Welfare analysis in a two-stage inverse demand model: an application to harvest changes in the Chesapeake Bay

Like many agricultural commodities, fish and shellfish are highly perishable and producers cannot easily adjust supply in the short run to respond to changes in demand. In these cases it is more appropriate to conduct welfare analysis using inverse demand models that take quantities as given and allow prices to adjust to clear the market. One challenge faced by economists conducting demand analysis is how to limit the number of commodities in the analysis while accounting for the relevant substitutability and complementarity among goods. A common approach in direct demand modeling is to assume weak separability of the utility function and apply a multi-stage budgeting approach. This approach has not, however, been applied to an inverse demand system or the associated welfare analysis. This paper develops a two-stage inverse demand model and derives the total quantity flexibilities which describe how market clearing prices respond to supply changes in other commodity groups. The model provides the means to estimate consumer welfare impacts of an increase in finfish and shellfish harvest from the Chesapeake Bay while recognizing that harvests from other regions are potential substitutes. Comparing the two-stage results with single-stage analysis of the same data shows that ignoring differentiation of harvests from different regions, or the availability of substitutes not affected by a supply shock, can bias welfare estimates.     

A family of inverse demand systems and choice of functional form

Barten's (1992) analysis of choice of functional form for quantity-dependent demand systems is extended to price-dependent or inverse demand systems. Alternative inverse demand systems combining the features of the Rotterdam inverse demand and almost ideal inverse demand systems are examined. Choice of functional form is made through a synthetic model which under appropriate restrictions yields the different inverse demand systems. The synthetic model itself can also be considered a more flexible specification.     

Monopoly with local knowledge of demand function

In this note, we propose a model where a quantity setting monopolist has incomplete knowledge of the demand function. In each period, the firm sets the quantity produced observing only the selling price and the slope of the demand curve at that quantity. Given this information and through a learning process the firm estimates a linear subjective demand curve. We show that the steady states of the dynamic equation are critical points of the objective profit function. Moreover, results depend on convexity/concavity of the demand. When the demand function is convex and the objective profit function has a unique critical point: the steady state is a globally stable maximum; conversely when then steady state is not unique, local maximums are locally stable, while local minimums are locally unstable. On the other hand when the demand function is concave, the unique critical point is a maximum: there can be stability or instability of the critical point and period two cycles around it via a flip bifurcation. Moreover, through simulations we can observe that, with a mixed inverse demand function, there are different dynamic behaviors, from stability to chaos and that we have transition to complex dynamics via a sequence of period-doubling bifurcations. Finally, we show that the same results can be obtained if the monopolist is a price setter.     

The Antonelli Versus Hicks Elasticity of Complementarity and Inverse Input Demand Systems

A true measure of input substitution associated with exogenous changes in input quantities requires that the output level be held constant. To this effect, this study presents the Antonelli elasticity of complementarity characterised by the distance function. The more common Hicks elasticity of complementarity assumes that marginal cost is constant and hence does not capture pure substitution effects. The two elasticities of complementarity are related to inverse demand systems and are shown to be equivalent under constant returns to scale. A framework for estimating the Antonelli elasticity from the uncompensated demand system is presented. Estimation results reveal substantial bias of input substitutability with the use of Hicks' measure.     

Functional separability within a quadratic inverse demand system

In this paper, a quadratic inverse (almost ideal) demand system (IQUAIDS) is derived, that generalizes the inverse (almost ideal) demand system (IAIDS). Starting from a flexible parameterization of the distance function, this model allows a more flexible specification by overcoming the potential restrictiveness of linear scale curves. However, at a point of normalization, the IQUAIDS boils down to the IAIDS, thus the additional flexibility pertains only to the specification of scale elasticities away from the point of approximation. Previous work on functional separability is extended to the case of inverse demands, and necessary and sufficient conditions for weak separability of the direct and indirect utility function derived, in terms of the Antonelli elasticities of complementarity and of the scale elasticities. Their proper parametric representation within the inverse specification is also derived. An empirical application to fish demand in Italy is provided, mainly for illustrative purposes.     

When does Learning by Doing generate current losses?

We study under which conditions a learning by doing effect in the industry causes a monopolist to operate at a loss for some initial periods. Those conditions involve a parameter of the learning process, the slope of inverse demand function and the discount parameter. In order to get results, we explore the analytical solution to a T-period learning by doing model, which is also a novelty. Numerical examples are presented.     

