Consider the following classical model of a closed economy. Note that the model's equations implicitly define...

 

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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<c'(y) <1, i'(r) <0 mol(r.y.p); <0, ly> 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. 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<c'(y) <1, i'(r) <0 mol(r.y.p); <0, ly> 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.

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a dy fLodLo dr irdr dp molrypdp ly dp ... View the full answer