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On learning and the economics of firm efficiency: a state-contingent approach

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Abstract

The paper investigates the microeconomics of learning for an owner-managed firm. The analysis relies on a general state-contingent approach to uncertainty. In the presence of price and production uncertainty, it examines the case where acquiring information is costly. It evaluates the microeconomic efficiency of decisions, with a focus on three factors: sure income, the value of information, and a risk premium (measuring the implicit cost of private risk bearing). The analysis stresses the role of information and learning in microeconomic decisions. Implications for efficiency and productivity measurements are discussed.

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Notes

  1. As an example, consider the event that a gamma ray burst will hit the earth within the next 10 years.

  2. Our focus on an owner-managed firm will simplify our analysis by avoiding two sets of issues: risk redistribution issues that would arise when ownership and control become separate; and asymmetric information issues in the presence of multiple agents.

  3. In our notation, “·” denotes the inner product, with \( {\mathbf{p}}_{\text{x1}} \cdot {\mathbf{x}}_{1} \equiv \sum\nolimits_{i = 1}^{\text{n}} {{\text{p}}_{{{\text{xi}}1}} {\text{x}}_{\text{i1}} } . \)

  4. Note that the analysis presented below could be easily extended to include labor-leisure allocation.

  5. As noted by Chambers and Quiggin (2000, p. 80–83), the state-contingent approach includes as special cases the expected utility (EU) model, rank-dependent expected utility (Quiggin 1982), prospect theory (Kaheman and Tversky 1979), and general smooth preferences (Machina 1982).

  6. How individuals process information is complex. While neuroscience is making significant progress on this issue (e.g., Camerer et al. 2005), developing a scientific understanding of how the brain processes information and makes decisions remains a very challenging task.

  7. Note that the maximization of utility in (5) does imply that period-one decisions x 1 are chosen in a way consistent with profit maximization: \( {\text{Max}}_{{{\mathbf{x}}_{1} }} \) {p x1 · x 1: (x 1, \( \widetilde{{\mathbf{x}}}_{ 2} \)) ∈ Z(P)}. But under incomplete risk markets and risk aversion (5) does not imply profit maximization with respect to period-two decisions \( \widetilde{{\mathbf{x}}}_{ 2} \).

  8. It is also conditional on the consumption decision c1, which is treated implicitly throughout the paper.

  9. Note that, for P ∈ P f, Eq. (8) and (11) imply that EE(x 1, \( {\tilde{\mathbf{x}}}_{ 2} \) c, P) = EEc(x 1, P), where \( {\tilde{\mathbf{x}}}_{ 2} \) c is the solution to (10). This shows that the two efficiency measures EE(x, P) and EEc(x 1, P) become identical when period-two decisions \( {\tilde{\mathbf{x}}}_{ 2} \) are efficient.

  10. As noted in footnote 8, our analysis is conditional on the consumption decision c1, meaning that v(w, x 1, P, \( {\tilde{\mathbf{q}}}_{\text{x2}} \)) in (12) is also implicitly a function of c1.

  11. As noted in the introduction, the role and value of information have been explored under the expected utility model (e.g., LaValle 1978; Athey 2000; Athey and Levin 2000; Chambers and Quiggin 2007). Our state-contingent analysis applies under broader conditions. This includes situations where probability assessments are not obtainable and/or where perfect information is not feasible.

  12. In situations where the agent has a subjective probability assessment of price uncertainty, this measure can be taken to be the expected discounted prices of x 2, \( \overline{{\mathbf{q}}}_{\text{x2}} \) ≡ \( \sum\nolimits_{s = 1}^{S} {} \)Pr(s) q x2(s), with Pr(s) denoting the subjective probability of facing state s. In this context, our approach is consistent with standard approaches found in the literature (e.g., Arrow 1965; Pratt 1964). However, as noted above, our state-contingent analysis applies under broader conditions.

  13. See Coelli et al. (1998) and Kumbhakar and Lovell (2000) for an overview of this literature.

  14. First, consider the case where the reference bundle g is defined such that inputs in g are zero and outputs are equal to the period-one outputs. Then, with a focus on period-one outputs, Shephard’s output distance function is obtained as 1/(1 + D(x, P)) (Shephard 1970; Färe and Grosskopf 2000). Second, consider the case where the reference bundle g is defined such that outputs in g are zero and inputs are equal to the period-one inputs. Then, with a focus on period-one inputs, Shephard’s input distance function is obtained as 1/(1 − D(x, P)) (Shephard 1970; Chambers et al. 1996). And Farrell’s measure of technical efficiency is obtained as (1 − D(x, P)) (Farrell 1957).

  15. Typically, econometric identification is achieved by assuming a symmetric distribution for measurement errors but a skewed distribution for technical inefficiency (see Aigner et al. (1977) and Kumbhakar and Lovell (2000)). For example, technical inefficiency would be underidentified if the inefficiency term and the measurement error term are both normally distributed.

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Acknowledgments

I would like to thank Brad Barham and two anonymous reviewers for useful feedback on an earlier version of this paper.

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  1. Department of Agricultural and Applied Economics, Taylor Hall, University of Wisconsin, Madison, WI, 53706, USA

    Jean-Paul Chavas

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Chavas, JP. On learning and the economics of firm efficiency: a state-contingent approach. J Prod Anal 38, 53–62 (2012). https://doi.org/10.1007/s11123-012-0268-0

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