Comparative Static Results Research Articles

Job Transfers and Incentives in Complex Organizations: Thwarting the Ratchet Effect

Many complex organizations, such as planned Soviet enterprises and the U.S. military, routinely transfer employees between jobs. Since this sacrifices job-specific human capital, the practice is puzzling. This article shows that regular job transfers may be part of an optimal incentive scheme in organizations plagued by the ratchet effect. The ratchet effect arises when an employer is uncertain as to the productivity of the various positions or jobs within an organization. Workers in highly productive jobs then have an incentive to disguise the productivity of their jobs by expending low effort and producing low output. This avoids having the employer construct more demanding remuneration schemes once the high productivity of a job becomes known. Job transfers break the link between current performance and future incentive schemes, and hence remove the incentive-stifling implications of the ratchet effect. This article examines the tradeoff between providing more effective incentives via job transfers and the accompanying sacrifice of job-specific human capital, establishes conditions under which job transfers are optimal, and develops comparative static results.

A median-voter model of economic regulation

A basic median-voter model is developed and extended to analyze issues of economic regulation and public policy outcomes. The model is used to generate comparative static results relating changes in public-policy outcomes to changes in relative group sizes, total population, information costs, and population heterogeneity. The model is also used to explore the issue of optimal group size — the size of the special-interest group that maximizes the group's per capita public policy gains. Comparative static analysis reveals how optimal group size and gains per capita are affected by changes in population heterogeneity, the size of the total population, and relative knowledge levels.

A Classical Model of the Class Struggle: A Game-Theoretic Approach

The class struggle is formalized as a differential game in a strictly supply-side model, an approach that synthesizes the models of Lancaster and Goodwin. Four different steady-state equilibria are derived, each corresponding to different assumptions about the degree to which each class is organized to promote its own interests. In particular, the Goodwin growth cycle is shown to emerge from a world characterized by unorganized capitalists and workers, in which individuals ignore the effects of their own actions on economywide variables. More relevant for discussion of modern capitalism are the hierarchical equilibria, especially the codetermination equilibrium in which the existence of a full-employment equilibrium turns out to be problematic. Finally, comparative-statics results suggest that the incentives for technological change differ widely among the four regimes.

Production theory under uncertain inflation

This paper examines Chen's [1980] model of asset valuation under uncertain inflation in order to derive a static and comparative static theory of production by a competitive firm. Given the value maximizing and the price taking assumptions, the firm behaves as a profit-maximizer. The sole effect of uncertain inflation is to distort the price structure. that is, the firm adjusts the expected price of an input or output to reflect the systematic risk of that price. Because a change in circumstances can affect the systematic risk of a given price, assessing the effects of a specific policy or event solely in terms of its effect on expected price can be misleading. Parametric variations affect the structure of certainty equivalent prices. Therefore, the comparative static derivatives of the value maximizing firm emerge as extensions of the comparative static derivatives of the profit maximizing firm under certainty. Many of these comparative static derivatives are of determinant sign. The effects of changes in market uncertainty and in inflation uncertainty, while they can be characterized mathematically, cannot be signed in the general case. Cross-sectional studies indicate wide variation in the effects of inflation, so that the preceding theoretical results appear plausible. Finally, in view of the wealth of static and comparative static results which can be derived from Chen's model, that model provides a convenient benchmark against which to judge other models. Precisely because of its simple nature, Chen's model is ideal for establishing limits of analysis.

The multifactor Illyrian firm revisited

Comparative static results for the single output, multifactor, short-run dividend-maximizing firm are derived and classified. Two determinate situations are identified; first, if the production technology is Hicksian-normal and homogeneous, both Ward perversions (negative responses of both labor and output to an increased product price) follow and, second, if labor is inferior, a positively sloped supply curve but a perverse labor response result. The possibility of labor responding positively to a price increase is demonstrated in which case the supply curve will be positively sloped. A distinction between labor-intensive and materials-intensive technologies indicates that the latter is more likely to exhibit Ward perversion. Implications for empirical work are discussed.

