8. (9 pt) Solve the competitive firm's profit-maximization use of labor and capital for the case where y(K, L) = K.25L-25 and p = 8, in which y(L,K) is a production function and p is the market price of the good. Suppose that the prices of labor and capital inputs are w = 2 and r = 2, respectively. (a) (2 pt) Show whether the production function y(K, L) is quasi-concave or quasi- convex. You must provide the boarder Hessian of the function. (b) (2 pt) Use the implicit function theorem to find the partial derivatives alak implied by the relationship of F(K, L, y) = K.25L.25 y = 0. (c) (3 pt) Find the solution of this profit-maximization problem and show whether the solution is a unique global max. (d) (2 pt) Find the global minimum subject to the constraints: 0