(a) In the New Keynesian model with the Philips Curve studied in class, if the central bank does not intervene and the government suddenly increases government spending, inflation and current output will respond to the shock in different ways.Graphical explanation: The diagram below depicts the effect of the government's sudden increase in spending on inflation and current output. In the short run, the Phillips curve (PC) will shift up, indicating a higher level of inflation for any given level of output. The aggregate demand (AD) curve will shift to the right, indicating a higher level of output and a higher price level.The equilibrium point, where the PC intersects the AD curve, will shift from point E1 to point E2. The new equilibrium level of output is higher, but so is the level of inflation. As a result, the economy will experience an increase in inflation and output levels. Verbal explanation: The increase in government spending will increase demand in the economy, pushing up the price level and increasing inflation. Since the increase in spending was sudden, it is unlikely that firms will be able to respond by increasing supply in the short run. As a result, the increase in demand will lead to an increase in output, but also an increase in inflation. (b) The central bank's optimal response to the shock would be to increase interest rates to counteract the effect of the government's increase in spending. By increasing interest rates, the central bank can reduce the demand in the economy, which will reduce the upward pressure on prices and prevent inflation from rising too high. However, this will also reduce output levels, as firms will be less willing to invest when interest rates are high. Therefore, the central bank will need to balance the need to keep inflation under control with the need to maintain output levels. It is possible for the government to achieve all of its goals, but only if it is willing to accept a trade-off between inflation and output. If the government wants to maintain both high levels of output and low levels of inflation, it will need to work with the central bank to coordinate their policies. However, this may not always be possible, as the goals of the government and the central bank may not always align.