Compare and contrast between the Ramsey model for the central planner and the solow model for economic growth including the assumption, important equations, phase diagram and its interpretation
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The Solow–Swan model is an economic model of long-run economic growth set within the framework of neoclassical economics. It attempts to explain long-run economic growth by looking at capital accumulation, labor or population growth, and increases in productivity, commonly referred to as technological progress.
The textbook Solow–Swan model is set in continuous-time world with no government or international trade. A single good (output) is produced using two factors of production, labor ( {\displaystyle L} L) and capital ( {\displaystyle K} K) in an aggregate production function that satisfies the Inada conditions, which imply that the elasticity of substitution must be asymptotically equal to one.[12][13]
{\displaystyle Y(t)=K(t)^{\alpha }(A(t)L(t))^{1-\alpha }\,} {\displaystyle Y(t)=K(t)^{\alpha }(A(t)L(t))^{1-\alpha }\,}
The Ramsey–Cass–Koopmans model, or Ramsey growth model, is a neoclassical model of economic growth based primarily on the work of Frank P. Ramsey,[1] with significant extensions by David Cass and Tjalling Koopmans.[2][3] The Ramsey–Cass–Koopmans model differs from the Solow–Swan model in that the choice of consumption is explicitly microfounded at a point in time and so endogenizes the savings rate. As a result, unlike in the Solow–Swan model, the saving rate may not be constant along the transition to the long run steady state. Another implication of the model is that the outcome is Pareto optimal or Pareto efficient.The Ramsey–Cass–Koopmans model starts with an aggregate production function that satisfies the Inada conditions, often specified to be of Cobb–Douglas type, {\displaystyle F(K,L)} {\displaystyle F(K,L)}, with factors capital {\displaystyle K} K and labour {\displaystyle L} L. Since this production function is assumed to be homogeneous of degree 1, one can express it in per capita terms, {\displaystyle F(K,L)=L\cdot F({\frac {K}{L}},1)=L\cdot f(k)} {\displaystyle F(K,L)=L\cdot F({\frac {K}{L}},1)=L\cdot f(k)}. The amount of labour is equal to the population in the economy, and grows at a constant rate {\displaystyle n} n, i.e. {\displaystyle L=L_{0}e^{nt}} {\displaystyle L=L_{0}e^{nt}} where {\displaystyle L_{0}>0} {\displaystyle L_{0}>0} was the population in the initial period.