The micro-foundations of intertemporal price discrimination

Summary. This paper investigates the optimality of intertemporal price discrimination for a durable-good monopoly in a model where infinitely-lived households face an intertemporal budget constraint, and consume both durable goods and non-durable goods. We prove that the optimal price of the durable good is not constant, and may decrease or increase over time. Some households may choose to purchase the durable good at a later date, and pay lower or higher prices, since the gain in discounted utility of consuming more of the non-durable good more than compensates for the loss in utility from delaying the consumption of the durable good.Received: 12 March 2004, Revised: 7 January 2005, JEL Classification Numbers: D40, D42, D91.I would like to thank C.D. Aliprantis, the Editor, and an anonymous referee for their generous advice, and constructive comments and suggestions. I have also enjoyed discussions with John Quah on the subject. Research support from the Wharton-SMU Research Centre, Singapore Management University, is gratefully acknowledged.     

Household Demand, Network Externality Effects and Intertemporal Price Discrimination

This paper examines the optimality of intertemporal price discrimination when network externality effects are present in the consumption of a durable good. We conduct our study in two settings. In a model with two household types, utilities are dependent on the cumulative proportion of households that have purchased the durable good. Next, in a model with a continuum of household types, we extend the analysis to the case where households consume both a durable good and a stream of non-durable goods. We show that in both settings, the presence of network externalities facilitates a sales strategy with intertemporal price discrimination.     

EVALUATING THE SOCIAL OPTIMALITY OF DURABLE PUBLIC GOOD PROVISION USING THE HOUSING PRICE RESPONSE TO PUBLIC INVESTMENT

Recent empirical work in public finance uses the housing price response to public investment to assess the efficiency of local durable public good provision. This article explores the theoretical justification for this technique. It points out that the logic justifying the technique for evaluating nondurable public good provision does not translate to the durable case. A model in which investment is determined by the interaction between a budget‐maximizing bureaucrat and a community's residents is used to demonstrate that the technique can falsely predict underprovision, falsely predict overprovision, or perform without error.     

ON THE TAXATION OF DURABLE GOODS

This article proposes a dynamic Mirrleesian theory of commodity taxation in the presence of durable goods. A uniform taxation across all goods is suboptimal even when the consumption preferences are separable from labor. If the consumption utility function is strictly concave and durable stocks are adjustable without friction, durable investment should be taxed at a higher rate than the purchase of nondurable goods. With adjustment frictions, the wedge on durable investment depends on substitution effects between durable and nondurable consumption and can be positive or negative. An application suggests that housing investment should face higher tax rates than regular consumption.     

The Slutsky matrix and homogeneity in intertemporal consumer theory

A dual vista of an intertemporal model of the consumer yields insights into its fundamental qualitative structure that previous research was heretofore unable to uncover. For example, the intertemporal Slutsky matrix and its properties of symmetry and negative semidefiniteness apply to the integral of the discounted open-loop demand and supply functions, not to the instantaneous open-loop demand and supply functions. The results are established in a general dynamic model of the consumer which accounts for durable and nondurable goods, installation costs for the durable goods, and a leisure/labor choice.     

Consumption and fiscal policy

This paper uses the life-cycle approach to derive an equilibrium intratemporal efficiency condition which relates the marginal utility of consumption of nondurable goods and services to the marginal utility of consumption of services from durable goods. Given this condition and the assumption that marginal utilities are affected by the level of public spending, a long-run relationship between components of private consumption and public expenditure is then postulated. The application of cointegration analysis to UK data supports the existence and uniqueness of such a long-run relationship, and estimates based on the error correction approach produce results which suggest that (i) a change in public spending has different effects on components of private consumption in the short-run, and (ii) the entire burden of long-run substitution falls on nondurable consumption.     