The Economic Impact of bGH on the New York State Dairy Sector: Comparative Static Results

The price and quantity effects of a forthcoming biotechnology product, bovine growth hormone (bGH), are explored in a simple partial equilibrium model. The model is based on previous theoretical work on technological change but is developed in terms of a sector output. A particular output curve is estimated using data from a random sample of New York State dairy farms. Information on the farm level production effects of bGH is used to shift the output curve and to solve for equilibrium levels of price and output. The model projects the bGH may lead to the exit of 5,400 New York dairy farms and a 20 percent reduction in herd size. Consumers will benefit from an approximately 30 percent drop in milk price. The effect on gradual diffusion of bGH on farm numbers is considered. To accommodate this technology policies encouraging an orderly transfer of resources out of the dairy sector should be examined.

INTERDEPENDENT BEHAVIOR WITH RELOCATION COSTS: THE COMPARATIVE STATICS OF SPATIAL HISTORY*

ABSTRACTRelocation costs are a form of sunk costs because they are relevant to new entrants, not to agents at their existing locations. With sufficiently high relocation costs, initial (historically given) locations and other conditions determine the equilibrium assignment of agents to locations. Comparative static results depend on initial conditions, i.e., history matters and historical persistence can be characterized.The model suggests empirically‐relevant results which can be tested by collecting data on relocation and transportation costs. For example, appropriate levels of these costs imply that suburbanization always occurs with the entry of new firms. Sequential entry strategies may be adopted by existing firms which earn pure profits. This may be contrasted with traditional NUE models which predict changes in the boundaries of central zones.

Moving costs and the microeconomics of intra-urban mobility

This paper considers the role of moving costs in long-term optimal moving strategies from a theoretical microeconomic point of view. Using a model of intertemporal utility maximization, we arrive at conditions for (i) the optimal number of moves, (ii) the optimal moving dates, and (iii) the optimal consumption of housing services and other goods in the periods between moves. Also, comparative static results are obtained.

Agricultural Development and Land Tenancy in a Peasant Economy: Reply

It is by now well known, particularly due to Bell and Braverman, that a model with constant returns to scale, sharecropping, and the wage-contract choice leads to a tendency for corner solution. In Bardhan (1979) I introduced a two-season production process interlinking land and credit markets and landlord monopoly power, not to avoid-as Datta and Nugent seem to imply-the problem of corner solutions, but only to introduce a dosage of realism in the model. The main problem for interior solutions in the context of the model was caused by the special assumption of constant returns to scale, which I used here, unlike in Bardhan and Srinivasan and Bardhan (1977), primarily to avoid cluttering up the equations. In any case, in peasant agricultural production functions with only land and labor as arguments and other factors suppressed (particularly managerial and animal labor input), the assumption of constant returns to scale is not very realistic. If my 1979 model is taken with diminishing returns to scale, the interior solution and most of the comparative-static results are more robust. It is not inconsistent for the landlord to be a monopolist in the land-lease market and at the same time be a competitive buyer in the labor market. In fact, I think this may be the more realistic case. As indicated in footnote 3 of Bardhan (1979), the demand for labor by others has been suppressed for convenience in equation (9); but, if one likes, one may introduce on the left-hand side of that equation a term D(W2) to represent the net demand for labor by others (say, by pure owner-cultivators) with usual properties of demand functions. None of the subsequent results in Bardhan (1979) changes. As far as I can see the empirical result reported in table 1 by Datta and Nugent on the basis of a normalized dependent variable is illegitimate. They combine the proportion of cultivated area under total tenancy given in Bardhan (1979) and the area under sharecropping as percentage of area under sharecropping and fixed-rental tenancy in Bardhan (1977) to get their normalized dependent variable, which is the percentage of land under share and wage contracts only. This they cannot do unless they use independent information on land under leasing arrangements other than share and fixed-rental tenancy, which in some states are significant.

A two-country disequilibrium model

The implications of wage and price rigidities for several open-economy macroeconomic questions are studied in a two-country framework, using comparative statics and numeric analytic solutions. In contrast to a small country disequilibrium approach, the proposed model highlights the critical dependence of trade balance stability and other comparative static results on the specification for the export rationing scheme. Although coordination of export rationing policies carries potential mutual benefits, it is shown that these may not be realized due to game-theoretic problems. The analysis also offers new illustrations and more general results which emphasize: (1) the dependence of the efficacy of macroeconomic policies on the specific set of wage and price rigidities as well as quantity constraints in both countries, and (2) the likelihood that a devaluation will have perverse trade balance effects in supply-constrained regimes.

