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An economy has a Cobb-Douglas production function of the form: Y=F(K ,L )=AK^α L^(1−α) Y denotes output, K describes the capital stock, L denotes labour force, A is total factor productivity (TFP) and α is the output elasticity of capital. The capital stock evolves according to:Kt − Kt−1 = sYt−1 − δKt−1,where s is the exogenous savings rate, sYt equals investment and δ is the depreciation rate.

Suppose that the production function is Cobb-Douglas. (a) Find expressions for k^*, y^*, and c^* as functions of the parameters of the model, s, n, δ, g, and α(b) What is the golden-rule value of k ? (c) What saving rate is needed to yield the golden-rule capital stock? | Numerade

Cobb-Douglas production function During the 1920 s, Charles Cobb and Paul Douglas modeled total production output P (of a firm, industry, or entire economy) as a function of labor hours involved x and capital invested y (which includes the monetary worth of all buildings and equipment). The Cobb-Douglas production function is given by P(x, y)=k x^α y^1-α where k and αare constants representative of a particular firm or economy. a. Show that a doubling of both labor and capital results in a dou

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