Intertemporal preference parameters for some European monetary union countries

In the European Monetary Union, the estimation and analysis of preference parameters in its members is of special interest because possible differences could help us to understand why a common monetary policy could have different effects on the different economies involved. In this article, we have focused our attention on the elasticity of intertemporal substitution, one of the key preference parameters in intertemporal macroeconomic models. Several studies have shown a possible underestimation of such elasticity for different countries. It is common practice to estimate the parameter using only nondurable goods and services consumption data, without referring to the flow of services generated by durable consumption. This is only admissible if the intratemporal utility can be separated among the different consumption components. Our first objective is, therefore, to test the assumption of intratemporal separability for a selection of European countries (Germany, Spain and France), and then to analyse the effect of durable consumption on the estimated values of the intertemporal elasticity of substitution of these countries, our ultimate goal. Knowledge of such elasticity will enable us to characterise how saving in these economies reacts to variations in the real interest rate.     

The dynamic effects of tax policies in a small open economy

We develop an intertemporal optimizing model of a small open economy with both durable and nondurable consumption to address the implications of alternative tax policies. An increase in lump sum taxes reduces the steady state level of consumption and improves the stock of foreign bonds. Consistent with empirical evidence, durable consumption exhibits initial excess volatility. Though an increase in the tax on durables increases the demand for nondurables and improves the bond holdings in the steady state, an increase in the tax on nondurables has insignificant effects on the stock of foreign bonds and the consumption of durables. Using quarterly data from the UK and estimating generalized impulse response functions we find empirical support. We also calibrate the welfare implications of different tax policies.     

Optimally eating a stochastic cake: a recursive utility approach

In this short paper, uncertainties on resource stock and on technical progress are introduced into an intertemporal equilibrium model of optimal extraction of a non-renewable resource. The representative consumer maximizes a recursive utility function which disentangles between intertemporal elasticity of substitution and risk aversion. A closed-form solution is derived for both the optimal extraction and price paths. The value of the intertemporal elasticity of substitution relative to unity is then crucial in understanding extraction. Moreover, this model leads to a non-renewable resource price following a geometric Brownian motion.     

The Effect of Exchange Rate Volatility on Trade in Durables

Because durable goods have the quality of an asset, risk-averse consumers wan to pay a lower price for durable than for nondurable goods so that they are compensated for the risk of price changes; they require risk premium. Since the exchange rate is a strong source of uncertainty in import prices, exchange rate volatility has a negative effect on the demand for imported durables. In an imperfectly competitive market, the volatility of the exchange rate is predicted to reduce the relative price of imported durables. The prediction is supported by an empirical investigation of US imports.     

The effects of periodic quotas limiting the stock of imports of durables

Analyses of trade quotas typically assume that the quota restricts the flow of some nondurable good. Many real-world quotas, however, restrict the stock of durable imports. We consider the cases where (1) anyone is free to export against such quotas and where (2) only those allocated portions of the total quota are free to export against such quotas. Recent econometric investigations of such quotas have focused on the price of the durable as an indicator of tightness induced by the quota. We show why this is an inappropriate indicator and suggest alternatives.     

Private consumption,public consumption and liquidity constraints in developing countries: some empirical evidence

This paper extends the empirical work of Giovannini (1983, 1985) in seeking to identify the elasticity of substitution in consumption in developing countries using the Euler equation approach. Allowing for liquidity constraints in capital markets which force a percentage of aggregate consumption growth to track income growth to track income growth, we report static and time-varying estimates of this percentage and the elasticity of intertemporal substitution, as well as estimates of substitution between private and public consumption and implied utility function parameters. Our results suggest that liquidity constraints are a pervasive feature of developing country consumption data and that the elasticity of intertemporal substitution is near-zero for the majority of countries considered.     

Status,Risk-Taking and Intertemporal Substitution in an Endogenous Growth Model

This paper examines intertemporal risk-taking in a stochastically growing economy with externalities in human capital accumulation where agents have preferences for social status. In order to isolate the effects of status concerns on long-run expected growth, the analysis is embedded in a non-expected utility setting, which disentangles the effects from risk aversion and intertemporal substitution. We examine the interaction between status desire and risk, risk aversion and intertemporal substitution. The externalities generated by the status game are able to correct the allocative distortions from the knowledge spillovers.Acknowledgement The author would like to thank an anonymous referee for his valuable comments.     

