IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/119118.html
   My bibliography  Save this paper

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

Author

Listed:
  • Guerrazzi, Marco
  • Candido, Giuseppe

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.

Suggested Citation

  • Guerrazzi, Marco & Candido, Giuseppe, 2023. "The determination of the price of capital goods: A differential game approach," MPRA Paper 119118, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:119118
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/119118/1/MPRA_paper_119118.pdf
    File Function: original version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Rubinstein, Ariel, 1982. "Perfect Equilibrium in a Bargaining Model," Econometrica, Econometric Society, vol. 50(1), pages 97-109, January.
    2. Alejandro Justiniano & Giorgio Primiceri & Andrea Tambalotti, 2011. "Investment Shocks and the Relative Price of Investment," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 14(1), pages 101-121, January.
    3. Calvo, Guillermo A, 1978. "On the Time Consistency of Optimal Policy in a Monetary Economy," Econometrica, Econometric Society, vol. 46(6), pages 1411-1428, November.
    4. Jonas D. M. Fisher, 2006. "The Dynamic Effects of Neutral and Investment-Specific Technology Shocks," Journal of Political Economy, University of Chicago Press, vol. 114(3), pages 413-451, June.
    5. Klaus Gugler & Dennis C. Mueller & B. Burcin Yurtoglu, 2004. "Marginal q, Tobin’s q, Cash Flow, and Investment," Southern Economic Journal, John Wiley & Sons, vol. 70(3), pages 512-531, January.
    6. Antoni Estevadeordal & Alan M. Taylor, 2013. "Is the Washington Consensus Dead? Growth, Openness, and the Great Liberalization, 1970s–2000s," The Review of Economics and Statistics, MIT Press, vol. 95(5), pages 1669-1690, December.
    7. Hergovich, Philipp & Merz, Monika, 2018. "The Price of Capital, Factor Substitutability, and Corporate Profits," IZA Discussion Papers 11791, Institute of Labor Economics (IZA).
    8. Piyusha Mutreja & Michael Sposi & B. Ravikumar, 2018. "Capital Goods Trade, Relative Prices and Economic Development," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 27, pages 101-122, January.
    9. Weicheng Lian & Natalija Novta & Evgenia Pugacheva & Yannick Timmer & Petia Topalova, 2020. "The Price of Capital Goods: A Driver of Investment Under Threat," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 68(3), pages 509-549, September.
    10. Carlsson, Bo, 1983. "The Machine Tool Industry – Problems and Prospects in an International Perspective," Working Paper Series 96, Research Institute of Industrial Economics.
    11. Jui-Lung Chen, 2018. "Status-quo and Development of Cutting-tool Industry in Taiwan and China," International Business Research, Canadian Center of Science and Education, vol. 11(8), pages 90-96, August.
    12. Niels Joachim Gormsen & Kilian Huber, 2023. "Corporate Discount Rates," NBER Working Papers 31329, National Bureau of Economic Research, Inc.
    13. Eaton, Jonathan & Kortum, Samuel, 2001. "Trade in capital goods," European Economic Review, Elsevier, vol. 45(7), pages 1195-1235.
    14. Russell W. Cooper & John C. Haltiwanger, 2006. "On the Nature of Capital Adjustment Costs," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 73(3), pages 611-633.
    15. Lambertini,Luca, 2018. "Differential Games in Industrial Economics," Cambridge Books, Cambridge University Press, number 9781107164680, December.
    16. Romano, Richard & Yildirim, Huseyin, 2005. "On the endogeneity of Cournot-Nash and Stackelberg equilibria: games of accumulation," Journal of Economic Theory, Elsevier, vol. 120(1), pages 73-107, January.
    17. Marco Guerrazzi, 2023. "Optimal growth with labor market frictions," International Journal of Economic Theory, The International Society for Economic Theory, vol. 19(4), pages 961-987, December.
