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,| u(C,|) s.t. Y = C + | (a) Write the Lagrangian for the household's problem and Derive the first order conditions