Exercise 5.2. This problem concerns the formulation of a model-based method for min imizing a twice-continuously...
linear optimization
Assume that f : D → R is twice continuously differentiable for all x D, where the domain D off is an open, convex subset of Rn. Sh ▽2f(x), is symmetric positive-semi-definite for all x E D if and only if f is a convex function on D Moreover, if its Hessian matrix. ▽2 (x), is symmetric positive-definite for all x E D, then f is a strictly convex function on D Show that the converse of this...
(Production function) Condsider a representitive firm with a production function which is (i) twice continuously differentiable; (ii) exhibits positive and diminishing marginal product and (ii) has constant return to scale: Y = F(K, L) Given the capital rental price R and the wage w, and the good price P is normalized to 1, the firm can choose K and L to maximize its profit: max F(K, L) - RK - wL K,L 3. (Solow Model) Denote that Y F(K, L)...