Answer the following questions: a) Show that Young's Theorem holds for the following function: f(x, y) = 9ye xy (5 points) b) Let z(x, y, w) = x + wy+w, where w (r,s) = r + s, x (r,s) = r- s and y (r, s) = r. s. Find the partial derivative=?(5 points) c) The foreign demand for our exports X depends on the foreign income Y, and our price level P: X = Y + P-. Find the partial elasticity of foreign demand for our exports with respect to our price level. (7.5 points) d) If production function is Q = A(t) K,L,, where A(t) is an increasing function of t, and K = Ko + at, and L = Lo + bt. Find the rate of change of output with respect to time? (7.5 points)