586 PA R T V I I Monetary Theory CHANGES IN NET EXPORTS (NX ) A rise in net exports adds directly to aggregate demand and raises the aggregate demand function, increasing aggregate output A fall directly reduces aggregate demand, lowers the aggregate demand function, and causes aggregate output to fall Therefore, aggregate output is positively related to net exports NX The aggregate demand function in the Keynesian cross diagrams shifts vertically by the full amount of the change in a, I, G, or NX, resulting in a multiple effect on aggregate output through the effects of the expenditure multiplier, 1/(1 + mpc) A change in taxes has a smaller effect on aggregate output because consumer expenditure changes only by mpc times the change in taxes (+mpc - ,T ), which in the case of mpc * 0.5 means that aggregate demand shifts vertically by only half of the change in taxes If there is a change in one of these autonomous factors that is offset by a change in another (say, I rises by $100 billion, but a, G, or NX falls by $100 billion or T rises by $200 billion when mpc * 0.5), the aggregate demand function will remain in the same position, and aggregate output will remain unchanged.5 SIZE OF THE EFFECTS FROM THE FIVE FACTORS THE ISL M M ODE L So far our analysis has excluded monetary policy We now include money and interest rates in the Keynesian framework to develop the more intricate ISLM model of how aggregate output is determined, in which monetary policy plays an important role Why another complex model? The ISLM model is versatile and allows us to understand economic phenomena that cannot be analyzed with the simpler Keynesian cross framework used earlier The ISLM model will help you understand how monetary policy affects economic activity and interacts with fiscal policy (changes in government These results can be derived algebraically as follows Substituting the consumption function allowing for taxes (Equation 6) into the aggregate demand function (Equation 1), we have Y ad * a + mpc - T mpc - Y I G NX If we assume that taxes T are unrelated to income, we can define autonomous spending in the aggregate demand function to be A * a + mpc - T I G NX The expenditure equation can be rewritten as Y ad * A mpc - Y In equilibrium, aggregate demand equals aggregate output, Y * A mpc - Y which can be solved for Y The resulting equation, Y = * A - mpc is the same equation that links autonomous spending and aggregate output in the text (Equation 5), but it now allows for additional components of autonomous spending in A We see that any increase in autonomous expenditure leads to a multiple increase in output Thus any component of autonomous spending that enters A with a positive sign (a, I, G, and NX ) will have a positive relationship with output, and any component with a negative sign (+mpc - T ) will have a negative relationship with output This algebraic analysis also shows us that any rise in a component of A that is offset by a movement in another component of A, leaving A unchanged, will also leave output unchanged