Suppose that we have a Solow model with one twist. The twist is that there is a government. Hence, the aggregate resource constraint is: Y = C + I + Gt. where G= Tt (public expenditure is financed by taxation) and T = TY. Define private output as Y = Y - Gt. Suppose that private investment is a constant fraction, s, of private output (consumption is then 1 - s times private output). A fraction of satis spent on public investment, which supplements the productive capital stock. Otherwise the model is the same as in the lecture. Derive the transition dynamic equation for this economy