The determination of the price of capital goods: A differential game approach

Guerrazzi, Marco and Candido, Giuseppe (2023): The determination of the price of capital goods: A differential game approach.

Abstract

In this paper, building upon a q-model of investment with adjustment costs, we address the strategic determinants of the price of newly installed productive capacity. Specifically, we develop a differential game in which a competitive producer of consumption goods deals with a seller of capital goods endowed with market power. From a theoretical perspective, we show that an open-loop Stackelberg equilibrium with non-cooperative features requires the producer of consumption goods to be more impatient than the seller of capital goods. Thereafter, relying on some numerical simulations, we show that our theoretical setting is able to replicate the countercyclical pattern of the relative price of capital goods as well as its negative relationship with the investment-output ratio.

• Item Type: MPRA Paper
• Language: English
• Keywords: Price of capital goods; Tobin's q; Internal and external adjustment costs; Differential games.
• Subjects: C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C72 - Noncooperative Games; D - Microeconomics > D2 - Production and Organizations > D24 - Production ; Cost ; Capital ; Capital, Total Factor, and Multifactor Productivity ; Capacity; E - Macroeconomics and Monetary Economics > E2 - Consumption, Saving, Production, Investment, Labor Markets, and Informal Economy > E22 - Investment ; Capital ; Intangible Capital ; Capacity; G - Financial Economics > G3 - Corporate Finance and Governance > G31 - Capital Budgeting ; Fixed Investment and Inventory Studies ; Capacity

References

Alogoskoufis, G. (2019), Dynamic Macroeconomics, MIT Press: Cambridge, MA.

Andrei, D., Mann, W., Moyen, N. (2019), Why Did the q Theory of Investment Start Working?, Journal of Financial Economics, Vol. 133, No. 2, pp. 251-272.

Basar, T., Olsder, G.J. (1999), Dynamic Noncooperative Game Theory, Second Edition, SIAM Classic in Applied Mathematics, No. 23, New York.

Beaudry, P., Moura, A., Portier, F. (2015), Reexamining the Cyclical Behavior of the Relative Price of Investment, Economics Letters, Vol. 135, No. C, pp. 108-111.

Bosi, S., Desmarchelier, D. (2019), Local Bifurcations of Three and Four-Dimensional Systems: A Tractable Characterization with Economic Applications, Mathematical Social Sciences, Vol. 97, No. C, pp. 38-50.

Bressan, A., Jiang, Y. (2020), Self-Consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games, Dynamic Games and Applications, Vol. 10, No. 2, pp. 328-360.

Carlsson, B. (1983), The Machine Tool Industry: Problems and Prospects in an International Perspective, Working Paper Series of the Research Institute of Industrial Economics, No. 96.

Calvo, G.A., (1978), On the Consistency of Optimal Policy in a Monetary Economy, Econometrica, Vol. 46, No., pp. 1411-1428.

Cass, D. (1966), Optimum Growth in an Aggregative Model of Capital Accumulation: A Turnpike Theorem, Econometrica, Vol. 34, No. 4, pp. 833-850.

Chen, J-L. (2018), Status Quo and Development of Cutting Tool Industry in Taiwan and China, International Business Research, Vol. 11, No. 8, pp. 90-96.

Christiano, L.J., Fisher, J.D.M. (2003), Stock Market and Investment Goods Prices: Implications for Macroeconomics, NBER Working Paper Series, No. 10031.

Cooper, R.W., Haltiwanger, J.C. (2006), On the Nature of Capital Adjustment Costs, Review of Economic Studies, Vol. 73, No. 3, pp. 611-633.

Cooper, R.W., Ejarque, J.M. (2003), Financial Frictions and Investment: Requiem in Q, Review of Economic Dynamics, Vol. 6, No. 4, pp. 710-728.

Cui, W. (2022), Macroeconomic Effects of Delayed Capital Liquidation, Journal of the European Economic Association, Vol. 20, No. 4, pp. 1683-1742.

Cummis, J.G., Hassett, K.A., Hubbard, R.G. (1994), A Reconsideration of Investment Behavior Using Tax Reforms as Natural Experiments, Brookings Papers on Economic Activity, Vol. 1994, No. 2, pp. 1-74.

Dinopoulos, E., Kreinin, M.E. (1991), The US VER on Machine Tools: Causes and Effects, in Baldwin, R.E. (ed.), Empirical Studies of Commercial Policy, University of Chicago Press: Chicago, pp. 113 -134.

Dockner, E., Jorgensen, S., Van Long, N., Sorger, G. (2000), Differential Games in Economics and Management Science, Cambridge University Press: New York.

Eaton, J., Kortum, S. (2001), Trade in Capital Goods, European Economic Review, Vol. 45, No. 7, pp. 1195-1235.

Eisner, R., Strotz, R.H. (1963), Determinants of Business Fixed Investment, in Commission on Money and Credit, Impacts of Monetary Policy, Englewood Cliffs, NJ: Prentice Hall, pp. 59-337.

Estevadeordal, A., Taylor, A.M. (2013), Is the Washington Consensus Dead? Growth, Openness, and the Great Liberalization, 1970s-2000s, Review of Economics and Statistics, Vol. 95, No. 5, pp. 1669-1690.

Fisher, J.D.M. (2006), The Dynamic Effects of Neutral and Investment-Specific Technology Shocks, Journal of Political Economy, Vol. 114, No. 3, pp. 413-451.

