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Professor Sir James Mirrlees was born in Scotland in 1936 and educated at Edinburgh University and Trinity College, Cambridge. He held academic posts at Trinity College and at Nuffield College, Oxford, and was awarded the Nobel Prize in economics in 1996 for his work on optimal income taxation and its extension to information and incentive problems in general. Mirrlees also made important contributions to growth theory, development economics and public economics.

Growth and Development

The initial work of Mirrlees focused upon technical progress in models of economic growth. Kaldor and Mirrlees (1962) assumed technical progress was embodied in new investment with the growth rate of productivity per worker operating on new machines an increasing concave function of the growth rate of investment per worker. The incorporation of externalities between different firms’ investment decisions made this paper a precursor of the literature on endogenous growth theory. The problem of optimal growth in an economy subject to deterministic technical change was discussed in Mirrlees (1967). An extension to stochastic diffusion in continuous time showing that increased uncertainty would often lead to more saving rather than less was given in Mirrlees’s Ph.D. dissertation and circulated in unpublished work (Mirrlees 1965). These themes were also addressed in Mirrlees (1974a).

Mirrlees contributed to development economics via the influential Little and Mirrlees (1968, 1974) handbook of project appraisal (‘the manual’). The manual was a practical guide to the use of cost–benefit analysis designed to contribute to improvements in the economic conditions of developing countries. It took as its starting point the use of shadow prices to value all inputs and outputs, regardless of whether they were marketable or non-marketable, and showed how shadow prices should be determined. In particular, it emphasized the use of border prices to value inputs and outputs when the project was located in a small country. When goods were not traded, it provided methods for valuing them based on the prices of traded goods. The manual emphasized that investment finance was scarce because of the government’s budget constraint, so social profits should be discounted at the internal rate of return for the marginal investment project. The manual also studied constraints upon policy choices and how these affected shadow prices.

The recommendations of the manual provided a simple but powerful methodology. Since its publication they have been subjected to much theoretical scrutiny that has generally confirmed their validity. The practical impact of the Little–Mirrlees approach can be judged from the number of donor agencies that adopted it to guide their decisions. Foremost among these was the World Bank, where cost–benefit analysis was the dominant decision-making method throughout the 1970s. Its use has steadily declined since, which is attributed by Little and Mirrlees (1994) to the changing nature of lending and the internal institutional structure of the World Bank.

Income Taxation

In a seminal paper Mirrlees (1971, p. 175) studied ‘what principles should govern an optimum income tax; what such a tax schedule would look like; and what degree of inequality would remain once it was established’. Addressing this question required a model that included a motive for the redistribution of income because of endogenously generated inequality, incentive effects in labour supply and a justification for using an income tax rather than lump-sum taxation. The success of Mirlees’s model was that it managed to capture all this but remained tractable and allowed the optimum tax to be characterized. No better model of income taxation has yet been proposed, although new results are still being discovered within the original framework and its specializations – see, for example, Diamond (1998), Saez (2001) and Hashimzade and Myles (2007).

The paper demonstrated that an optimum income tax leads to an allocation in which pre-tax income is increasing with ability, and that the marginal tax rate is between zero and one. Furthermore, unemployment is possible at the optimum and, when it occurs, is of the lowest-ability workers. The numerical analysis provides some of the most surprising findings. The optimal marginal rate of tax is low, at least compared with the rates applied in many countries at the time the paper was written. Furthermore, the marginal tax rate is fairly constant, so the tax function is close to being linear. These results motivated Mirlees’s observation (1971, p. 207) that ‘I had expected the rigorous analysis of income-taxation in the utilitarian manner to provide an argument for high tax rates. It has not done so.’

The analysis of the model required Mirrlees to formulate and solve a series of novel theoretical problems. In doing so he developed a series of techniques that have since become standard tools of economic analysis. In the income tax problem the government must offer the workers a budget constraint along which each chooses an optimal location through utility maximization. Since the budget constraint can be nonlinear it is possible for there to be multiple optimal choices for a worker, so choice cannot be represented by a demand function. The fundamental contribution of the paper was to show how this problem could be circumvented by viewing the government as selecting an allocation (an income–consumption pair) for each worker. If every worker prefers his allocation to that of any other, then each will willingly select the allocation intended for him. This is the notion of incentive compatibility: a worker of ability level s must find that the allocation designed for someone of this ability gives at least as much utility as the allocation designed for any other ability s’. The government then conducts its optimization over the set of incentive-compatible allocations. The imposition of incentive compatibility reduces the set of feasible allocations and is responsible for the second-best nature of the optimum tax.

