exercise 1

1. Consider the equation: F(y;w,z) =yzzw2+w+y=0 1where y is the endogenous variable and w and z are the exogenous variables. (a) Use the Implicit Function Theorem to argue whether there exists an implicit function y = f (10,2) in the neighborhood of (y,w, z) = (2,3,1). You must check whether the assumptions of the Implicit Function Theorem are satised. (b) Use the Implicit Function Theorem to nd 3% at (y, w, z) = (2, 3, 1). (c) Actually, y can be solved for as an explicit function of w and z. Use the explicit function of y to calculate 5% again at (y,w,z) = (2,3,1). Compare your answer here to that obtained in (b)