1. Consider the following Solow-Swan model of growth: Y(t)L(t)A(t)K(t)I(t)=[K(t)][A(t)L(t)]1=L(0)ent=1forallt=I(t)K(t)=S(t)=sY(t) where 0L(0)ns0>0>0 and I(t) is the investment, s is the exogenous saving rate. Other variables are as discussed in class. (a) Show that the Cobb-Douglas production function satisfies the following properties: diminishing marginal returns in capital and labor; constant returns to scale (CRS) in both labor and capital; Inada conditions in both labor and capital. (b) Write down the production function in intensive form: y=f(k) (c) Write down the fundamental equation of this model (i.e. the law of motion for capital), which describes the evolution of capital per worker, k(t). Graph this and show the unique and stable solution on this diagram. (d) What is the steady-state growth rate of capital per worker, k(t) ? What is the steady state growth rate of capital K(t) and output Y(t) ? (e) Solve for the steady-state levels of capital per worker k, output per worker y and consumption per worker c as functions of the exogenously given parameters. 1. Consider the following Solow-Swan model of growth: Y(t)L(t)A(t)K(t)I(t)=[K(t)][A(t)L(t)]1=L(0)ent=1forallt=I(t)K(t)=S(t)=sY(t) where 0L(0)ns0>0>0 and I(t) is the investment, s is the exogenous saving rate. Other variables are as discussed in class. (a) Show that the Cobb-Douglas production function satisfies the following properties: diminishing marginal returns in capital and labor; constant returns to scale (CRS) in both labor and capital; Inada conditions in both labor and capital. (b) Write down the production function in intensive form: y=f(k) (c) Write down the fundamental equation of this model (i.e. the law of motion for capital), which describes the evolution of capital per worker, k(t). Graph this and show the unique and stable solution on this diagram. (d) What is the steady-state growth rate of capital per worker, k(t) ? What is the steady state growth rate of capital K(t) and output Y(t) ? (e) Solve for the steady-state levels of capital per worker k, output per worker y and consumption per worker c as functions of the exogenously given parameters