Consider the following classical model of a closed economy. Note that the model's equations implicitly define the equilibrium values of aggregate income (y*), the interest rate (r*), and the aggregate price level (p*), as functions of exogenously given values for government purchases (go), the money supply (mo), and the aggregate labor supply (Lo), each of which is assumed to be positive. y=f(Lo): f'(Lo) > 0 y = c(y) + i(r) +go: 0 0, p > 0 . a. Find the total differentials of all 3 equations. b. Rewrite the system of equations from (a) as a matrix equation (Ax = b), where the vector x is defined as x= [dy dr dp*]T c. Use Cramer's rule to find the total differential of the implicitly defined function that relates the equilibrium price level to its exogenous determinants (i.e. - find dp') d. Write down expressions for Op/aLo and Op/am, and determine their signs.