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In the book we develop and solve the Ramsey model in terms of its implications for consumption and capital per worker

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In the book we develop and solve the Ramsey model in terms of its implications for consumption and capital per worker. In this question we study the Ramsey model in terms of its implications for capital per worker and the savings ratio. Recall that the savings ratio, s(t), is the proportion of income that is saved and invested: I(t) s(t) = S(t) K(t) +8K(t) (Q13.18) Y(t) Y(1) Y(1) It follows from (Q13.18) that consumption per worker is: c(t) = (1 - s(t)) y(t), (Q13.19) where y(t) = f (k(t)) is the intensive-form production function. The fundamental differential equation for the capital stock is: k(t) = s(t)f (k(t)) - (8 +nL) k(t). (Q13.20) Assume that the technology is Cobb-Douglas, i.e. y(t) = Ak(t)with 0 < a < 1, and that the felicity function is iso-elastic with intertemporal substitution elasticity 0. Abstract from technological change. (a) Solve the optimization problem in terms of the savings rate and the capital stock per worker. = = (b) Derive the fundamental differential equations for k and s.