Non-Renewable Resources and Disequilibrium Macrodynamics

Robert Marks

• Publisher: Routledge
• Year: 2017
• ISBN:
  9781351610513
• Edition: 1
• Topic: Business
• Subtopic: Business General
• Index: Business

This study, first published in 1979, continues by examining the question of whether a competitive economy can efficiently allocate a stock of non-renewable natural resources through time. Long-run analyses of competitive economies with such resources have concluded that, without perfect foresight or a complete set of future markets extending infinitely far into the future, there is no economic mechanism to guarantee that the initial price is set so that the economy converges to the socially desirable path of balanced growth. This title will be of interest to students of environmental and natural resource economics.

CHAPTER I: INTRODUCTION

1.1. The economics of non-renewable natural resources.

In the past few years there has been an increasing awareness of the finite “limits” of the “Spaceship Earth.” In economics this has shown itself in a renewed interest in the role of natural resources in the economic process, and the effects of the institutions and level of activity of the economy in the conservation and use of natural resources. This study is concerned with both of these aspects of the economics of non-renewable natural resources. In particular, does the existence of non-renewable natural resources in the economy have any short-run effects on the interactions of the economy—does their existence affect short-run stabilisation policies, and, if so, how? When we consider the short-run micro-foundations of economic behaviour is there any reason to believe that the competitive economy will exploit the resources at the socially desirable rate? We hope to show that the role of natural resources in the economy does lead to alterations in the conventional, Keynesian, policy prescriptions for unemployment. We hope to show that, in the short run, a necessary (but not sufficient) condition for the efficient intertemporal allocation of non-renewable natural resource, the Hotelling principle, will not be satisfied, and that the economy will tend towards a state which cannot be intertemporally optimal.

Almost all of the theoretical economic analyses of resource economics have been micro-economic in nature: in the past four years there have been many efforts to extend and apply the principles of micro-economic theory to the discovery, extraction, and utilization of natural resources. In particular there have been several studies on optimal growth in an economy including exhaustible natural resources. In such a study, the long-run stability has been examined by Stiglitz (1974b), who considers an economy moving along an equilibrium path along which expectations about future prices are realized and along which markets clear at every moment. He shows that without a complete set of futures markets extending infinitely into the future there is no economic mechanism to guarantee that the initial price will be set so that the economy converges to balanced growth: if the initial price of natural resource is set too low the resource stock will be used up in a finite time; if the initial price is set too high there is always a finite amount of resource stock remaining—an inefficient situation with over-saving of resource. Stiglitz also shows that, unlike the heterogeneous capital growth model, the natural resource model exhibits long-run instability with even slow rates of adaptive expectation formation of the rate of change of resource price.

But this analysis is made with the assumption that the economy is in equilibrium with markets clearing at every “moment,” where each moment is vanishingly short so that a continuous analysis can be made. In particular, the explicit assumption is made that the asset market (including stocks of non-renewable natural resource) is in equilibrium so that the return on holding stocks of natural resources (the proportional change of resource price, net of extraction costs) is equal to the rate of return on other assets (the interest rate). This, briefly stated, is the Hotelling principle. If all markets clear, what leads to the change of resource price? Traditionally we have considered prices to change in response to an imbalance of supply and demand. We shall look more closely at this question in Chapter V.

Short-run stability is concerned with perturbations around the long-run path: if the economy suffers a shock exogenous to the model (such as a change in price expectation formation, or a change in household saving behaviour, or a new discovery of resource, or a change in government policy, or a change in production technology), will equilibrium (in the sense of markets clearing with expectations realized) be regained, and if so will the previous equilibrium path be regained? To answer these questions the short-run equilibrium must be analyzed for existence, uniqueness, and stability.

Stiglitz (1974b) suggests that it is possible in the short run that disequilibrium in the natural resource market (stemming from exogenous disturbances of the supply of resource, for instance) may be translated into disequilibria in other markets (output, asset, and labour). The consequent adjustments in these markets would affect the level of employment and the wage rate, the supply of output and the price level, and the rate of investment and the interest rate.

The linkage between the natural resource market and the asset market could be the cause of a knife-edge instability. With perfectly competitive markets we should expect the price of the flow of resources to equal the price of the stock of resources. The knife-edge occurs when people's expectations of the rate change of the resource price change: if the expected proportional rate of change of resource price exceeds the interest rate, and if this situation is expected to continue, then traders in the asset market will attempt to increase their stocks of resources. This increase in the demand for stocks will lead to a greater increase in the resource price than would have occurred before, and since traders' expectations are fulfilled they will continue to view resource stocks as a better investment than other assets. At the same time there may be an effect downwards on the interest rate: the increase in resource price will lead to a substitution away from resource flow as a factor input, towards men and machines, which will lead to a change in the utilization of machines and hence to a change in the marginal and average products of capital, in turn leading to a change in the interest rate. If the final effect on the interest rate is downwards then there is even stronger stimulus to hold stocks of resources, and the disequilibrium is exacerbated—hence the knife-edge.

