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(c) What saving rate is needed to yield the golden-rule capital stock? 4. Consider a Natural
resource depletion Solow model where output is given by the CRS production function Y(t)=K(t)R(t
)(A(t)L(t))1,0<,<1 Where R(t) denotes a stock of resources that depletes at rate >0 R(t)=R(t) The
rest of the model is as standard with constant savings rate s, depreciation rate , productivity
growth g and employment growth n. i. Let gY(t) and gK(t) denote the growth rates of output and
the capital stock. Derive a formula for gY(t) in terms of gK(t). ii. Let gY and gK denote the growth
rates of output and the capital stock along a balanced growth path. Show that along any balanced
growth path gY=gK. Solve for this growth rate.

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  • 1. (c) What saving rate is needed to yield the golden-rule capital stock? 4. Consider a Natural resource depletion Solow model where output is given by the CRS production function Y(t)=K(t)R(t )(A(t)L(t))1,0<,<1 Where R(t) denotes a stock of resources that depletes at rate >0 R(t)=R(t) The rest of the model is as standard with constant savings rate s, depreciation rate , productivity growth g and employment growth n. i. Let gY(t) and gK(t) denote the growth rates of output and the capital stock. Derive a formula for gY(t) in terms of gK(t). ii. Let gY and gK denote the growth rates of output and the capital stock along a balanced growth path. Show that along any balanced growth path gY=gK. Solve for this growth rate.