The 3-equation model (IS-PC-MR) form Carlin, W. and Soskice, D., 2006. Macroeconomics: imperfections, institutions, and policies.

Q: Consider an economy at its medium-run equilibrium with output at ye and inflation at the target level of ?t. Assume that policy affects the economy with a one-period lag and households form their expectations adaptively. Answer the following questions:

1. Suppose the economy exits from a trade and economic union. As a result, the economy suffers from a permanent loss in productivity. Carefully draw a 3-equation diagram and provide a period by period explanation of the adjustment process of the economy to its new medium-run equilibrium.

2. Now, suppose at the same time that the productivity falls, households cut their spending in anticipation of lower income. Use the 3-equation diagram and explain how the economy adjusts to its new medium-run equilibrium.

3. Draw the impulse response function of real interest rate for the above two scenarios. How does the movement in household spending matter for monetary policy making?

?I can solve a similar problem, but I can't solve this one?below is the problem I have solved.?

Consider an economy that initially stays at its long-run equilibrium with output at Ye and inflation at the target level of ?T. The policy affects the economy with a one-period lag.

1 Suppose households form their expectations adaptively, use the 3-equation model and diagrams to provide a period by a period explanation of the adjustment process for the case where the economy is hit by a permanent negative aggregate supply shock.

2 Draw the impulse response functions for output, inflation, and the real interest rate after the shock.

3 How would the adjustment process differ from the case of a temporary shock? What is the implication for the central bank when implementing monetary policy?

4 Now, suppose households form their expectations rationally, will the impact of the shock of question 1 on output be mitigated? Why?

3.1 Period 0 Since the economy shocked by a permanent negative impact of total supply. Firstly, the equilibrium level of economic output decreasing from y, to y'?. At point A, the economy is above equilibrium output and there is pressure on inflation to increase. Phillips curve moves up from PC (1 = ], ye ) to PC (15 = IT, y'e) . There is a new equilibrium level. The economy develops from A to B. the output level of the two points is at the initial level, but the inflation rises to To. The central bank predicts that this kind of shock is a permanent supply shock. The central bank will move the MR curve inward to ensure that the optimal output of the central bank is equal to y', and inflation is equal to nT. Because point B is not on the central bank's new monetary rule curve MR'. The central bank began to forecast the Phillips curve for the next period. At present, the output is higher than the new equilibrium level y's, which means that PC will shift in the next period, and PC curve will move to PC (m; = To . y'e ) . On this PC curve, the central bank wants to locate it at point C on the new monetary rule curve, and the central bank sets the interest rate to ro. Because the impact of interest rates on the economy takes a time lag, Therefore, at the end of the period 0, the inflation is To, the output is ye, and the interest rate is To Period 1. After a period of time, the first new interest rate has an impact on output. Higher interest rates reduce demand and investment. This makes the output drop, the economy moves to the C point, the output is lower than the new equilibrium level at y,, and the inflation rate is my . The central bank began to forecast the PC curve for the next period. The current output is far from the new equilibrium point, so in the next period, the PC curve will continue tochange and move to PC (n2 = m1, y'e) . On this PC curve, the central bank wants to position it at point D on the MR curve. Therefore, the interest rate needs to be reduced to r, . However, interest rate can only affect economic output in a period of time lag. Therefore, at the end of this period 1, the inflation rate is my , the output is y,, and the interest rate is 1. Period 2, lower interest rates increased demand and the economy moved to point D. Output increases to y2 and inflation decreases to 12. This process is repeated until the economy returns to equilibrium at the z-point. When the economy is at equilibrium point Z, the adjustment of negative supply shock is over, the output is at y's, the inflation is at the target inflation , and the interest rate is at r, C YS y TL y y. He ye PC ( Tus# = 1, y'e) PC ( 71 = TV . y'e ) B PC( TWO = NV. ye ) A MR MR' 3 Ya y'e ye y Figure : The adjustment of the Economy to a permanent negative aggregate Supply shock3.2 TV Shock inflation TV . TUT time ye output time Real interest Rate Y's time3.3 Demand shocks will cause the economy to deviate from the initial equilibrium output level in a number of periods. the permanent shock will lead to a new level of equilibrium output. In the face of permanent supply shock, the IS curve remains unchanged, and the central bank needs to predict the PG curve in different periods. In the face of shocks. the central bank must predict the position ofthe Phillips curve in the next cycle, Then set the appropriate interest rate. The more timely and accurate the central bank forecasts when implementing monetary policy. the more likely it is to offset these changes and limit its impact on ination. 3,4 The impact of the stock on output will be mitigated, because the householder can expectations rationally, They understand that the economy will always return to equilibrium. Rational expectations can directly aect people's ination expectations. Before reducing ination expectations. The central bank does not have to bear the employment losses of low ination. The introduction of rational expectation eliminates the lag between the change of interest rate and the change of output, which means that the central bank no longer needs to adjust the interest rate gradually to guide the economy along the MR curve. As soon as the interest rate changes+ the economy jumps to a new equilibrium point. If ination expectations are reasonably shaped, Therefore. in addition to the unpredictable shocks. the economy is in a balanced state, so the impact of the shocks on the economy will be reduced