Fransman, M. (1986), International Competitiveness, Technical Change and the State: The Machine Tool Industry in Taiwan and Japan, World Development, Vol. 14, No. 12, pp. 1375-1396.

Foley, D.K., Sidrauski, M. (1970), Portfolio Choice, Investment and Growth, American Economic Review, Vol. 60, No. 1, pp. 44-63.

Fuchs, W., Green, B., Papanikolaou, D. (2016), Adverse Selection, Slow-Moving Capital, and Misallocation, Journal of Financial Economics, Vol. 120, No. 2, pp. 286-308.

Gomme, P., Lkhagvasuren, D. (2013), Calibration and Simulation of DSGE Models, in Hashimzade, N., Thornton, M.A. (ed.s), Handbook of Research Methods and Applications in Empirical Macroeconomics, Cheltenham (UK): Edward Elgar Publishing, pp. 575-592.

Gould, J.P. (1968), Adjustment Costs in the Theory of Investment of the Firm, Review of Economic Studies, Vol. 35, No. 1, pp. 47-55.

Greenwood, J., Hercowitz, Z., Krusell, P. (1997), Long-Run Implications of Investment-Specific Technological Change, American Economic Review, Vol. 87, No. 3, pp. 342-362.

Guerrazzi, M. (2023), Optimal Growth with Labor Market Frictions, International Journal of Economic Theory, Vol. 19, No. 4, pp. 961-987.

Guerrazzi, M. (2020), Wage and Employment Determination in a Dynamic Insider-Outsider Model, Evolutionary and Institutional Economics Review, Vol. 17, No. 1, pp. 1-23.

Guerrazzi, M. (2011), Wage Bargaining as an Optimal Control Problem: A Dynamic Version of the Right-to-Manage Model, Optimal Control Applications and Methods, Vol. 32, No. 5, pp. 505-526.

Hayashi, F. (1982), Tobin's Marginal q and Average q: A Neoclassical Interpretation, Econometrica, Vol. 50, No. 1, pp. 213-224.

Huber, K., Gormsen, N.J. (2023), Corporate Discount Rates, CEPR Discussion Papers, No. 18221.

Hunemberg, R., Huttman, A. (2003), Performance as a Basis for Price-setting in the Capital Goods Industry: Concepts and Empirical Evidence, European Management Journal, Vol. 21, No. 6, pp. 717-730.

Itskhoki, O., Moll, B. (2019), Optimal Development Policies with Financial Frictions, Econometrica, Vol. 87, No. 1, pp.139-173.

Justiniano, A., Primiceri, G.E., Tambalotti, A. (2011), Investment Shocks and the Relative Price of Investment, Review of Economic Dynamics, Vol. 14, No. 1, pp. 102-121.

Keynes, J.M. (1936), The General Theory of Employment, Interest and Money, London: MacMillan and Company.

Kim, Y-Z., Lee, K. (2008) Sectoral Innovation System and a Technological Catch-up: The Case of the Capital Goods Industry in Korea, Global Economic Review, Vol. 37, No. 2, pp. 135-155.

Kultti, K. (2021), Monopoly and Demand Uncertainty, Research in Economics, Vol. 75, No. 4, pp. 354-364.

Kydland, F.E., Prescott, E.C. (1982), Time to Build and Aggregate Fluctuations, Econometrica, Vol. 50, No. 6, pp. 1345-1370.

Lambertini, L. (2018), Differential Games in Industrial Economics, Cambridge University Press: New York.

Lian, W.,Novta, N., Pugacheva, E., Timmer, Y., Topalova, P. (2020), The Price of Capital Goods: A Driver of Investment Under Threat, IMF Economic Review, Vol. 68, No. 3, pp. 509-549.

Lipton, D., Poterba, J., Sachs, J., Summers, L. (1982), Multiple Shooting in Rational Expectations Models, Econometrica, Vol. 50, No. 5, pp. 1329-1333.

Lucas, R.E., Jr. (1967), Adjustment Costs and the Theory of Supply, Journal of Political Economy, Vol. 75, No. 4, pp. 321 334.

Mino, K. (1987), A Model of Investment with External Adjustment Costs, Economic Studies Quarterly, Vol. 38, No. 1, pp. 76-85.

Mutreja, P., Ravikumar, B., Sposi, M. (2018), Capital Goods Trade, Relative Prices, and Economic Development, Review of Economic Dynamics, Vol. 27, pp. 101-122.

Restuccia, D., Urrutia, C. (2001), Relative Prices and Investment Rates, Journal of Monetary Economics, Vol. 47, No. 1, pp. 93-121. Rubinstein, A. (1982), Perfect Equilibrium in a Bargaining Model, Econometrica, Vol. 50, No. 1, pp. 97-109.

Summers, L.H. (1981), Taxation and Corporate Investment: A q-Theory Approach, Brookings Papers on Economic Activity, No. 1, pp. 67-127.

Stanula, P., Praetzas, C., Kohn, O., Metternich, J., Weigold, M., Buchwald, A. (2020), Stress-Oriented, Data-Based Payment Model for Machine Tools, Procedia CIRP, Vol. 93, pp. 1526-1531.

van der Ploeg, F. (1987), Trade Unions, Investment and Employment. A Non-Cooperative Approach, European Economic Review, Vol. 31, No. 7, pp. 1465-1492.

Yoshikawa, H. (1980), On the "q" Theory of Investment, American Economic Review, Vol. 70, No. 4, pp. 739-743.