Consider a simple model of presidential elections. It is well established by political scientists that economic factors affect the popularity of an incumbent. An incumbent's chance of reelection may thus depend upon variables such as the unemployment rate, U, and the inflation rate, π, in the year of the election. A simple function that captures this relationship relates the ratio of the votes going to an incumbent relative to those going to the challenger, V, as a function of the unemployment rate and the inflation rate: V = f(U, π).Reflecting our assumption that higher unemployment or higher inflation lowers theproportion of votes going to the incumbent. Suppose we assumed that unemployment is a function of both monetary and fiscal policies as U = f(M,F) and inflation is also a function of both monetary and fiscal policies as π=g(M,F).
A) Find the partial derivate of both unemployment and inflation with respective to monetary and fiscal policies and interpret the result?
B) Find the derivative of the vote ratio with respect to both monetary and fiscal policies and interpret the result?