Consider an economy with a production function given by Y_t = A*K_t + B*L_t
Suppose that individuals save 20% of their disposable income, and that population size is fixed and equal to 1 million.
How would you derive the law of motion for this economy? (i.e. derive an expression for Y_t+1 as a function of Y_t)
How would the law of motion change if the government introduces a 30% tax on all sources of income (wages, capital payments, and profits), and the revenue is used every period to purchase non-durable public goods that have NO impact on total factor productivity?