Abstract
Starting with a simple Robinson Crusoe economy, then adding in sequence one, then many random variables, we consider the effect of an innovation in the means of production. We then consider a many-agent economy that utilizes money. The success of the innovation for Crusoe depends on the availability of physical goods, his decisions, and chance. The success of innovation in a money-utilizing, many-person economy depends on financing and the locus of financial control, as well as the amount of resources invested and on one or more random events. The coordination and guidance problems posed by the latter are orders of magnitude more difficult than the former. Utilizing a parallel dynamic programming approach, we present models for which the insights of Schumpeter are consistent with the observations of general equilibrium but involve a complex vista of a dynamic economy with finance and incomplete markets and a recognition of the coordination problems irrelevant to general equilibrium theory. Our simple mathematical models illustrate the breaking of the circular flow of income. Here we concentrate on the case where there is only one opportunity for innovation and consider the conditions for the emergence of a new equilibrium. When innovation may take place at any period, the outcome to any individual becomes path dependent. History counts and financial guidance is critical. We limit our modeling of the financial structure to a central bank.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsNotes
- 1.
Although he may find accounting useful as an aide memoire, and with a stretch of the imagination, could set up a virtual market to calculate virtual prices for himself.
- 2.
Prices will depend on details of initial conditions and asset structure as well as default and issue conditions.
- 3.
A work which is in considerable agreement in spirit but different in technique is that of Godely and Lavoie (2007) heavily devoted to a balance sheet and transaction flow model of the monetary and financial control system of a modern economy. This work utilizes simulations and is far closer to applied macroeconomic problems. It also stresses Kaldor’s concern with the tendency of economic theorizing to gloss over the difficulties inherent in differentiating stocks from flows.
- 4.
We have also dealt elsewhere (Shubik and Sudderth (2011)) with equilibrium in an open monetary economy with innovation. An open economy model ignores detailed feedbacks to small individuals. It serves to study partial equilibrium possibilities.
- 5.
The justification for the acceptance of reserve ratio banking is in the dynamics along with acceptance of fiat [see, for example, Bak et al. (1999)].
- 6.
Central bank reserves in a fiat money economy are a creation of law and possibly economic theology. Mathematically, they are just societal rules of the game or an algorithm stating how the central bank can create money. They specify its strategy set. In actuality, the strategy set is also bounded by political pressures.
- 7.
In general, central banks do not accept deposits from natural persons, but for modeling simplicity here we permit them to do so.
- 8.
The term “cash-in-advance” is misleading when combined with a finite grid size where no attention is given to how long the time interval is meant to be. The key item of importance is the recognition that individuals form prices. They are only given prior prices, and how these are to be utilized is a matter of behavioral specification.
- 9.
This reflects the payment of the 100 % dividend, the timing of which is irrelevant in a perfect credit rating competitive economy.
- 10.
In a less Draconian abstraction, the difference between retirees and capitalists is not merely age, but expertise. The role of competent financing as a perception and evaluating device cannot be overstressed.
- 11.
In institutional fact, a large firm has a considerable constituency of customers, employees, the government, and others, as well as the owners.
- 12.
Of course, the proportion ν has to be strictly less than one; for otherwise, there is no one to engage in productive activity, own the firms, or receive their profits, and the model unravels.
- 13.
These are crude approximations based on the Statistical Abstract of the United States for GNP, amount and age of capital, and Cobb–Douglass production.
- 14.
Bankruptcy in a basic way is similar to innovation in the sense that it involves a nonequilibrium redeployment of assets.
- 15.
The full justification and fleshing out of these comments requires a book length manuscript and such an almost completed manuscript exists at this time enlarging on all the points noted here (Shubik and Smith 2016).
