We start with the household side of the model. We saw in the data that the investment rate in the economy is stable in the long run. Our goal in solving the household side of the model is to show that household choose to invest a constant share of income. Households have utility u(C,I) over consumption C and investment I. The household has income Y which it spends on C and I. Therefore the household's maximization problem is: maxC,I u(C,I) s.t. Y = C + I

Using the two equations Y (the budget constraint , household's utility function in functional form ,and two unknowns (C and I). Use these equations to show that investment I is always the share of income Y .