Initial Capital Stock Research Articles

A sensitivity analysis on optimal economic growth

A model of capital accumulation is considered and the relation between the optimal path and the initial capital stock is analyzed. Mathematically speaking, the model is a convex model of infinite horizon in continuous time. The existence of optimal paths of capital accumulation is proved. By using the continuity of the value function, it is proved that the optimal path of capital accumulation is a continuous function of the initial capital stock. The analysis is so general that neither the smoothness of the model nor the interiority of the optimal path are made.

The socialist labor-managed firm and bank-financed investment: Some theoretical issues

Under a labor-managed system of the Yugoslav type of 1965–1971, the process of capital formation is subject to special difficulties, linked to the structure of property rights. Workers possess neither permanent nor transferable claims on capital assets but are, nevertheless, required by law to maintain the value of the firm's initial capital stock and of any additions to it. The law is intended to protect the nation's capital stock but is ill designed for this purpose. Its immediate effect is to reduce the collective's willingness to undertake bank-financed investment, and thus it promotes inefficient intertemporal allocation.

Two Theorems on Generalized Diminishing Returns and their Applications to Economic Analysis*

Under certain weak assumptions such as free disposal and non‐satiety, it is shown that the concavity of utility and of technology implies that the maximum value of the set of all attainable programmes is a concave function of the initial capital stocks. For time‐independent problems, this implies that along an optimal path, as a capital stock is accumulated, its shadow price falls. The usefulness of the theorems is demonstrated in a number of examples, including Kemp's cake‐eating problem and Forster's pollution‐control problem.

Optimal growth with depletable resources

Optimal growth trajectories for Cobb-Douglas economies facing a depletable resource constraint and possessing a utilitarian objective function are examined. It is shown that for a large enough discount factor, there exists a locus of initial ‘balanced endowments’ from which the ‘balanced endowments trajectory’ is characterized by linear closed-loop optimal controls and exponentially growing or decaying economic activity. The rate of technical progress requisite to assure continual per capita economic growth is derived. Optimal solutions from arbitrary endowments are characterized. If a balanced endowments trajectory exists, then the optimal path from arbitrary initial capital and resource stocks converges monotonically to a balanced endowments trajectory. Initial endowments of capital and the resource both influence the long-run levels of economic activity, although not the long-run growth rates. The comparative magnitude of the elasticity of marginal utility and capital's share of output are critical in determining whether a larger initial capital stock leads to greater or smaller levels of long-run economic activity, but increases in the resource stock always lead to long-run increases in economic activity.

Some Notes on Time Inconsistency and Rawls' Maximin Criterion

In a recent paper Dasgupta [3] has neatly demonstrated that the Rawlsian maximin criterion may be inadequate for problems of intergenerational justice by showing that, under some specific utility functions exhibiting altruism towards future generations, plans which are optimal from the standpoint of a given generation will not be continued by future generations even when the latter are true believers in the virtues of maximin, i.e. time inconsistency would arise. This is undoubtedly an alarming result which, if proved to be a common feature of maximin, would give us sufficient grounds to dismiss it altogether as a principle of intergenerational justice. In this paper we present some results aimed at furthering our understanding of that issue. In Section 2 we analyse the question of whether time inconsistency is possible if we make generations choose between arbitrary pairs of consumption sequences. The answer to that question is a resounding yes; in the presence of altruism-defined in a rather general way which includes as a special case the utility function employed by Dasgupta-not only is it possible to find pairs of consumption sequences where maximin proves to be time inconsistent, but we are able to show that there are infinitely many of them. On this account the results of Dasgupta get further support. In Section 3 we constrain the set of consumption sequences to be feasible according to a neoclassical technology and study time consistency of optimal plans when a generation's utility can be represented by a discounted sum of (instantaneous) utilities. This is akin to the problem analysed by Dasgupta, except that the utility function is changed as indicated above. Here the picture is drastically different: for every relevant initial capital stock, k, there is a time-consistent optimal plan. Furthermore, if k is smaller than, or equal to, Golden-Rule capital the optimum is unique. The conclusions are briefly stated in Section 4.

THE GOLDEN RULE OF ACCUMULATION UNDER ALTERNATIVE SAVINGS ASSUMPTIONS 1

IN the early 1960s several economists enunciated a result called 'the neoneo-classical theorem' or 'the golden rule of accumulation' (GR).2 This is the proposition that consumption per head is maximized on a steady state path along which the rate of profit is equal to the rate of growth. In the context of the neoclassical one-commodity model it was left to Koopmans3 and Phelps4 to elicit the rather limited optimality implications of the GR. They established that paths along which the capital to labour ratio remains permanently bounded above the GR value are inefficient in the sense that there always exists another path which, starting from the same initial capital stock, provides more consumption at some time and never less consumption. In other words they showed that it was possible to 'over-save' and therefore to have too much capital. The present note inquires into the existence and significance of GR paths in a two-commodity long run equilibrium model. More specifically the well-known Hicksian model5 together with alternative savings assumptions is examined.6 The main result is that in the multi-technique case profitmaximizing capitalists may be unable to choose a path along which the rate of profit equals the rate of growth.