References
Angerer, M., Huber, J., Shubik, M., Sunder, S.: An economy with personal currency: theory and experimental evidence. Ann. Finance 6 (4), 475–509 (2010)
Bak, P., Nørrelykke, S.F., Shubik, M.: Dynamics of money. Phys. Rev. E 60 (3), 2528–2532 (1999)
Baumol, W.J.: The Free-Market Innovation Machine. Princeton University Press, Princeton (2002)
Bechtel, S.D., et al.: Managing innovation. Deadelus 125 (2), 147–166 (1996)
Bewley, T.F.: An integration of equilibrium theory and turnpike theory. J. Math. Econ. 10, 233–268 (1982)
Boldrin, M., Levine, D.K.: Perfectly competitive innovation. J. Monetary Econ. 55 (3), 435–453 (2008)
Caiaini, A., Godin, A., Lucarelli, S.: A stock flow consistent analysis of a Schumpeterian innovation economy. Metroeconomica 65 (3), 397–429 (2013)
Day, R.H.: Bounded rationality and the co-evolution of market and state. In: Day, R.H., Eliasson, G., Wilborg, C. (eds.) The Markets for Innovation, Ownership and Control. North-Holland, Amsterdam and New York (1993)
Day, R.H., Eliasson, G., Wilborg, C.: The Markets for Innovation, Ownership and Control. North-Holland, Amsterdam and New York (1993)
Dosi, G., Freeman, C., Nelson, R., Silverberg, G., Soete, L.: Technical Change and Economic Theory. Pinter, London and New York (1988)
Dosi, G., Fagiolo, G., Napolitano, M., Rovertini, A.: Income distribution, credit and income policies in an agent-based Keynesian model. J. Econ. Dyn. Control. 37, 1748–1767 (2013)
Godely, W., Lavoie, M.: Monetary Economics: An Integrated Approach to Credit, Money, Income, Production and Wealth. Palgrave, MacMillan, New York (2007)
Karatzas, I., Shubik, M., Sudderth, W.: Construction of stationary Markov equilibria in a strategic market game. Math. Oper. Res. 19, 975–1006 (1994)
Karatzas, I., Shubik, M., Sudderth, W.: Production, interest, and saving in deterministic economies with additive endowments. Econ. Theory 29 (3), 525–548 (2006)
Keynes, J.M.: The General Theory of Employment, Interest and Money. MacMillan, London ((1936) 1957). Reprint
Kirman, A.P.: Whom or what does the representative agent represent? J. Econ. Perspect. 6, 117–136 (1992)
Koopmans, T.C.: Concepts of optimality and their uses. Am. Econ. Rev. 67 (3), 261–274 (1977)
Lamoreaux, N., Sokoloff, K.L. (eds.): Financing Innovation in the United States: 1870 to the Present. MIT Press, Cambridge (2007)
Levhari, D., Srinivasan, T.N.: Optimal savings under uncertainty. Rev. Econ. Stud. XXXVI(2), 153–163 (1969)
Lucas, R.W.: Nobel lecture: monetary neutrality. J. Pol. Econ. 104, 661–682 (1996)
Minsky, H.: Stabilizing an Unstable Economy. Yale University Press, New Haven, CT (1986)
Nelson, R.: The Sources of Economic Growth. Harvard University Press, Cambridge (1996)
Nelson, R.R., Winter, S.G.: An Evolutionary Theory of Economic Change. Harvard, Belknap, Cambridge (1982)
Schumpeter, J.A.: The Theory of Economic Development. Harvard University Press, Cambridge (1934). Original in German 1911
Schumpeter, J.A.: Business Cycles. Mcgraw-Hill, London (1939)
Shubik, M.: Innovation and equilibrium. In: Papadimitriou, D., Wray, L.R. (eds.): The Elgar Companion to Hyman Minsky, pp. 153–168. Edward Elgar Publishing, Northampton, MA (2010)
Shubik, M., Smith, E.: The Guidance of a Enterprise Economy. M.I.T. Press, Cambridge (2016)
Shubik, M., Sudderth, W.: Cost innovation, Schumpeter and equilibrium. Part 1. Cowles Foundation Discussion Paper 1786 (2011)
Thompson, G.L., Shubik, M.: Games of economic survival. Nav. Res. Logist. Q. 6 (2), 111–123 (1959)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Shubik, M., Sudderth, W.D. (2016). Breaking the Circular Flow: A Dynamic Programming Approach to Schumpeter. In: Pinto, A., Accinelli Gamba, E., Yannacopoulos, A., Hervés-Beloso, C. (eds) Trends in Mathematical Economics. Springer, Cham. https://doi.org/10.1007/978-3-319-32543-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-319-32543-9_1
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-32541-5
Online ISBN: 978-3-319-32543-9
eBook Packages: Economics and FinanceEconomics and Finance (R0)