Please answer all if possible thanks. 4. Define the following sets (30 points) (a) X...
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Please answer all if possible thanks.
4. Define the following sets (30 points) (a) X = {(x, y) R 2 : y = f(x) = 3x + 3y 42} (b) Y = {(x, y) R 2 : y = f(x) = 2x + 2y 42} (c) Z = X Y (d) Prove whether or not each set defined above is convex?
5. Let X be the set of risky assets and Y the set of positive real numbers. Define the function f : X Y to be y is the expected return of x Is f one-to-one? (30 points)
6. Is g f (a) concave or convex (b) increasing or decreasing if (30 points) (a) f : R2 R : f(x1, x2) = y = 2x1 3x2 g : R R : g(y) = y 2 ? (Please us two points (1 and 2) and = 4 5 ) (b) f : R R : f(x) = y = x 4 4 g : R R : g(y) = 4 2 y? (Please us two points (1 and 2) and = 4 5 ) (c) f : R R : f(x) = y = x 4 9 3 g : R R : g(y) = 3 y + 3? (Please us two points (1 and 2) and = 4 5 )
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