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含有預期和時滯的經濟周期模型穩定性分析

Stability analysis of a business cycle model including anticipation and delay

  • 摘要: 將預期的資本存量引入現階段的投資決策函數,同時考慮資本積累過程中的投資時滯,構建一個含有預期和時滯的經濟周期模型.首先利用微分動力系統相關的理論研究系統的穩定性,然后把投資時滯或資本存量的預測時間作為分支參數,討論由此參數導致Hopf分支的條件,并執行一些數值模擬以驗證所得結論.研究結果表明:資本存量預期和投資時滯共同構成經濟周期的誘導因素;對資本存量進行短期合理的預測,據此制定投資決策,能夠在一定程度上沖銷由投資時滯所造成的經濟波動.

     

    Abstract: A business cycle model with anticipation and delay was constructed by introducing anticipated capital stock into the investment decision function in the present period and considering investment delay in the capital accumulation process. This system's stability was investigated by using related theories of differential dynamical systems first. Then investment delay or the prediction time of capital stock was taken as a bifurcation parameter, and the conditions of Hopf bifurcation caused by the parameter were discussed. Last, some numerical simulations were carried out to confirm the obtained conclusions. It is shown that capital stock anticipation and investment delay together constitute the induced factors of business cycle. Economic fluctuations caused by investment delay can be dampened to some extend if the government makes investment decision based on short-term reasonable forecast on capital stock.

     

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