This problem is similar to other speculative “bubbles,” and is similar too to the Hahn problem which occurs with heterogeneous capital goods: if the price of one capital good were initially set “too high,” the price of the asset would have to rise faster, for market-clearing of the particular capital good, than it would if the price were lower, to offset the lower value of the rentals per dollar invested. Thus in the next period the price would be even further “out of line.” One motivation for the following work has been to attempt to build an analytical model to study this behaviour. Insight into possible linkages in the economy between the supply schedule of the natural resource and the adjustments of the markets for output and labour will lead to more effective policy prescriptions; and the work will more fully integrate natural resources into short-run macroeconomic theory.

Since the analysis is concerned with disequilibrium interactions among such macroeconomic variables as output, employment, and inflation, the final model will include four markets: a market for output, a market for labour services, a market for the resource, and a market for assets. Corresponding to these four markets there will be four prices: a money price of output, a money wage, a money price of resource, and an interest rate.

1.2. Disequilibrium adjustment with non-market-clearing trading.

In order to examine the interaction of the markets during the disequilibrium adjustment, the assumption of no non-market-clearing trading will be relaxed. This traditional assumption has been explained by two equivalent descriptions of price determination: either that prices adjust to excess demands instantaneously, or that prices are determined by a Walrasian tatonnement process (or Edgeworthian recontract-ing process) in which no production or exchange occur until the equilibrium price vector is reached. The alternative assumption will be made that prices do not adjust instantaneously, but that production and exchange can occur at “false” (that is, non-market-clearing) prices.

As Hicks (1946) argues, trading at “false” prices leads to income effects, which will only be negligible if all traders' expenditures on a good are only a small part of their total incomes, with the market ending up very close to the equilibrium price. But in an aggregate macro model these expenditures will not be small in relation to each economic actor's total income, and the income effects from trading at “false” prices will affect the final market price, and will have to be included in the model. Realization of this leads to Clower's (1965) “dual decision hypothesis” formulation of “income-constrained” processes, in which income as well as prices is an argument in each trader's demand (supply) function. Clower speaks of “notional” demand and supply schedules with no quantity constraints (no non-market-clearing trading), and “effective” schedules which include the quantity constraints which result from non-market-clearing trading. (The Keynesian aggregate demand function is an example of an effective demand schedule: income, as well as prices, is an argument.) Leijonhufvud (1968) stresses that income-constrained processes result whenever the speed of price adjustment is less than infinite. Thus analysis of disequilibrium adjustment requires both price and quantity adjustments.

Four markets lead to four prices and four quantities. A general disequilibrium analysis would involve explicit adjustments in these eight variables. In fact Solow and Stiglitz (1968) describe a disequilibrium macro model with explicit adjustments for employment, the money wage, and the money price of output. They define short-run equilibrium as occurring when the level of employment and the real wage rate are constant, a definition which includes not only the conventional equilibrium with all variables constant, but also Hansen's (1951) “quasi-equilibrium” in which real prices are constant but money prices are changing at equal proportional rates, with (positive or negative) excess demand resulting from lack of market clearing. But the technical problems of eight separate adjustment processes are great, and it is possible to reduce the number of independent adjustments without destroying the essential disequilibrium nature of the model.

The complexity of continuous adjustment models is a great incentive to adopt a discrete treatment of time into “periods,” which requires a qualitative ranking of the adjustment speeds of the variables in the system. It is then convenient to treat variables adjusting relatively slowly as data, and to treat variables adjusting relatively rapidly as having worked out their effects. Thus the explicit adjustment processes are reduced to those of interest only. The model to be developed below makes the assumption that quantities adjust infinitely faster than prices, which Leijonhufvud (1968) asserts is the “revolutionary” element in Keynes’ General Theory. With this assumption, in an ultra-short-run period or “momentary situation,” all prices are given, and on the basis of these prices all plans are formulated and quantities adjust on each market according to derived rules. If at the given prices there are non-zero excess demands, then price changes will be generated at the transition from one momentary situation to the next, in which the new set of prices will lead to formulation of a new set of plans and a new set of quantities. Following Korliras (1973) and Benassy (1973), in the “short-run” period of explicit analysis price changes are accompanied by instantaneous adjustments in quantities and plans which can thus be derived from current prices.

The earliest disequilibrium models were developed by Patinkin and Clower. Patinkin (1965) analyses the demand for labour in the situation where there is an excess supply of output: demand for labour is reduced and the possibility of involuntary unemployment is introduced, associated with excess (effective) labour supply. Clower (1965) analyses the other side of the coin: the demand for output and the demand for money balances subject to an employment constraint to derive effective demand functions of the same form as the usual Keynesian consumption and saving functions. These two complementary models have been brought together by Barro and Grossman (1971) and (1976).

