An Expanded Multiplier-Accelerator Model

Todorova, Tamara and Kutrolli, Marin (2019): An Expanded Multiplier-Accelerator Model. Published in: Journal of Economics and Political Economy , Vol. 6, No. 4 (1 December 2019): pp. 368-382.

Abstract

This paper revisits the standard multiplier-accelerator model, as advanced by Samuelson. While borrowing on the main assumptions of the multiplier-accelerator, we check the validity of Keynesian theory. Using higher-order difference equations and advanced-level mathematical techniques we solve the tax-augmented multiplier-accelerator model, as well as the open economy one. We find that the values of equilibrium national income are identical to the simple national-income model in the absence of the accelerator. We solve the simple multiplier-accelerator model both in present terms and with prolonged consumption. We solve for equilibrium consumption, tax, and imports which are unaffected by the accelerator. All results conform to Keynesian theory where investment, government spending and exports have a favorable multiplying effect on national income through their respective multipliers. The accelerator coefficient affects neither those multipliers, nor the income and the non-income tax multipliers. Expanding the multiplier-accelerator by the volume of foreign trade, taxation or both does not change the values of Keynesian variables. Adding an accelerator leaves optimal values unaffected but, more importantly, reinforces Keynesian theory.

• Item Type: MPRA Paper
• Language: English
• Keywords: multiplier; accelerator; open economy; difference equations; Keynesian national-income model; tax multiplier; exports multiplier
• Subjects: C - Mathematical and Quantitative Methods > C6 - Mathematical Methods ; Programming Models ; Mathematical and Simulation Modeling > C65 - Miscellaneous Mathematical Tools; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E21 - Consumption ; Saving ; Wealth; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E22 - Investment ; Capital ; Intangible Capital ; Capacity

References

Bruno, M., & Sachs, J. D. (1985). Economics of Worldwide Stagflation. Cambridge: Harvard University Press.

Devarajan, S., & Go, D. S. (1998). The simplest dynamic general-equilibrium model of an open economy. Journal of Policy Modeling, 20(6), 677-714. doi.org/10.1016/S0161-8938(98)00011-8.

Friedman, M., & Schwartz, A. J. (1963). Money and business cycles. Review of Economics and Statistics, 45(2), 32-64.

Harris, R. (1984). Applied general equilibrium analysis of small open economies with scale economies and imperfect competition. American Economic Review, 74(5), 1016-1032.

Harrod, R. F. (1936). The Trade Cycle: An Essay. Oxford: Clarendon Press.

Harrod, R. F. (1939). An essay in dynamic theory. Economic Journal, 49(193), 14-33.

Matsumoto, A., & Szidarovszky, F. (2015). Nonlinear multiplier-accelerator model with investment and consumption delays. Structural Change and Economic Dynamics, 33(C), 1-9. doi. 10.1016/j.strueco.2015.01.003.

Puu, T., Gardini, L., & Sushko, I. (2005). A Hicksian multiplier-accelerator model with floor determined by capital stock. Journal of Economic Behavior and Organization, 56(3), 331-348. doi.org/10.1016/j.jebo.2003.10.008.

Samuelson, P. A. (1939). Interactions between the multiplier analysis and the principles of acceleration. Review of Economic Statistics, 21, 75-78.

Westerhoff, F. (2006). Samuelson's multiplier-accelerator model revisited. Applied Economics Letters, 13(2), 89-92. doi. 10.1080/13504850500390663.