The paper also showed that the problem can be reduced further if workers’ preferences over allocations are consistently related to ability. The restriction upon preferences introduced in Mirrlees (1971) has since become known as the single-crossing condition and implies that at every point in income–consumption space the indifference curve of a high-ability worker is flatter than that of a low-ability worker. Under single crossing, incentive compatibility requires high-ability workers to earn higher incomes and enjoy higher levels of consumption. The single-crossing condition has since found countless applications in problems involving the design of contracts for populations with agents of differing characteristics. With a continuum of consumers, it is not practical to state the incentive compatibility constraints directly. Mirlees (1971) surmounted this problem in a simple but ingenious way by showing that incentive compatibility is equivalent to utility being maximized at a worker’s true skill level. The first-order condition for this optimization generates a differential equation that determines the evolution of utility as a function of ability. The differential equation can be used as a constraint on the optimization. This technique has since become known as the first-order approach to ‘maximization subject to maximization’. The first-order condition is necessary but not sufficient, so there exists the possibility that the tax function arising from the optimization analysis may violate the monotonicity requirement. A direct solution to this problem is to incorporate the second-order condition into the optimization (see Ebert 1992). The 1971 income tax paper appreciated this issue, and the limitations of the first-order approach remained an issue that was addressed further in Mirlees’s later work on the principal–agent problem.

That the optimum involved monotonicity implied an important observation: those with higher skills earn and consume more, so, although the government cannot directly observe skill, in equilibrium it can infer skill from income. Hence, given the optimum tax function, the announcement by a consumer of an income level is just a proxy for the direct announcement of a level of skill. This observation was later formalized in the revelation principle (Dasgupta et al. 1979; Myerson 1979) that shows it is possible to replace the income tax with an equivalent direct mechanism in which each consumer announces a skill level and, furthermore, announcing the true skill level is a dominant strategy. The revelation principle is now applied routinely in the analysis of incentive problems.

Commodity Taxation

Diamond and Mirrlees (1971a, b) revolutionized the theory of commodity taxation. The papers clarify the separation between consumer and producer prices and show that the choice of untaxed commodity is just a normalization that plays no role in determining the optimum allocation. They were among the first to employ the emerging duality methods and used the indirect utility function to phrase the problem in terms of the after-tax consumer prices that were the natural choice variables. As well as these innovations, the commodity taxation papers contain two fundamental results. The first is the simple rule of thumb that the imposition of an optimum commodity tax system requires an equal proportionate reduction in compensated demand for all commodities. This conclusion emphasizes that the real effect of a tax system is on consumers’ demands and that the effect on prices is of secondary importance. The second result, now known as the production efficiency lemma, is more surprising and of significant practical value for policy.

The production efficiency lemma states that the optimum commodity tax system results in an equilibrium that is on the frontier of the production set. There are some limitations to this result, most notably non-constant returns to scale, which imply that achieving efficiency may require some firms to be shut down, thus adversely affecting their owners’ incomes. Such restrictions are clarified in Mirrlees (1972). The policy value of the lemma follows from observing that efficiency is only possible if there are no distortions in the input prices faced by producers. Input taxes should not therefore be a feature of the optimum set of commodity taxes, implying that intermediate goods should not be taxed. This observation justifies the use of value-added taxation with tax rebates available for producers who purchase intermediate goods. It also suggests that capital held by firms should not be subject to taxation, though dividends paid to consumers can and probably should be, along with their realized capital gains.

Theoretically, the production efficiency lemma is especially surprising when contrasted with the conclusions of Lipsey and Lancaster’s (1956) second-best theory. The central message of Lipsey and Lancaster was that a distortion in any sector of the economy should generally be offset by introducing distortions in all other sectors. This finding had achieved great prominence at the time the Diamond–Mirrlees article was published. In contrast, the lemma states that, even when distortionary taxes and subsidies are being introduced into consumer decisions in order to redistribute real income or to finance public goods, there is no reason to distort producer decisions. This special case runs counter to the general message of Lipsey–Lancaster.

Principal–Agent

The third area to which Mirrlees made a fundamental contribution is the principal–agent problem that arises when one party wishes another to undertake an act on his or her behalf. If the act undertaken cannot be observed directly and its consequences observed only with some random error, then moral hazard can occur: the agent can attempt to hide behind the randomness to take an action which is less costly to the agent but which yields a lower expected return to the principal. Such a problem can arise in any economic relationship based on contingent contracts, for example between the owner and the manager of a firm. Mirrlees (1974b, 1975) analysed the problem facing the principal in designing a contract that provides an incentive to the agent to take the action that yields the highest expected payoff to the principal. There are considerable analytical similarities between the design of this contract and the choice of an optimum income tax. These similarities arise because the principal is choosing the contract to maximize expected payoff subject to the agent choosing an action to maximize his or her payoff. This leads again to a situation of maximization subject to maximization and its analysis via incentive compatibility.