The family of inverse demand systems

A set of inverse demand systems derived from some well-known utility functions is presented, in which the Hotelling-Wold identity has been used for such a derivation. The functional forms of the inverse demand systems obtained by this study are theoretically integrable and empirically operations.     

Trade distance functions and the derivation of inverse demand for imports

This article introduces a new representation of trade preferences termed as the trade distance function, which measures the maximum amount by which import quantities must be deflated or inflated to reach the indifference surface. The properties of this function are discussed and employed to derive systems of inverse demand for imported goods. We illustrate its usefulness by proposing two new parametric forms of trade distance functions. While the trade distance function directly yields Hicksian inverse demand functions of imports, they usually lack closed-form representations in terms of observable variables. This problem, however, need not hinder estimation and could be solved by using the numerical inversion estimation method. Results generally indicate that the suggested modelling and estimation methods are operationally, implying that the trade distance function approach is a promising tool of the empirical analysis of import demands subjected to tight theoretical conditions.     

Multi-product costs and standby capacity derived from queuing theory: the case of Belgian hospitals

Empirical hospital cost function studies can be divided into two categories: studies estimating traditional multi-product cost functions and studies including demand uncertainty (assuming that hospitals provide standby capacity to cope with uncertain demand and stressing that the relationship between the uncertain demand, excess capacity and costs should be investigated). Most studies include (the inverse of) the occupancy rate in a relatively basic cost function. The first contribution of this paper is to incorporate an indicator of reserve capacity into a genuine multi-product cost function. The second contribution is to propose an alternative indicator to proxy the reserve margin. The often used occupancy rate has an important shortcoming: the same occupancy rate can hide different turnaway probabilities and waiting times, obscuring the true degree of reservation quality. Since turnaway probabilities and waiting times are typical queuing theory indicators, an indicator for average waiting time (derived from queuing theory) is incorporated into a proper multi-product cost function to capture the degree of standby capacity into a proper multi-product cost function. The study uses 1997 data on Belgian general care hospitals to estimate a multi-product cost function and calculate cost elasticities, marginal costs and the degree of economies of scale. The results further show that providing standby capacity has a significant impact on total costs.     

A Theory of Mergers and Merger Waves

We consider a sequential merger game between Cournot firms with homogeneous product and quadratic cost. A large slope of the marginal cost function or a small slope of inverse market demand are both predicted to increase the incentive to merge. The profitability of any merger increases with the number of mergers having already taken place. Thus, mergers tend to occur in waves in industries that have experienced exogenous shocks affecting firms’ cost or demand. We also show some mergers that are not profitable for merged firms in the short-run may take place in the early stage of a wave.     

The empirical content of Cournot competition

We consider the testable implications of the Cournot model of market competition. Our approach is nonparametric in the sense that we abstain from imposing any functional specification on market demand and firm cost functions. We derive necessary and sufficient conditions for (reduced form) equilibrium market price and quantity functions to be consistent with the Cournot model. In addition, we present identification results for the corresponding inverse market demand function and the firm cost functions. Finally, we use our approach to derive testable restrictions for the models of perfect competition, collusion and conjectural variations. This identifies the conditions under which these different models are empirically distinguishable from the Cournot model. We also investigate empirical issues (measurement error and omitted variables) related to bringing our testable restrictions to data.     

MONETARY TARGETING IN WEST GERMANY,HOLLAND, AND SWITZERLAND

Links between fluctuations in domestic money supplies and subsequent fluctuations in rates of real output have been less visible in Western Europe than in the United States. This paper discusses some of the causes and investigates the stability of the demand for money in West Germany, the Netherlands and Switzerland. In all three countries, temporary changes in short-term interest rates temporarily affect the demand for money. These temporary changes in the demand for money are reflected in temporary blips in the monetary statistics, as agents substitute among various monetary assets. The hypothesis that aggregate demand responds only to longer-lasting changes in interest rates is tested by a two-step procedure. First, the official data on European money supplies are corrected for temporary disturbances caused by temporary changes in domestic interest rates. Second, changes in real activity are regressed on a measure of monetary stimulus, which takes into account the correction for temporary disturbances. This two-step procedure avoids some of the bias present in ordinary estimates of the demand-for-money function. The results show that the links between changes in money and subsequent changes in output are somewhat more tenuous in West Germany, the Netherlands, and Switzerland than in the U.S. but significant effects do exist. These effects are more easily documented when corrected time series for the European money supplies are used.     