    18. Bosi, Stefano & Desmarchelier, David, 2019. "Local bifurcations of three and four-dimensional systems: A tractable characterization with economic applications," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 38-50.
    19. Marco Guerrazzi, 2020. "Wage and employment determination in a dynamic insider–outsider model," Evolutionary and Institutional Economics Review, Springer, vol. 17(1), pages 1-23, January.
    20. Jason G. Cummins & Kevin A. Hassett & R. Glenn Hubbard, 1994. "A Reconsideration of Investment Behavior Using Tax Reforms as Natural Experiments," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 25(2), pages 1-74.
    21. Wei Cui, 2022. "Macroeconomic Effects of Delayed Capital Liquidation," Journal of the European Economic Association, European Economic Association, vol. 20(4), pages 1683-1742.
    22. Liao, Shushu & Nolte, Ingmar & Pawlina, Grzegorz, 2024. "Can Capital Adjustment Costs Explain the Decline in Investment–Cash Flow Sensitivity?," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 59(5), pages 2399-2424, August.
    23. Andrei, Daniel & Mann, William & Moyen, Nathalie, 2019. "Why did the q theory of investment start working?," Journal of Financial Economics, Elsevier, vol. 133(2), pages 251-272.
    24. Claudio Baccianti & Andreas Löschel, 2015. "Investment-specific versus Process Innovation in a CGE Model of Environmental Policy. WWWforEurope Working Paper No. 85," WIFO Studies, WIFO, number 57893, January.
    25. Klaus Gugler & Dennis C. Mueller & B. Burcin Yurtoglu, 2004. "Marginal q, Tobin’s q, Cash Flow, and Investment," Southern Economic Journal, Southern Economic Association, vol. 70(3), pages 512-531, January.
    26. J. P. Gould, 1968. "Adjustment Costs in the Theory of Investment of the Firm," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 35(1), pages 47-55.
    27. Robert E. Hall, 2004. "Measuring Factor Adjustment Costs," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 119(3), pages 899-927.
    28. Joao F. Gomes, 2001. "Financing Investment," American Economic Review, American Economic Association, vol. 91(5), pages 1263-1285, December.
    29. Oleg Itskhoki & Benjamin Moll, 2019. "Optimal Development Policies With Financial Frictions," Econometrica, Econometric Society, vol. 87(1), pages 139-173, January.
    30. Collins, William J. & Williamson, Jeffrey G., 2001. "Capital-Goods Prices And Investment, 1870–1950," The Journal of Economic History, Cambridge University Press, vol. 61(1), pages 59-94, March.
    31. Fuchs, William & Green, Brett & Papanikolaou, Dimitris, 2016. "Adverse selection, slow-moving capital, and misallocation," Journal of Financial Economics, Elsevier, vol. 120(2), pages 286-308.
    32. Kydland, Finn E & Prescott, Edward C, 1982. "Time to Build and Aggregate Fluctuations," Econometrica, Econometric Society, vol. 50(6), pages 1345-1370, November.
    33. Beaudry, Paul & Moura, Alban & Portier, Franck, 2015. "Reexamining the cyclical behavior of the relative price of investment," Economics Letters, Elsevier, vol. 135(C), pages 108-111.
    34. Kalafsky, Ronald V & MacPherson, Alan D, 2002. "The Competitive Characteristics of U.S. Manufacturers in the Machine Tool Industry," Small Business Economics, Springer, vol. 19(4), pages 355-369, December.
    35. Russell Cooper & Joao Ejarque, 2003. "Financial Frictions and Investment: Requiem in Q," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 6(4), pages 710-728, October.
    36. Foley, Duncan K & Sidrauski, Miguel, 1970. "Portfolio Choice, Investment and Growth," American Economic Review, American Economic Association, vol. 60(1), pages 44-63, March.
    37. Kultti, Klaus, 2021. "Monopoly and demand uncertainty," Research in Economics, Elsevier, vol. 75(4), pages 354-364.
