Optimum Commodity Taxation in Pooling Equilibria

This paper extends the standard model of optimum commodity taxation (Ramsey (1927) and Diamond-Mirrlees (1971)) to a competitive economy in which some markets are inefficient due to asymmetric information. As in most insurance markets, consumers impose varying costs on suppliers but firms cannot associate costs to customers and consequently all are charged equal prices. In a competitive pooling equilibrium, the price of each good is equal to average marginal costs weighted by equilibrium quantities. We derive modified Ramsey-Boiteux Conditions for optimum taxes in such an economy and show that they include general-equilibrium effects which reflect the initial deviations of producer prices from marginal costs, and the response of equilibrium prices to the taxes levied. It is shown that condition on the monotonicity of demand elasticities enables to sign the deviations from the standard formula. The general analysis is applied to the optimum taxation of annuities and life insurance.asymmetric information, pooling equilibrium, Ramsey-Boiteux Conditions, annuities

Bounded Rationality and Socially Optimal Limits on Choice in a Self-Selection Model

When individuals choose from whatever alternatives available to them the one that maximizes their utility then it is always desirable that the government provide them with as many alternatives as possible. Individuals, however, do not always choose what is best for them and their mistakes may be exacerbated by the availability of options. We analyze self-selection models, when individuals know more about themselves than it is possible for governments to know, and show that it may be socially optimal to limit and sometimes to eliminate individual choice. As an example, we apply Luce’s (1959) model of random choice to a work-retirement decision model and show that the optimal provision of choice is positively related to the degree of heterogeneity in the population and that even with very small degrees of non-rationality it may be optimal not to provide individuals any choice.logit, self-selection, moral-hazard, retirement

Taxation, Inflation, and Monetary Policy

Given that application of the principle with full loss offset to all assets is impracticable, we may wish to consider provision of only a partial inflation-exclusion to assets for which it is feasible. The problem is examined in this paper by means of a simple model of anticipated inflation, in which individuals may invest either in assets for which full or partial inflation-exclusion is provided, or in cash, for which no loss offset is allowed. Among other issues, we shall examine the short and long run effects of taxation and of the provision of an inflation deduction on the rate of inflation and on the level of savings. We do not discuss the long-run optimum tax and deduction rates, because it turns out that for a given tax revenue, these instruments are perfect substitutes, i.e. their relative size does not affect the equilibrium configuration.

Longevity and Aggregate Savings

For the last fifty years, countries in Asia and elsewhere have witnessed a surge in aggregate savings per capita. Some empirical studies attribute this trend to the increases in life longevity of the populations of these countries. It has been argued that the rise in savings is short-run, eventually to be dissipated by the dissaving of the elderly, whose proportion in the population rises along with longevity. This paper examines whether these conclusions are supported by economic theory. A model of life-cycle decisions with uncertain survival is used to derive individuals' consumption and chosen retirement age response to changes in longevity from which changes in individual savings are derived. Conditions on the age-profile of improvements in survival probabilities are shown to be necessary in order to predict the direction of this response. Population theory (e.g. Coale, 1952) is used to derive the steady-state population age density function, enabling the aggregation of individual response functions and a comparative steady-state analysis. Under certain conditions, increased longevity is shown to increase aggregate savings per capita. These conclusions pertain to an economy with a competitive annuity market. The absence of such market compels individuals to leave unintended bequests, whose size depends on the (random) age of death. While an increase in longevity raises individual savings for given endowments, it is shown that the effect on expected steady-state aggregate savings, taking into account the endogenous ergodic distribution of endowments, cannot be determined a-priori.longevity, annuities, life cycle savings, retirement age, steady-state, aggregate savings

Optimum and Risk-Class Pricing of Annuities

When information on longevity (survival functions) is unknown early in life, individuals have an interest to insure themselves against future ’risk-class’ classification. Accordingly, the First-Best typically involves transfers across states of nature. Competitive equilibrium cannot provide such transfers if insurance firms are unable to precommit their customers. On the other hand, public insurance plans that do not distinguish between ’risk-class’ realizations are also inefficient. It is impossible, a-priori, to rank these alternatives from a welfare point of view.

Note on the Optimum Pricing of Annuities

In a perfectly competitive market for annuities with full information, the price of annuities is equal to individuals’ (discounted) survival probabilities. That is, prices are actuarially fair. In contrast, the pricing implicit in social security systems invariably allows for cross subsidization between different risk groups (males/females). We examine the utilitarian approach to the optimum pricing of annuities and show how the solution depends on the joint distribution of survival probailities and incomes in the population.

Uncertain Longevity and Investment in Education

It has been argued that increased life expectancy raises the rate of return on education, causing a rise in the investment in education followed by an increase in lifetime labor supply. Empirical evidence of these relations is rather weak. Building on a lifecycle model with uncertain longevity, this paper shows that increased life expectancy does not suffice to warrant the above hypotheses. We provide assumptions about the change in survival probabilities, specifically about the age dependence of hazard rates, which determine individuals’ behavioral response w.r.t. education, work and age of retirement. Comparison is made between the case when individuals have access to a competitive annuity market and the case of no insurance.longevity, survival functions, education, work, age of retirement, annuities

A Model of Social Security and Retirement Decisions

The purpose of the present paper is to focus on the potential inducement to retire earlier in the presence of social security and on the implied effects on lifetime savings. This problem is analyzed within the framework of a model of intertemporal utility maximization. The organization of this work is as follows. Section 1 introduces the topic. Section 2 presents the model of individual optimization and of the market equilibrium. Sections 3 through 5 present the comparative statistics analysis. Section 3 evaluates the effects on the equilibrium retirement age, section 4 modifies the benefits formula to depend on retirement age and section 5 examines the wealth-income ratio effect. Section 6 introduces the intergenerational transfer problem. Section 7 presents the general model underlying the previous sections.

Optimum Delayed Retirement Credit

A central question for pension design is how benefits should vary with the age of retirement beyond early eligibility age. It is often argued that in order to be neutral with respect to individual retirement decisions benefits should be actuarially fair, that is, the present value of additional contributions and benefits (’Delayed Retirement Credit’ - DRC) due to postponed retirement should be equal. We show that in a self-selection, asymmetric information model, because individual decisions are suboptimal, the socially optimal benefit structure should be less than actuarially fair.delayed retirement credit, self-selection, moral hazard