On the Theory of the Competitive Firm under Uncertainty When Initial Wealth Is Random

Since Sandmo's seminal paper on the theory of the competitive firm under output price uncertainty, there has been considerable research on this topic [2; 5; 6; 10; 11; 14]. In all these studies, it is assumed that, in the absence of complete contingent markets, output price risk is the only source of uncertainty for the firm. However, this may not be a realistic assumption. In particular, as argued by Kihlstrom et al. [7], it appears reasonable to consider the case where some of the initial wealth of the firm is held in risky assets. In that case, initial wealth is uncertain and should be modelled as a random variable. The objective of this paper is to investigate the introduction of random initial wealth in Sandmo's theory of the firm under price uncertainty. In Sandmo's model, a number of important comparative static results (e.g., the conditions under which the supply function is upward sloping [14, 69], or under which increased price uncertainty reduces supply [5] depends critically on the sign of a particular expression' stated in Lemma 2 in Ishii [5]. While Sandmo [14, 69] shows this expression is non-negative under Arrow-Pratt decreasing absolute risk aversion, it can be verified that his proof no longer holds when initial wealth is random. Therefore, the comparative static analysis conducted by Sandmo [14], Batra and Ullah [2] and Ishii [5] is no longer valid and gives ambiguous results under initial wealth uncertainty. The reason is that the Arrow-Pratt measures of risk aversion [1; 12] are too weak for making comparisons in situations where there is more than one source of uncertainty [13]. Then, what can be deduced from the theory of the competitive firm in the (realistic) case where both initial wealth and output price are uncertain? We will show here that meaningful results on the behavior of the competitiv firm under uncertainty can be obtained provided that the Arrow-Pratt measures of risk aversion [1; 12] are replaced by the Ross measures of risk aversion [13]. In particular, a comparative static analysis of the production decisions using Ross characterization of risk behavior is presented. A number of new results are derived on the properties of risk responsive supply and input demand functions under both price and initial wealth uncertainty.

Firm location and city size: Reduced productivity advantages as a factor in the decline of manufacturing in urban areas

This paper develops a model of firm location and city size that arrives at theoretical conclusions that differ from those of other authors. Comparative-statics results suggest that changes in national wage levels and productivity levels create no determinate (dis)advantage for large cities relative to small ones as sites for manufacturing activity. Increased wage and reduced productivity premiums of large cities, however, result in unambiguous disadvantages. Statistical analysis indicates that the productivity advantages of large cities have declined in as many as eight two-digit manufacturing industries that provide more than one-third of metropolitan production worker employment.

A model of rental and owner-occupied housing

A complete model of owner-occupied and rental housing is developed. The model allows for the endogenous determination of rents, the user cost of owner-occupied housing and housing tenure choice by individuals. In the short run, structure prices are endogenous, while in the long run the size of the housing stock adjusts to equate structure prices to exogenous construction costs. Comparative static results emphasize the importance of marginal tax rates and distinguishing between the short and long run for a complete understanding of the impacts of inflation on housing markets.

Labor Union Objectives and Collective Bargaining

We consider a model oflabor union behavior in which workers make decisions about wages and employment by simple majority rule. We show that under general conditions such a union has a well-behaved objective function, different from those previously postulated in the literature. We then show that the union's majority preferences generally lack a von Neumann-Morgenstern utility representation and thus cannot be inserted into traditional bargaining models. We then develop and characterize the solutions to a new bargaining model that is consistent with the structure of union preferences. Several comparative-statics results are presented.

Rationing macroeconomics: A Graphical Exposition

The paper provides a graphical exposition of the most significant results of comparative statics obtained in a four-market macroeconomic model with fixed commodity prices and wages. The main tool of analysis remains the usual IS-LM apparatus modified to account for the possibility of rationing on the goods as well as on the labour market.

Non-linearities in applied general equilibrium models

In this paper we discuss some extensions of the general equilibrium model Keller (1980) used to analyze tax-incidence. We compute the comparative static results of Keller on tax-incidence, now taking into account non-linearities. This is done by employing a method of iterative linearization. It turns out that the error made by linearization is small.