    38. Hayashi, Fumio, 1982. "Tobin's Marginal q and Average q: A Neoclassical Interpretation," Econometrica, Econometric Society, vol. 50(1), pages 213-224, January.
    39. Tomat, Gian Maria, 2008. "Modeling the Effects of Financial Constraints on Firm's Investment," Economics - The Open-Access, Open-Assessment E-Journal (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 2, pages 1-26.
    40. Konstantin Kogan & Charles S. Tapiero, 2007. "Supply Chain Games: Operations Management And Risk Valuation," International Series in Operations Research and Management Science, Springer, number 978-0-387-72776-9, January.
    41. Restuccia, Diego & Urrutia, Carlos, 2001. "Relative prices and investment rates," Journal of Monetary Economics, Elsevier, vol. 47(1), pages 93-121, February.
    42. Yoon-Zi Kim & Keun Lee, 2008. "Sectoral Innovation System and a Technological Catch-up: The Case of the Capital Goods Industry in Korea," Global Economic Review, Taylor & Francis Journals, vol. 37(2), pages 135-155.
    43. Philipp Hergovich & Monika Merz, 2018. "The Price of Capital, Factor Substitutability and Corporate Profits," Vienna Economics Papers 1801, University of Vienna, Department of Economics.
    44. Bosi, Stefano & Desmarchelier, David, 2019. "Local bifurcations of three and four-dimensional systems: A tractable characterization with economic applications," Mathematical Social Sciences, Elsevier, vol. 97(C), pages 38-50.
    45. Lawrence H. Summers, 1981. "Taxation and Corporate Investment: A q-Theory Approach," Brookings Papers on Economic Activity, Economic Studies Program, The Brookings Institution, vol. 12(1), pages 67-140.
    46. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, December.
    47. Klaus Gugler & Dennis C. Mueller & B. Burcin Yurtoglu, 2004. "Marginal q, Tobin's q, Cash Flow, and Investment," Southern Economic Journal, John Wiley & Sons, vol. 70(3), pages 512-531, January.
    48. Alberto Bressan & Yilun Jiang, 2020. "Self-consistent Feedback Stackelberg Equilibria for Infinite Horizon Stochastic Games," Dynamic Games and Applications, Springer, vol. 10(2), pages 328-360, June.
    49. Yoshikawa, Hiroshi, 1980. "On the "q" Theory of Investment," American Economic Review, American Economic Association, vol. 70(4), pages 739-743, September.
    50. Robert E. Lucas & Jr., 1967. "Adjustment Costs and the Theory of Supply," Journal of Political Economy, University of Chicago Press, vol. 75(4), pages 321-321.
    51. Lawrence J. Christiano & Jonas D. M. Fisher, 2003. "Stock Market and Investment Goods Prices: Implications for Macroeconomics," NBER Working Papers 10031, National Bureau of Economic Research, Inc.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Guerrazzi, Marco, 2025. "A complete characterization of equilibrium paths in a labour-less two-sector model of optimal growth," MPRA Paper 124225, University Library of Munich, Germany.
    2. Guerrazzi, Marco, 2024. "Wage bargaining and capital accumulation: A dynamic version of the monopoly union model," MPRA Paper 121433, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guerrazzi, Marco, 2025. "A complete characterization of equilibrium paths in a labour-less two-sector model of optimal growth," MPRA Paper 124225, University Library of Munich, Germany.
    2. Guerrazzi, Marco, 2024. "Wage bargaining and capital accumulation: A dynamic version of the monopoly union model," MPRA Paper 121433, University Library of Munich, Germany.
    3. Tsoukalas, John D., 2011. "Time to build capital: Revisiting investment-cash-flow sensitivities," Journal of Economic Dynamics and Control, Elsevier, vol. 35(7), pages 1000-1016, July.
    4. François Gourio & Jianjun Miao, 2010. "Firm Heterogeneity and the Long-Run Effects of Dividend Tax Reform," American Economic Journal: Macroeconomics, American Economic Association, vol. 2(1), pages 131-168, January.