At a higher level of abstraction, Benassy (1973) has formalized disequilibrium economics to the level of the Arrow-Debreu model of equilibrium economics. He makes the “Keynesian” assumption of instantané-ous quantity adjustment and relatively slow price adjustment, and defines a “K-equilibrium” for a set of prices as a situation in which quantities have no tendency to move, more precisely a set of self-reproducing effective demands, which generate “perceived” constraints which in turn will generate the original set of effective demands. A simplified Keynesian model is built to examine the stagflation, deflation, and inflation. Price movements in response to effective excess demands follow with an examination of long-run dynamics and the Phillips curve. Benassy extends the analysis with a chapter on monopolistic competition and finally an economy with an uncertain future and where money links successive equilibria only as a store of value.

1.3. The basic assumptions.

In order to analyse the short-run disequilibrium adjustments of economy including non-renewable natural resource, we have formulated a basic model. The model includes three goods: labour services, a homogeneous output, and resource. There are three types of economic actor: firms, households, and resource suppliers. The labour services and resources are the two variable inputs in the production process: other inputs are fixed in the short-run, and have no alternative use and zero user cost. All current output is produced by the same technology, and can be considered to assume its specific identity according to the buyer: firms buy investment goods and households buy consumables. Monetary factors are ignored: it is assumed that the monetary authorities manage to keep the real rate of interest constant, and that the monetary variables do not influence aggregate demand. Firms demand labour and resource and supply homogeneous output. Firms are assumed to maximize profits, which can be considered as a return to non-variable inputs, of which each firm possesses a predetermined and fixed amount. Households supply labour. They demand consumables from firms and savings balances. They receive income from the sale of labour services, from the sale of resources, and from profits, all of which accrue only to households. It is assumed that the household decision to save can be characterized by the standard assumption of constant and equal marginal and average propensities to save out of income. The government taxes households' gross income and buys homogeneous output. In the basic model, resource flow and labour services are treated symmetrically.

The basic model is first analysed for the case in which no non-market-clearing trading occurs, that is, for the recontracting or tatonnement case. The analysis, following that of Barro and Grossman (1976) for a single variable factor input, considers comparative statics and dynamic stability of the market-clearing equilibrium that occurs with notional supply and demand schedules. In contrast the model is then analysed for the case of non-market-clearing trading, in which trading occurs during the adjustment process and effective supply and demand schedules result.

Dropping the assumption of trading only at market clearing has two essential implications for the determination of the quantities supplied and demanded. First, the quantities traded cannot be determined simply with reference to market-clearing conditions. There is no equivalence between actual transactions and the quantities supplied and demanded. In order to analyse quantity determination under non-market-clearing conditions, the actual trading process must be examined. The model includes the assumption of “voluntary exchange”: no economic actor can be forced to buy more than he demands or sell more than he supplies. Consequently, the actual level of total transactions will be determined by the “short” side of the market (that is, by suppliers if there is excess demand, by demanders if excess supply), and economic actors on the “long” side will be constrained in their transactions.

These constraints lead to the second implication: not every economic actor will generally act as if he can buy or sell any amount which he demands or supplies at the existing price vector. In particular, economic actors on the “long” side of the market (that is, suppliers if excess supply, demanders if excess demand) will face quantity constraints on their transactions, to be taken into account when formulating their supplies and demands on other markets, leading to effective schedules. The notional schedules derived in a market-clearing model do not in general describe the economic behaviour of firms and households in a disequilibrium model (unless the economic actor finds himself on the “short” side of every market). The economic actor must derive his demand (supply) functions taking into account fully the information about the other markets.

In this model with three markets and instantaneous quantity adjustments, two state variables can be derived: the real wage (w) and the real resource price (v). Analysis of the model at all points in the positive quadrant of the (w, v) plane leads to eight regions in which various combinations of markets clear. These eight regions can be shown to correspond to four categories of Keynesian short-run equilibria. Thus macro behaviour has been derived from a model with profit-maximizing representative firms. The next step is to allow the prices in the three markets to adjust, using some function of the excess demands on the markets to determine the possibility of equilibria or quasi-equilibria. These can then be analyzed for stability. The models can be analysed for the comparative statics of the equilibria as the system is shocked by the changes in exogenous parameters. The model treats resource flow and labour services symmetrically.

An extension of the basic model allows the non-renewable nature of the natural resource to be included. A fourth market, that for assets, is introduced, on which stocks of non-renewable resource can be traded. The Hotelling principle, with the proportional rate of change of resource price rising at the rate of return of other assets, the interest rate, is a description of equilibrium on the asset market. We do not analyse the asset market explicitly, but assume that resource owners atte...

Table of contents

• Cover Page
• Half Title
• Title Page
• Copyright Page
• Table of Contents
• Chapter One: Introduction
• Chapter Two: The Basic Model
• Chapter Three: A Simple Fix-Price Disequilibrium Model
• Chapter Four: Price Adjustments in the Disequilibrium Model
• Chapter Five: Expectations and the Supply of Resource Flow
• Chapter Six: Conclusion
• References
• Appendix A1
• Appendix B1
• Appendix C1
• Appendix D1
• Index of Names