TAXES ON PAYROLL, REVENUES AND PROFITS IN THREE MODELS OF COLLECTIVE BARGAINING

Variations in company taxes are analysed for a right-to-manage model, an efficient bargaining setting and a seniority approach. Taxes cannot be shifted forward by the risk-neutral firm. Alternative income and bargaining power are allowed to vary with taxes. Employing asymmetric Nash solution it is found that changes in a payroll, revenue or profit tax can have differing implications for labour demand curve models and efficient bargaining solutions. This distinction might provide a novel basis for empirical work. Variations in bargaining power and-within a labour demand curve setting-the union's objective function do not change results.     

A semiflexible normalized quadratic inverse demand system: an application to the price formation of fish

We propose a new inverse demand system, the normalized quadratic distance function, which is similar to the normalized quadratic expenditure function of Diewert and Wales (1988a). Aside from being able to maintain concavity in quantities globally, the resulting specification is also `flexible.' In addition, to obtain more parsimonious specifications, we apply the rank reduction procedures of Diewert and Wales (1988b) to the model's Antonelli matrix. We illustrate the techniques by estimating a system of inverse demands for bi-monthly fish landings, 1971–1991, for U.S. Great Lakes ports. To illustrate the model's usefulness, exact welfare measures associated with catch restrictions are derived. First version received: May 1999/Final version received: November 2000     

Cournot equilibrium without apology: Existence and the Cournot inverse demand function

In a multi-commodity framework with absence of wealth effects, we prove the existence of equilibrium for Cournot oligopoly, and that the concept is completely non-ambiguous. We also obtain a uniquely defined endogenous inverse demand function, depending only on the competitive sector.     

A Bayesian approach to aggregation in demand systems: smoothing with perfect substitution priors

Demand analysis requires aggregation of commodities. Some are imposed at the data collection level, leaving some for the estimation level. When data are collected, the implicit assumption underlying the aggregation is perfect substitutability: one gallon of gasoline is viewed by consumers as equivalent to another gallon; hence, the two are added together. While such aggregation can be carried out further by the data analyst, it is difficult to incorporate perfect substitutability into the estimation of direct demand systems. Perfect substitution in that context implies discontinuous demand functions, which are not nested within standard empirical demand systems. Perfect substitution is much more easily handled in a system of inverse demands, though an empirical method to impose perfect substitutability in an inverse demand system has not previously appeared in the literature. In this article, we develop such a method, which allows perfect substitutability to be imposed as a prior restriction. We use Leamer’s information contract curve as a tool to flexibly impose the substitution restriction and to investigate consistency between the data and prior. We illustrate the method with an application to inverse demands for fish in Korea.     

EMPLOYMENT FUNCTIONS AND THE SLOWDOWN IN UK PRODUCTIVITY GROWTH

This paper investigates the employment demand function in the light of recent developments in econometric modelling procedures. The evidence for structural breaks in the equation for the UK manufacturing sector in 1966/67 and 1973/74 is re-examined, and the behaviour of employment in the post-1979 recession is analysed. The empirical results illustrate the problems raised for estimating employment equations by the productivity slowdown in the 1970s, and the implications of the different methods used to model this phenomenon for interpreting the more recent experience are examined. The implicit dynamics of the equations estimated in error-correction form are derived and are discussed in terms of both employment and productivity behaviour.     

Relative Emission Standard versus Tax under Oligopoly: The Role of Free Entry

We compare the effects of an emission tax, and those of a relative emission standard, on welfare and pollution levels under oligopolistic market structures. We consider the cases where the number of firms is fixed and where there is free entry and exit of firms. When the number of firms is fixed, (i) a relative emission standard is welfare-superior to an emission-equivalent emission tax, and (ii) an emission tax is emission-superior to a welfare-equivalent relative emission standard. Under free entry and exit, the results are just the opposite when the inverse demand function is concave.     

Cournot games with biconcave demand

Biconcavity is a simple condition on inverse demand that corresponds to the ordinary concept of concavity after simultaneous parameterized transformations of price and quantity. The notion is employed here in the framework of the homogeneous-good Cournot model with potentially heterogeneous firms. The analysis leads to unified conditions, respectively, for the existence of a pure-strategy equilibrium via nonincreasing best-response selections, for existence via quasiconcavity, and for the uniqueness of the equilibrium. The usefulness of the generalizations is illustrated in cases where inverse demand is either “nearly linear” or isoelastic. It is also shown that commonly made assumptions regarding large outputs are often redundant.