QUESTION 3 (a) Find the elasticity of substitution for the following production func- tions: (i) F(K, L) = AKL' (1i) F(K, L) = A(aK P + bI -p)-m/p where A > 0, a > 0, b >0, m # 0, p > -1 and p 0. (8 marks) (b) Determine whether the following functions are homogeneous or not. If a function is homogeneous, verify that Euler's Theorem holds. (i) f (x, y) = x2 + 6xy + Ty (ii) f (x, y) = = (iii) f (x, y) = 20310.4 (iv) f (x, y) = 23+ 2xy + y" (12 marks) (c) Consider the function F(K, L) = H (y), where y = f (K, L) = Ka[' and H (y) = In(y). Show that function F is homothetic, but not homogeneous