Estimating the elasticity of intertemporal substitution taking into account the precautionary savings motive

This paper estimates the elasticity of intertemporal substitution for U.S. aggregate time series data, taking into account the precautionary savings motive. By making use of a recursive utility function, we estimate an Euler equation, via GMM. This procedure leads consumption growth rate to depend on asset returns, and on a time-varying variance, which captures the precautionary motive. When significant, the elasticity of intertemporal substitution estimates ranges from 0.4 to 1.8, which are higher than most of the results found in the literature. Furthermore, the evidence suggests that consumers react to risk; however, the contribution of precautionary motive to consumption growth seems to be limited.     

Is food consumption a good proxy for nondurable consumption?

This paper examines whether there is a discrepancy in estimating the elasticity of intertemporal substitution using food consumption instead of nondurable consumption data. We show that a discrepancy exists and that the discrepancy increases as nondurable consumption increases.     

Exploring consumption-based asset pricing model with stochastic-trend forcing processes

Using Canadian data, the consumption-based asset pricing model is studied, defined in terms of nondurable and durable goods consumption. A two-stage estimation procedure is used, which takes account of the presence of common stochastic trends in the forcing processes. This method yields more reasonable estimates of the preference parameters than the previous studies did, and the asset-pricing equation is not rejected by the data. Moreover, the preference specification adopted in this paper allows a number of useful economic information to be obtained. The additive separability assumption and the Cobb–Douglas functional form of the utility function are ruled complements in the sense of Edgeworth and Pareto.     

A life-cycle analysis of social security with housing

This paper incorporates two features of housing in a life-cycle analysis of social security: housing as a durable good and housing market frictions. We find that both housing quantities and homeownership rates respond strongly to eliminating social security. Accordingly, the aggregate impacts of this policy reform are significantly larger in an economy with explicit housing choices than in a standard life-cycle economy. Our analysis shows that the key mechanism behind these results is the substitution effects of a change in interest rates and, thus, the price of housing services on the choice of nondurable consumption versus housing services.     

Durability in a Monopoly With a Small Number of Buyers

This paper shows that the number of buyers is a crucial demand characteristic for a monopolist's choice of durability. When he sells to a few large buyers, he offers a more durable good than when selling to many small buyers. By increasing durability of the good sold to large buyers, the monopolist encourages current purchasing and can thus engage in greater intertemporal price discrimination and make more profit. Therefore Bulow's proposition of minimal durability does not survive in the case of few buyers. This has not been pointed out thus far.     

MULTIATTRIBUTE UTILITY THEORY,INTERTEMPORAL UTILITY,AND CORRELATION AVERSION

Convenient assumptions about qualitative properties of the intertemporal utility function have generated counterintuitive implications for the relationship between atemporal risk aversion and the intertemporal elasticity of substitution. If the intertemporal utility function is additively separable, then the latter two concepts are the inverse of each other. We review a theoretical specification with a long lineage in the literature on multi‐attribute utility and use this theoretical structure to guide the design of a series of experiments that allow us to identify and estimate intertemporal correlation aversion. Our results show that subjects are correlation averse over lotteries with intertemporal income profiles.     

Advance-purchase discounts as a price discrimination device

In an intertemporal setting in which individual uncertainty is resolved over time, advance-purchase discounts can serve to price discriminate between consumers with different expected valuations for the product. Consumers with a high expected valuation purchase the product before learning their actual valuation at the offered advance-purchase discount; consumers with a low expected valuation will wait and purchase the good at the regular price only in the event where their realized valuation is high. We characterize the profit-maximizing pricing strategy of the monopolist. Furthermore, adopting a mechanism design perspective, we provide a necessary and sufficient condition under which advance-purchase discounts implement the monopolist's optimal mechanism.