Labour Supply under Uncertainty with Piecewise Linear Tax Regimes

The analysis of labour supply under uncertainty has been developing rapidly in recent years. Papers by Block and Heineke (1973), Stiglitz (1976), Cowell (1981a, b), Eaton and Rosen (1980a, b), Stern (1980) and Tressler and Menezes (1980) have all presented analyses of the problem. Almost without exception, the focus of the analysis has been the effects of (in the rate or in non-labour income) on the labour supply decision of the individual. Not surprisingly, therefore, the well-known comparative static results of Rothschild and Stiglitz (1971) and Diamond and Stiglitz (1974), on how increases in risk influence the optimal choice of a control variable, have been found to be useful in this literature. Some of the above-mentioned papers have also considered the problem of labour supply under uncertainty when there are taxes in operation. Thus Stiglitz (1976), Cowell (1981a, b) and Eaton and Rosen (1980a, b) all analyse the role of taxation. However, none of these papers has examined labour supply under uncertainty with regimes of the type we observe in practicewhich are typically piecewise-linear.1 Moreover, in all the studies I am aware of the regime itself is held to be constant-thus, the role of tax risk, as opposed to wage risk, remains unanalysed. The object of this paper, therefore, is to advance the literature on labour supply under uncertainty in these two directions. First, we ask the more common question about the impact of greater risk on labour supply, but this time in the context of piecewise-linear regimes. It will be seen that the answers now have to be modified in interesting ways. In particular, it will be shown that the problem belongs to a general class of problems in decision-making under uncertainty, analysed in Kanbur (1980, 1982), where the pay-off function has a kink (or non-differentiability) at a critical value of the random variable. In such a setting the Rothschild-Stiglitz (1971) and Diamond-Stiglitz (1974) results are no longer directly applicable. We have to use their generalized counterparts, developed in Kanbur (1981). Second, we ask a question that has not been asked in the literature up to now: what is the impact of greater uncertainty about the regime on labour supply decisions? It will be seen that the piecewise-linear regime allows us to parametrize such regime risk in a convenient and manageable way. The plan of this paper is as follows. Section I introduces the model and, in the context of the model, gives a precise statement of the questions that this paper asks. Section II begins the analysis by considering the effects of greater risk in the rate and in non-labour income. Sections III and IV then consider the question of regime risk. Section V concludes the paper.

The comparative statics of cumulative distribution function changes for the class of risk averse agents

The primary question addressed is, When does a particular change in the cumulative distribution function (CDF) describing a random variable always cause all risk averse decision makers to adjust the choice variable in the same direction? A necessary and sufficient condition, involving both the decision model and the CDF change, is derived. This condition allows the researcher to determine the tradeoff between assumptions on the economic model, and the CDF changes, which are necessary and/or sufficient to yield determinate comparative static results. Several applications are included.

Monopoly Markets in Public Goods: the Case of the Uniform All-or-None Price

This article explores the provision of a price-excludable public good under conditions of monopoly, in which the monopolist sets a uniform all-or-none price-output package to all consumers. The reasons for interest in this particular monopoly model are twofold First, many public goods are amenable to exclusion on an all-or-none basis. Second, the model does not presume the monopolist to have any information beyond that normally assumed for sellers in private goods markets. The profit-maximizing outcome under these conditions is developed and several striking comparative static results derived. The monopoly outcome is compared with the outcome under the most closely analogous perfectly competitive model (Oakland, 1974). It is shown that, under certain conditions, the monopoly result is superior to the competitive outcome in a welfare sense and indeed that optimality can emerge under monopoly in conditions where it would not under competition. The possibility that the monopolist might oversupply the public good is also explored.

The effects of a change in the variability of irrigation water

This paper examines the short‐run effects upon several variables of an increase in the variability of an input. The measure of an increase in the variability is the “mean preserving spread” suggested by Rothschild and Stiglitz (1970). The variables examined are real income (utility), expected profits, expected output, the quantity used of the controllable input, and the shadow price of the stochastic input. Four striking features of the results follow: (1) The concepts that have been useful in summarizing deterministic comparative static results are nearly absent when an input is stochastic. (2) Most of the signs of the partial derivatives depend upon more than concavity of the utility and production functions. (3) If the utility function is not “too” risk averse, then the risk‐neutral results hold for the risk‐aversion case. (4) If the production function is Cobb‐Douglas, then definite results are achieved if the utility function is linear or if the “degree of risk‐aversion” is “small.”