Question 1. (20 marks) Consider the production function F(K, L) = A(KP + LP)-m/p. 1. Find the derivatives, FK, FL. 2. Find the marginal rate of substitution of capital for labour, RKL. 3. Find the Elasticity of Substitution, KL. 2 Question 2. (20 marks) Consider the following macro model of an economy Y=C+I+ X + G C = f(Y) where I is investment, X is net exports, G is government spending, C is consumption, Y is income and 0 < f'(Y) < 1 1. Differentiate both equations. 2. Find the differentials of Y and C, dY and dC. 3. What is Y/OG? 4. What is the sign of and the economic interpretation of Y/OG? Question 3. (10 marks) Consider a production function Y = F(K, L) = AK/4L2/3 1. Show that this function is homogeneous and determine the degreee of homogeneity. 2. What happens to output if both inputs are doubled? Question 4. (15 marks) Let 4 f(x, y) = xxy In x + 2x y4 1. Compute the first and second order partial derivatives of f(x, y), de- noting these f(x, y), fry(x, y) and so on. 2. What is the relationship between fry (x, y) and fyr (x, y)? By what theorem is this the case?