When the agent must choose from a finite set of actions the incentive compatibility constraints can be employed directly. This is impractical for the continuous case where there would be an uncountable infinity of constraints. Consequently, it again becomes necessary to use the first-order conditions for the agent’s choice problem as a constraint on the optimization of the principal. Although this had been used prior to Mirrlees’s analysis of the principal–agent problem (Zeckhauser 1970), it had not been noticed that the approach might fail to generate the optimum. This possibility was made very clear in Mirrlees (1975), which provided an example where the first-order approach failed to generate the optimum and proceeded to discuss how the problem could be overcome. The method proposed identified the possible maxima and incorporated them as constraints into the optimization. This method works but has proved unwieldy in practice, so most analyses rely on the first-order approach despite its known weaknesses. These issues were explored even further in Mirrlees (1986) and in Mirrlees and Roberts (1980).

A further issue that arises in principal–agent relationships is the conditions that guarantee the reward from the contract is monotonic: that is, the payment to the agent increases as observed output increases. If there are only two possible output levels, monotonicity arises naturally. With three possible output levels, monotonicity can easily fail (Grossman and Hart 1983). Mirrlees (1976) introduced the monotone likelihood ratio condition that is sufficient for monotonicity. This condition requires that actions that are more costly for the agent to undertake make more profitable outcomes relatively more likely. Although weaker conditions are available (Jewitt 1988), the monotone likelihood ratio condition has become another essential component of the economic theorist’s toolkit. It is, of course, closely related to the single-crossing property that plays such an important role in the income tax paper.

The work of Mirrlees has contributed to the understanding of economic policy via the manual and the papers on tax policy. His work also laid the foundation for the analysis of incentive problems in the presence of asymmetric information. Taken together, incentive compatibility, the extension of the first-order approach, the single-crossing property and the monotone likelihood ratio condition provide the basic tools that no economic theorist can be without. There has not been a single area of economics in which they have not been used to great advantage.

See Also

Selected Works

  • 1962. (With N. Kaldor.) A new model of economic growth. Review of Economic Studies 29: 174–90.

  • 1965. Optimal capital accumulation under uncertainty. Unpublished manuscript.

  • 1967. Optimum growth when technology is changing. Review of Economic Studies 34: 95–124.

  • 1968. (With I. Little.) Manual of industrial project analysis in developing countries, Vol. II: Social cost–benefit analysis. Paris: OECD.

  • 1971. An exploration in the theory of optimum income taxation. Review of Economic Studies 38: 175–208.

  • 1971a. (With P. Diamond.) Optimal taxation and public production I: Production efficiency. American Economic Review 61: 8–27.

  • 1971b. (With P. Diamond.) Optimal taxation and public production II: Tax rules. American Economic Review 61: 261–78.

  • 1972. On producer taxation. Review of Economic Studies 39: 105–11.

  • 1974. (With I. Little.) Project Appraisal and Planning for Developing Countries. London: Heinemann.

  • 1974a. Optimal allocation under uncertainty. In Allocation Under Uncertainty, ed. J. Drèze. London: Macmillan.

  • 1974b. Notes on welfare economics, information and uncertainty. In Essays in Equilibrium Behavior under Uncertainty, ed. M. Balch, D. McFadden and S. Wu. Amsterdam: North-Holland.

  • 1975. The theory of moral hazard and unobservable behaviour, Part I. Mimeo. Oxford: Nuffield College. Published in Review of Economic Studies 66 (1999): 3–21.

  • 1976. The optimal structure of incentives and authority within an organization. Bell Journal of Economics 7: 105–31.

  • 1980. (With K. Roberts.) Functions with multiple maxima. Mimeo. Oxford: Nuffield College.

  • 1986. The theory of optimal taxation. In Handbook of Mathematical Economics, vol. 3, ed. K. Arrow and M. Intriligator. Amsterdam: North-Holland.

  • 1994. (With I. Little.) The costs and benefits of analysis: project appraisal and planning twenty years on. In Cost–benefit analysis, ed. R. Layard and S. Glaister. Cambridge: Cambridge University Press.