Full-Time Schooling in Life-Cycle Models of Human Capital Accumulation

A reduced-form equation relating length of formal schooling to market, endowment, and parameters was derived for a lifecycle human capital accumulation model with alternative assumptions: (a) equal borrowing and lending rates and (b) no loans for human capital investment. Length of formal schooling increases when loans are unavailable. For both cases, length of formal schooling varies directly with length of work life, a Hicks-neutral ability index, and the ratio of the human capital rental rate to the price of associated inputs, and varies inversely with the discount rate, deterioration rate, and initial human capital stock.

On the Relative Stability and Optimality of Consumption in Aggregative Growth Models: A Critical Analysis

This paper stems from the recent discussion in this Journal between J. C. Liu and K. Kubota [2] and J. K. Sengupta [4]. This discussion was based on part (a) of an earlier paper by Sengupta [3], and concerned certain mathematical manipulations that had been performed there.2 To avoid repetition, we assume that the reader is acquainted with problems, arguments, notation, etc., in the above papers. In what follows we concentrate mainly on part (a) of the Sengupta paper. We argue that the discussants have missed a fundamental point. When the planning horizon is infinite, optimal paths for the Sengupta model do not always exist. Furthermore, when they do exist, we have an analogous situation to that of a static maximization problem with the solution on the boundary of the feasible set. Explicitly, we show that for a> n there exists no optimal programme, irrespective of the level of the initial capital stock, denoted by Ko. Also for a =n and Ko> 0 there exist no optimal paths. For a = n and Ko = 0 an optimal programme does exist, but optimal K(t) = 0 for all t. For a 0, we have optimal K(t) > 0 for t E [0, T), and optimal K(t) = 0 for t > T, where the value of T is determined by certain properties of the optimal paths. Our results imply that calculations of asymptotic rates, comparisons, etc., are redundant, especially when no optimal paths exist. It is well known that when the utility integral, as welfare criterion, does not converge, it does not really make sense to require that its value be maximized. Hence in what follows we order alternative feasible consumption streams employing the Weizsacker-Atsumi (W-A) criterion.3 We shall say that a path is W-A optimal if it overtakes all other feasible paths. Sengupta also refers in [4] to the need of employing the overtaking criterion when the planning horizon is infinite, but he seems to expect that this supports his argument.

Optimal Capital Accumulation by an Economy Facing an International Capital Market

