The household maximize utility from consumption over an infinite horizon. The per period utility function is...

  

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The household maximize utility from consumption over an infinite horizon. The per period utility function is the standard CRRA utility function u(c(t)) where is positive but different from one. Optimal household behavior implies that the household follows the consumption rule (t) c(t) as well as the requirement that c(t)-0-1 1-0 - (r(t) - p) lim X(t)a(t)= 0 To ensure finite utility we impose the parameter condition p> n + (1-0) g. Finally it is subject to the following flow budget constraint (1) The representative firm operates a Cobb-Douglas technology Y = K(t) (A(t) L(t)) -a (2) (t)=ra(t) + w- c(t)- na(t), a(0) given (3) The notation is the standard one from the textbook: c is per capita consumption, a is per capita wealth, r is the real rate, w is the real wage, A is the shadow value of wealth, p is the rate of time preference, n is the rate of population growth and g is the rate of technological change. Question 1. Comment on equation (1) (3). What are their economic impli- cations? and maximizes profits while taking factor prices as given. Hence the unit cost of capital is wages w(t) and the usercost of capital r(t) + 8 where & is the rate of capital depreciation (a positive constant). The household maximize utility from consumption over an infinite horizon. The per period utility function is the standard CRRA utility function u(c(t)) where is positive but different from one. Optimal household behavior implies that the household follows the consumption rule (t) c(t) as well as the requirement that c(t)-0-1 1-0 - (r(t) - p) lim X(t)a(t)= 0 To ensure finite utility we impose the parameter condition p> n + (1-0) g. Finally it is subject to the following flow budget constraint (1) The representative firm operates a Cobb-Douglas technology Y = K(t) (A(t) L(t)) -a (2) (t)=ra(t) + w- c(t)- na(t), a(0) given (3) The notation is the standard one from the textbook: c is per capita consumption, a is per capita wealth, r is the real rate, w is the real wage, A is the shadow value of wealth, p is the rate of time preference, n is the rate of population growth and g is the rate of technological change. Question 1. Comment on equation (1) (3). What are their economic impli- cations? and maximizes profits while taking factor prices as given. Hence the unit cost of capital is wages w(t) and the usercost of capital r(t) + 8 where & is the rate of capital depreciation (a positive constant).