=I = = 2. (6 pts) Let f(x,y) be a continuous and differentiable function of u and y. the function f is said to be homogeneous of degree one if f(cx, cy) = cf(x,y) Euler's theorem states that if f is homogeneous of degree one, then a f(x,y) f(x,y) + y 2 f (1,9) Let up(x, y) = xua +yub and op(x, y) = Vx?o + yj2o}} + 2xYO AB (a) (3 pt) Show that up(x, y) and op(x, y) are homogeneous of degree 1 (for op(x, y) assume c> 0) (b) (3 pt) In a portfolio where the portion x is invested in asset A and the portion y is invested in asset B, the partial derivatives a , ac are called the marginal contributions to risk of A and B , respectively. The contributions to risk of assets A and B are given by a a cop(x,y) and 42,0p(,y), y ar respectively. Find the expression of the marginal risks and the contribution to risk of assets A and B. p(x,y) and 6.00P(1, )