    5. Weicheng Lian & Natalija Novta & Evgenia Pugacheva & Yannick Timmer & Petia Topalova, 2020. "The Price of Capital Goods: A Driver of Investment Under Threat," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 68(3), pages 509-549, September.
    6. Missaka Warusawitharana, 2007. "Corporate asset purchases and sales: theory and evidence," Finance and Economics Discussion Series 2007-27, Board of Governors of the Federal Reserve System (U.S.).
    7. Weicheng Lian & Natalija Novta & Evgenia Pugacheva & Yannick Timmer & Petia Topalova, 0. "The Price of Capital Goods: A Driver of Investment Under Threat," IMF Economic Review, Palgrave Macmillan;International Monetary Fund, vol. 0, pages 1-41.
    8. Andrew B. Abel, 2015. "The Analytics of Investment, q, and Cash Flow," NBER Working Papers 21549, National Bureau of Economic Research, Inc.
    9. Warusawitharana, Missaka, 2008. "Corporate asset purchases and sales: Theory and evidence," Journal of Financial Economics, Elsevier, vol. 87(2), pages 471-497, February.
    10. Abel, Andrew B., 2018. "The effects of q and cash flow on investment in the presence of measurement error," Journal of Financial Economics, Elsevier, vol. 128(2), pages 363-377.
    11. Monika Merz & Eran Yashiv, 2007. "Labor and the Market Value of the Firm," American Economic Review, American Economic Association, vol. 97(4), pages 1419-1431, September.
    12. Andrei Polbin & Sergey Drobyshevsky, 2014. "Developing a Dynamic Stochastic Model of General Equilibrium for the Russian Economy," Research Paper Series, Gaidar Institute for Economic Policy, issue 166P, pages 156-156.
    13. Jason G. Cummins & Kevin A. Hassett & Stephen D. Oliner, 2006. "Investment Behavior, Observable Expectations, and Internal Funds," American Economic Review, American Economic Association, vol. 96(3), pages 796-810, June.
    14. Jun Li, 2019. "Explaining Momentum and Value Simultaneously," Management Science, INFORMS, vol. 64(9), pages 4239-4260, September.
    15. Bazdresch, Santiago, 2013. "The role of non-convex costs in firms' investment and financial dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 37(5), pages 929-950.
    16. Hennessy, Christopher A. & Levy, Amnon & Whited, Toni M., 2007. "Testing Q theory with financing frictions," Journal of Financial Economics, Elsevier, vol. 83(3), pages 691-717, March.
    17. Lin, Xiaoji & Wang, Chong & Wang, Neng & Yang, Jinqiang, 2018. "Investment, Tobin’s q, and interest rates," Journal of Financial Economics, Elsevier, vol. 130(3), pages 620-640.
    18. Abel, Andrew B., 1990. "Consumption and investment," Handbook of Monetary Economics, in: B. M. Friedman & F. H. Hahn (ed.), Handbook of Monetary Economics, edition 1, volume 2, chapter 14, pages 725-778, Elsevier.
    19. Peters, Ryan H. & Taylor, Lucian A., 2017. "Intangible capital and the investment-q relation," Journal of Financial Economics, Elsevier, vol. 123(2), pages 251-272.
    20. Caggese, Andrea, 2007. "Testing financing constraints on firm investment using variable capital," Journal of Financial Economics, Elsevier, vol. 86(3), pages 683-723, December.

    More about this item

    Keywords

    Price of capital goods; Tobin's q; Internal and external adjustment costs; Differential games.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D24 - Microeconomics - - Production and Organizations - - - Production; Cost; Capital; Capital, Total Factor, and Multifactor Productivity; Capacity
    • E22 - Macroeconomics and Monetary Economics - - Consumption, Saving, Production, Employment, and Investment - - - Investment; Capital; Intangible Capital; Capacity
    • G31 - Financial Economics - - Corporate Finance and Governance - - - Capital Budgeting; Fixed Investment and Inventory Studies

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:119118. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.