Please answer with all the math details

1. Consider the following economy. There is an aggregate Cobb Douglas production function that produces output y ye = zkim where ke is the capital and ne is labor input to production. The output can be consumed " or can be used as investment It. Each unit of investment adds - unit of new capital where q > 1. In other words investment of It, adds It/q to the stock of capital. Existing capital depreciates at rate o. Representative household has 1 unit of time every period t which can be used to work or enjoy leisure. They also have the following preferences Blog at ,0