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Exercise 1: : Consider the following macroeconomic model defined as follows: national product/income: Y =C+I+G* where government expenditure G* > 0. - consumption: C = aY + B where 0 0. - investment: I = yr + where y0 and r interest rate. - money supply: M; = k1Y + kar where ki > 0, k2 0. The parameters are a, 6, 7, 8, ki and ka. An asterisk (*) den otes an exogenous variable. (a) Write this system in matrix form. (b) Use Cramer's rule to show that M:(1 - a) - k(+8+G*) T= k2(1 - a)+2k1 (c) Using (b) find an expression for the effect on the interest rate of a rise in government expenditure, and determine whether this effect is positive or negative (everything else being equal) Exercise 1: : Consider the following macroeconomic model defined as follows: national product/income: Y =C+I+G* where government expenditure G* > 0. - consumption: C = aY + B where 0 0. - investment: I = yr + where y0 and r interest rate. - money supply: M; = k1Y + kar where ki > 0, k2 0. The parameters are a, 6, 7, 8, ki and ka. An asterisk (*) den otes an exogenous variable. (a) Write this system in matrix form. (b) Use Cramer's rule to show that M:(1 - a) - k(+8+G*) T= k2(1 - a)+2k1 (c) Using (b) find an expression for the effect on the interest rate of a rise in government expenditure, and determine whether this effect is positive or negative (everything else being equal)

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