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Equilibria Under Negligence Liability

How the Standard Claims Fall Apart
  • Allan Feldman and Ram Singh EMAIL logo
Published/Copyright: April 12, 2021
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Review of Law & Economics
From the journal Review of Law & Economics Volume 17 Issue 1

Abstract

In many accident contexts, the expected accident harm depends on observable as well as unobservable dimensions of the precaution exercised by the parties involved. The observable dimensions are commonly referred to as the ‘care’ levels and the unobservable aspects as the ‘activity’ levels. In a seminal contribution, Shavell, S (1980). Strict liability versus negligence. J. Leg. Stud. 9: 1–25 extended the scope of the economic analysis of liability rules by providing a model that allows for the care as well as activity level choices. Subsequent works have used and extended Shavell’s model to predict outcomes under various liability rules, and also to compare their efficiency properties. These works make several claims about the existence and efficiency of equilibria under different liability rules, without providing any formal proof. In this paper, we re-examine the prevalent claims in the literature using the standard model itself. Contrary to these prevalent claims, we show that the standard negligence liability rules do not induce equilibrium for all of the accident contexts admissible under the model. Under the standard model, even the ‘no-fault’ rules can fail to induce a Nash equilibrium. In the absence of an equilibrium, it is not plausible to make a claim about the efficiency of a rule per-se or vis-a-vis other rules. We show that even with commonly used utility functions that meet all of the requirements of the standard model, the social welfare function may not have a maximum. In many other situations fully compatible with the standard model, a maximum of the social welfare function is not discoverable by the first order conditions. Under the standard model, even individually optimum choices might not exist. We analyze the underlying problems with the standard model and offer some insights for future research on this subject.

Keywords: observable and non-observable care; activity levels; negligence liability; no-fault liability; second best; nash equilibrium; accident loss; first best
JEL Classification: K1; K12; K13; K41
Corresponding author: Ram Singh, Department of Economics, Delhi School of Economics, University of Delhi, Delhi, India, E-mail:

Acknowledgment

We are extremely thankful to the Editor and four anonymous referees for very helpful comments and suggestions on an earlier version of this paper. We thank Satish Jain and Hans-Bernd Schäfer for valuable feedback on this work. Drupad Nair provided excellent research support. Institutional support by the Centre for Development Economics, Delhi School of Economics and the University of Delhi are gratefully acknowledged. We are responsible for any errors.

Appendix (Tables)

Tables 1–3.

Table 1:

Based on class C3.

Function parametersFOC solutionNSB(.) at FOC solutionFirst best solutionNSB(.) at first best
δ = 0.10.056070.3306824.963702.50358
0.337190
D = 500.056075.13773 × 10−5
0.3371934.32330
δ = 0.010.058290.340972499.9625.0004
0.353630
D = 500.058295.0141 × 10−7
0.35363352.551
δ = 0.0010.058520.342022.50000 × 1052.50000 × 102
0.355290
D = 500.058525.00141 × 10−9
0.355293.53453 × 103
δ = 0.000010.058550.342132.5 × 1092.50000 × 104
0.355470
D = 500.058555.00002 × 10−13
0.355473.53553 × 105
δ = 0.10.004980.0954224.996502.50035
1.995040
D = 50000.004985.01346 × 10−7
1.995043.52528 × 102
δ = 0.0010.005050.096412.50000 × 1052.50000 × 102
2.012050
D = 50000.005055.00014 × 10−11
2.012053.53543 × 105
δ = 0.000010.005050.096422.49994 × 1092.50000 × 104
2.012220
D = 50000.005059.07487 × 10−15
2.012223.54363 × 106

  1. Columns 2 and 4 give solutions to the maximization problem in the order s, x, t, y from top to bottom.

Table 2:

Based on class C4.

Function parametersFOC solutionNSB(.) at FOC solutionFirst best solutionNSB(.) at first best
δ = 20.051110.086911.000031.0
0.299260
D = 500.051110
0.299260
δ = 50.226430.864432.500086.25
1.182380
D = 500.226430
1.182380
δ = 80.500003.000004.0000316.0
2.000000
D = 500.500000
2.000000
δ = 100.094500.667485.0000425.0
2.937000
D = 5000.094500
2.937000
δ = 150.202542.120257.5000656.25
4.531640
D = 5000.202540
4.531640
δ = 200.348584.8449310.0001100.0
6.100950
D = 5000.348580
6.100950

  1. Columns 2 and 4 give solutions to the maximization problem in the order s, x, t, y from top to bottom.

Table 3:

Based on class C5.

Function parametersFOC solutionNSB(.) at FOC solutionFirst best solutionNSB(.) at first best
δ = 10.035790.240230.122760.25786
0.168940
D = 500.035790.00989
0.168941.47753
δ = 20.023730.181610.027490.18176
0.044590
D = 500.023730.02099
0.044590.17242
δ = 10.026610.208570.135260.24375
0.315610
D = 1000.026610.00456
0.315612.67777
δ = 20.018730.163730.033080.16609
0.184320
D = 1000.018730.01124
0.184320.81889
δ = 10.012930.147280.149740.22558
0.771210
D = 5000.012930.00083
0.771217.65261
δ = 50.005160.080280.006370.08060
0.302920
D = 5000.005160.00431
0.302920.78401

  1. Columns 2 and 4 give solutions to the maximization problem in the order s, x, t, y from top to bottom.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/rle-2020-0049).

Received: 2020-09-10
Revised: 2021-02-12
Accepted: 2021-03-12
Published Online: 2021-04-12

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Articles
  3. Equilibria Under Negligence Liability
  4. Does an Inclusive Citizenship Law Promote Economic Development?
  5. The Effects of Enforcement on Corporate Environmental Performance: The Role of Perceived Fairness
  6. Economic Analysis of Accident Law: A New Liability Rule that Induces Socially Optimal Behaviour in Case of Limited Information
  7. To Settle or to Fight to the End? Case-level Determinants of Early Settlement of Investor-State Disputes
  8. The (Mixed) Effects of Minimum Asset Requirements When There is a Possibility of Technological Change
  9. The Effect of Constitutional Commitment to Social Security on Social Expenditure Schemes
  10. Case Note
  11. Who Bears an Employee’s Special Annual Payment?
  12. A Note on the Article by Mark Ramseyer, published in RLE 2020
https://doi.org/10.1515/rle-2020-0049
Keywords for this article
observable and non-observable care; activity levels; negligence liability; no-fault liability; second best; nash equilibrium; accident loss; first best

Articles in the same Issue

  1. Frontmatter
  2. Articles
  3. Equilibria Under Negligence Liability
  4. Does an Inclusive Citizenship Law Promote Economic Development?
  5. The Effects of Enforcement on Corporate Environmental Performance: The Role of Perceived Fairness
  6. Economic Analysis of Accident Law: A New Liability Rule that Induces Socially Optimal Behaviour in Case of Limited Information
  7. To Settle or to Fight to the End? Case-level Determinants of Early Settlement of Investor-State Disputes
  8. The (Mixed) Effects of Minimum Asset Requirements When There is a Possibility of Technological Change
  9. The Effect of Constitutional Commitment to Social Security on Social Expenditure Schemes
  10. Case Note
  11. Who Bears an Employee’s Special Annual Payment?
  12. A Note on the Article by Mark Ramseyer, published in RLE 2020
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