Super thanks if anyone could help me with the above questions.

Consider a Ramsey model with population growth rate n>0 and technology progress with rate g>0. (That is, L(t)=L(0)ent and A(t)=A(0)egt, where L(0) and A(0) are normalized to be equal to one.) Let H be the number of households in the economy. Suppose each household maximizes the life-time utility per household member. 0etU(c(t))HL(t)dt where c(t) is per capita consumption at time t. (a) Show that this function is equivalent to: HL(0)0e(n)tU(c(t))dt (b) In what follows, assume H=1 (i.e. there is only one household). The flow budget constraint for the household is K(t)=w(t)L(t)+r(t)K(t)c(t)L(t). Let k(t)K(t)/L(t) (asset per capita). Show that the budget constraint is equivalent to k(t)=w(t)+r(t)k(t)c(t)nk(t). (c) Maximize the life-time utility subject to the budget constraint. Show that c(t)cc(t)=[r(t)][U(c(t))U(c(t))c(t)]1 Consider a Ramsey model with population growth rate n>0 and technology progress with rate g>0. (That is, L(t)=L(0)ent and A(t)=A(0)egt, where L(0) and A(0) are normalized to be equal to one.) Let H be the number of households in the economy. Suppose each household maximizes the life-time utility per household member. 0etU(c(t))HL(t)dt where c(t) is per capita consumption at time t. (a) Show that this function is equivalent to: HL(0)0e(n)tU(c(t))dt (b) In what follows, assume H=1 (i.e. there is only one household). The flow budget constraint for the household is K(t)=w(t)L(t)+r(t)K(t)c(t)L(t). Let k(t)K(t)/L(t) (asset per capita). Show that the budget constraint is equivalent to k(t)=w(t)+r(t)k(t)c(t)nk(t). (c) Maximize the life-time utility subject to the budget constraint. Show that c(t)cc(t)=[r(t)][U(c(t))U(c(t))c(t)]1