Suppose the representative firm's production function is Y (K, N) = AK/2 N/2 where K is the use of capital, N is the use of labor and A> 0 is the total factor productivity. I 7.1) Find the marginal product of labor. 7.2) Show that the production function features diminishing marginal prod- uct of capital. Suppose the real wage is denoted by w and the real rental rate of physical capital is denoted by r. 7.3) Please write down the firm's profit as a function of A, K, N, w, and r. 7.4) Please write down the profit-maximization condition and the labor de- mand function. Suppose the emergence of AI raises total factor productivity from A to A and provides the representative firm labor-replacing robotics equivalent to 10 units of labor at no cost. 7.5) Please write down the firm's profit as a function of A, K, N, w, and r. 7.6) Please write down the profit-maximization condition and the labor de- mand function.