8. Consider the following classical model of a closed economy. Note that the model's equations implicitly define the equilibrium values of aggregate income (W), the interest rate (r*), and the aggregate price level (p*), as functions of eitogenouslvr 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'(Lu)>0 - y=C(y)+i(r)+gn: 00, lp>0 In 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 (Le. find dp'} d. Write down expressions for (SW/61.0 and 6p*/6m0 and determine their signs