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On optimal extinction in the matchbox two-sector model

Author

Listed:
  • Liuchun Deng

    (Yale-NUS College)

  • Minako Fujio

    (Yokohama National University)

  • M. Ali Khan

    (The Johns Hopkins University)

Abstract

We provide a complete characterization of optimal extinction in a two-sector model of economic growth through three results, surprising in both their simplicity and intricacy. (i) When the discount factor is below a threshold identified by the well-known $$\delta $$ δ -normality condition for the existence of a stationary optimal stock, the economy’s capital becomes extinct in the long run. (ii) This extinction may be staggered if and only if the investment-good sector is capital-intensive. (iii) We uncover a sequence of thresholds of the discount factor, identified by a family of rational functions, that represent bifurcations for optimal postponements on the path to extinction. We also report various special cases of the model having to do with unsustainable technologies and equal capital-intensities that showcase long-term optimal growth, all of topical interest and all neglected in the antecedent literature.

Suggested Citation

  • Liuchun Deng & Minako Fujio & M. Ali Khan, 2023. "On optimal extinction in the matchbox two-sector model," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 76(2), pages 445-494, August.
    • Handle: RePEc:spr:joecth:v:76:y:2023:i:2:d:10.1007_s00199-022-01462-0
    DOI: 10.1007/s00199-022-01462-0
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    More about this item

    Keywords

    Extinction; Capital intensity; Two-sector; $$delta $$ δ -Normality; Bifurcation;
    All these keywords.

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • D90 - Microeconomics - - Micro-Based Behavioral Economics - - - General
    • O21 - Economic Development, Innovation, Technological Change, and Growth - - Development Planning and Policy - - - Planning Models; Planning Policy

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