Previous articleNext article No AccessOptimal Capital Accumulation by an Economy Facing an International Capital MarketKoichi HamadaKoichi Hamada Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Journal of Political Economy Volume 77, Number 4, Part 2Jul. - Aug., 1969Part 2: Symposium on the Theory of Economic Growth Article DOIhttps://doi.org/10.1086/259557 Views: 4Total views on this site Citations: 32Citations are reported from Crossref Copyright 1969 The University of ChicagoPDF download Crossref reports the following articles citing this article:Manoranjan Sahoo, Hrushikesh Mallick, Mantu Mahalik, Stelios Bekiros Factors influencing India's current account balance: Implication for achieving its external sector sustainability, Journal of Public Affairs 22, no.11 (Aug 2020).https://doi.org/10.1002/pa.2311Bhavesh Garg, K.P. 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Why Prices in Japan Do Not Rise Despite Quantitative Easing, (Oct 2019): 63–86.https://doi.org/10.1007/978-3-030-23053-1_5Anne Edle von Gaessler, Thomas Ziesemer Optimal education in times of ageing: The dependency ratio in the Uzawa–Lucas growth model, The Journal of the Economics of Ageing 7 (Apr 2016): 125–142.https://doi.org/10.1016/j.jeoa.2016.03.001Pierre-Olivier Gourinchas, Hélène Rey External Adjustment, Global Imbalances, Valuation Effects, (Jan 2014): 585–645.https://doi.org/10.1016/B978-0-444-54314-1.00010-0HYEON-SEUNG HUH, TADASHI INOUE, HYUN-HOON LEE OPTIMAL FOREIGN BORROWING REVISITED, Japanese Economic Review 61, no.33 (Aug 2010): 367–381.https://doi.org/10.1111/j.1468-5876.2009.00490.xTarlok Singh INTERTEMPORAL OPTIMIZING MODELS OF TRADE AND CURRENT ACCOUNT BALANCE: A SURVEY, Journal of Economic Surveys 21, no.11 (Feb 2007): 25–64.https://doi.org/10.1111/j.1467-6419.2007.00270.xMartin A. van Tuijl, Robert J. de Groof, Ad H.J. Kolnaar Fiscal policy and public capital in interdependent economics, Economic Modelling 14, no.22 (Apr 1997): 279–300.https://doi.org/10.1016/S0264-9993(96)01035-8Maurice Obstfeld, Kenneth Rogoff Chapter 34 The intertemporal approach to the current account, (Jan 1995): 1731–1799.https://doi.org/10.1016/S1573-4404(05)80014-0Alvaro Rodriguez Precautionary saving and the Laursen-Metzler effect, Journal of International Money and Finance 12, no.33 (Jun 1993): 332–343.https://doi.org/10.1016/0261-5606(93)90018-7Ernst Baltensperger Monetäre Außenwirtschaftstheorie, Journal of Contextual Economics – Schmollers Jahrbuch 112, no.44 (Apr 1992): 505–565.https://doi.org/10.3790/schm.112.4.505P. P. Athanasoglou, G. A. Zombanakis External Debt and Macroeconomic Policy in a Small, Open Economy: The Case of Greece, (Jan 1992): 262–295.https://doi.org/10.1007/978-1-349-22453-1_11APOSTOLIS PHILIPPOPOULOS MACROECONOMIC DYNAMICS AND OPTIMAL EXTERNAL BORROWING IN AN IMPERFECT WORLD CAPITAL MARKET, The Manchester School 59, no.11 (Mar 1991): 12–23.https://doi.org/10.1111/j.1467-9957.1991.tb00435.xNGO VAN LONG Cyclical International Capital Flows, (Jan 1991): 265–274.https://doi.org/10.1016/B978-0-12-682230-4.50018-XRichard Manning, Koon Lam Shea Perfect discrimination and the long-run national advantage, Journal of Economics Zeitschrift f�r National�konomie 49, no.33 (Oct 1989): 299–313.https://doi.org/10.1007/BF01226946PAN LONG TSAI FOREIGN INVESTMENT, TECHNOLOGY TRANSFER AND FOREIGN CAPITAL IMPACT FUNCTION, International Economic Journal 3, no.22 (Jun 1989): 43–56.https://doi.org/10.1080/10168738900080011Jonathan Eaton Chapter 25 Foreign public capital flows, (Jan 1989): 1305–1386.https://doi.org/10.1016/S1573-4471(89)02012-7 International Monetary Fund The External Debt Problem of Sub-Saharan Africa, IMF Working Papers 89, no.2323 (Jan 1989): 1.https://doi.org/10.5089/9781451921021.001CHANGHEE CHAE HAMILTONIAN APPROACHES TO THE ANALYSIS OF EXTERNAL DEBT, International Economic Journal 1, no.44 (Dec 1987): 19–33.https://doi.org/10.1080/10168738700080025Yasuoki Takagi Inflation and cumulative debt outstanding of less-developed countries, Journal of International Economics 21, no.1-21-2 (Aug 1986): 61–80.https://doi.org/10.1016/0022-1996(86)90005-XCasper van Ewijk Interest payments and the stability of the government budget deficit in an open and growing economy, De Economist 134, no.22 (Jun 1986): 143–164.https://doi.org/10.1007/BF01706286Reuven Glick, Homi J. Kharas The costs and benefits of foreign borrowing: A survey of multi‐period models, Journal of Development Studies 22, no.22 (Jan 1986): 279–299.https://doi.org/10.1080/00220388608421981Michael Carlberg External versus internal public debt — A theoretical analysis of the long-run burden, Zeitschrift für Nationalökonomie 45, no.22 (Jun 1985): 141–154.https://doi.org/10.1007/BF01284386Maurice Obstfeld, Alan C. Stockman Chapter 18 Exchange-rate dynamics, (Jan 1985): 917–977.https://doi.org/10.1016/S1573-4404(85)02009-3Eric V. Clifton The maximin objective function and less developed countries, Atlantic Economic Journal 11, no.11 (Mar 1983): 71–72.https://doi.org/10.1007/BF02301767Oded Hochman, Assaf Razin Debt and capital accumulation in a two-sector model with non-traded goods, European Economic Review 8, no.22 (Aug 1976): 165–180.https://doi.org/10.1016/0014-2921(76)90011-8Gershon Feder, Uri Regev International Loans, Direct Foreign Investment, and Optimal Capital Accumulation, Economic Record 51, no.33 (Sep 1975): 320–325.https://doi.org/10.1111/j.1475-4932.1975.tb00257.xR. Manning Wages policy and savings of conservative governments along major and minor turnpikes∗, New Zealand Economic Papers 7, no.11 (Nov 2009): 96–108.https://doi.org/10.1080/00779957309543933R. Manning Optimal Taxation when Borrowing Alters the Foreign Supply Curve for Capital, Economic Record 48, no.33 (Sep 1972): 400–410.https://doi.org/10.1111/j.1475-4932.1972.tb00787.x REFERENCES AND BIBLIOGRAPHY, (Jan 1972): 269–296.https://doi.org/10.1016/B978-0-12-691650-8.50009-3Sheng Cheng Hu OPTIMAL CAPITAL ACCUMULATION AND REGIONAL ALLOCATION, Metroeconomica 23, no.11 (Feb 1971): 16–34.https://doi.org/10.1111/j.1467-999X.1971.tb00161.xHanns Abele Über geldwirtschaftliche Wachstumsmodelle, Zeitschrift für Nationalökonomie 30, no.1-21-2 (Mar 1970): 125–158.https://doi.org/10.1007/BF01289994