S (2002) p.193.
  14. ^ Bade and Parkin, pp. 353-54.
  15. ^ Landsburg, S (2002) p.193
  16. ^ Png, I: (1999) p.102.
  17. ^ Landsburg, S (2002) p.194
  18. ^ Krugman & Wells: p. 342
  19. ^ Krugman & Wells: p. 342
  20. ^ Frank, R and Bernanke, B (2007) p.175..
  21. ^ Besanko and Braeutigam (2002) p. 310.
  22. ^ Pindyck, R & Rubinfeld, D (2001) p. 260.
  23. ^ Mnakiw, (2007) 296.
  24. ^ Landsburg, S (2002) p.193.
  25. ^ Landsburg, S 2002.p.193.
  26. ^ Landsburg, S (2002).
  27. ^ Mankiw, N Principles of Microeconomics 4th ed. (Thomson 2007) p 298.
  28. ^ In the long run there is no distinction between average variable and average costs because all costs are variable. Landsburg, S (2002) p.167
  29. ^ As Boyes notes the long run options of a firm are not limited to exiting or remaining in the industry - the firm can " expand, contract, relocate, enter a new business, exit any line of business or quit doing business altogether."Boyes, W. (2004) p. 105.
  30. ^ Perloff, J:2008 page 266.
  31. ^ Landsburg, S (2002) p. 230.
  32. ^ Mankiw (2007) 298.
  33. ^ Mankiw (2007) 298.
  34. ^ Binger & Hoffman, (1998) 313-314.
  35. ^ Frank, R., (2008) Mc-Graw-Hill
  36. ^ Frank, R., (2008)
  37. ^ Frank, R., (2008) (Mc-Graw-Hill)
  38. ^ Frank (2008) p. 387.
  39. ^ Perloff p. 252.

[edit] See also

[edit] References

  1. Bade, R and M. Parkin, 2009 Foundations of Microeconomics 4th ed. Pearson
  2. Besanko, D. & Beautigam, R 2005, Microeconomics 2nd ed. Wiley.
  3. Boyes, W. 2004 The New Managerial Economics, Houghton Mifflin
  4. Frank, R., Microeconomics and Behavior 7th ed. (Mc-Graw-Hill) ISBN 978-007-126349-8.
  5. Frank, R and Bernanke, B Principles of Microeconomics 3rd ed. (2007) McGraw-Hill.
  6. Krugman, P and R, Wells 2009 Microeconomics 2d ed. Worth
  7. Landsburg, S 2002 Price Theory & Applications, 5th ed. South-Western.
  8. Mankiw, N 2007 Principles of Microeconomics 4th ed. Thomson.
  9. Melvin & Boyes, 2002 Microeconomics 5th ed. Houghton Mifflin.
  10. Perloff, J. 2009 Microeconomics 5th ed. Pearson. ISBN 0321584391
  11. Perloff, J: 2008 Microeconomics Theory & Applications with Calculus Pearson. ISBN 0321277945
  12. Pindyck, R & Rubinfeld, D: 2001 Microeconomics 5th ed. Prentice-Hall. ISBN 0130196738
  13. Png, I: 1999 Managerial Economics page 102 Blackwell. ISBN 1557869278
  14. Samuelson, W & Marks, S 2003 Managerial Economics 4th ed. Wiley. ISBN 0470000449
  15. Samuelson, W & Marks, S 2006 Managerial Economics 5th ed. Wiley. ISBN 047166362X

[edit] Further reading

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