단위탄력적 성장모형과 램지최적 경로의 존재
Existence of Ramsey-optimal Paths in Unit-elastic Models of Economic Growth
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우리는 이 논문에서 할인이 없는 이산시간 최적성장 모형을 분석한다. 구체적으로 우리는효용함수가 ln c_t 이고 생산함수가 k^a_t 이며 할인요소가 1인 단위탄력성의 경우를 분석한다. 우리는지속상태의 효용수준에서 각 기의 효용수준을 뺀 것의 합계를 ‘램지격차’로 정의하고 그것을최소화하는 경로를 ‘램지최적 경로’로 정의하여 최적성장 경로를 도출한다. 우리는 여기에서효용수준의 비교대상으로 지속상태의 효용을 취하는데, 그 점에서 ‘희열수준’을 취하여 분석한 램지(1928)의 분석과 비교된다. 우리는 단위탄력성 모형에 대해 램지최적 경로의 존재를 증명하며초기자본이 k_0일 때 그 램지격차는 a/1 − a[ln a^(1/(1−a)) − ln k_0]로 도출한다. 이 분석방법은 할인요소가 1인 경우의 최적성장을 분석하는 방법의 하나로 간주할 수있다.
Abstract
We consider discrete-time optimal growth models without discounting. Specifically, we analyze unitelastic models with utility function ln c_t and production function k^a_t , where the discount factor is 1. We define the Ramsey Gap as the summation of steady-state utility minus the utility achieved at each period (Equation (9), in the text), and define the Ramsey-optimal paths as feasible paths which minimize the Ramsey Gap. Here we take the steady-state utility level as the level to be compared to, while Ramsey (1928) himself takes the so-called Bliss level. We show that a Ramsey-optimal path exists in our model. Also, the value of Ramsey Gap of the Ramsey-optimal path in our model is shown to be a/1 − a[ln a^(1/(1−a)) − ln k_0] when the initial stock of capital is k_0 (Equation (12)). This approach may be regarded as a method which can be used to analyze optimal growth models when discount factor is 1.
참고문헌 (12)
- Atsumi, Hiroshi, "Neoclassical growth and the efficient program of capital accumulation", Review of Economic Studies, pp.127~136 (1965)
- Barro, Robert J, "Economic Growth, 2nd. ed" (2004), The MIT Press
- Cass, David, "Optimum growth in an aggregative model of capital accumulation", Review of Economic Studies, pp.233~240 (1965)
- Chakravarty, S, "The Existence of an Optimum Savings Program", Econometrica, pp.178~187 (1962)
- Koopmans, Tjalling C, "On the concept of optimal economic growth, in: The Econometric Approach to Development Planning", pp.225~300 (1965), North-Holland
- McKenzie, Lionel W, "Optimal Economic Growth, Turnpike Theorems and Comparative Dynamics, in Handbook of Mathematical Economics, Vol. III", pp.1281~1355 (1986)
- McKenzie, Lionel W, "Turnpikes: Richard T. Ely Lecture", American Economic Review, pp.1~14 (1998)
- Phelps, Edmund, "The Golden Rule of Accumulation: A Fable for Growthmen", American Economic Review, pp.638~643 (1961)
- Ramsey, F. P, "A mathematical theory of savings", Economic Journal, pp.543~559 (1928)
- Stokey, Nancy L, "Recursive Methods in Economic Dynamics" (1989), Harvard University Press
- Weizsacker, C. C. von, "Existence of optimal programs of accumulation for an infinite time horizon", Review of Economic Studies, pp.85~104 (1965)
- Yi, Gyoseob, "Classical Welfare Theorems in Economies with the Overtaking Criterion", Journal of Mathematical Economics, pp.57~75 (1989)