1.Explain the concept of rational expectations. How does this view on how expectation is formed differ from the assumption that workers formed expectations of current and future price levels based on past information about prices?
Rational expectations assume that people learn from past mistakes. Implications for economic policy. The impact of expansionary fiscal policy will be different if people change their behavior because they expect the policy to have a certain outcome. For example, if expansionary fiscal policy causes inflation last year, they will factor this into future expectations. Therefore, in the second year, if the government pursue more fiscal stimulus, unemployment may not fall at all, because people immediately adjust their inflation expectations in response to government policy.
The reason why expectation is formed from assumption is differ from formed expectations of current and future price levels based on past information about prices is because of historical data on the variable of interest has been found to be less logically satisfactory than alternative assumptions that have formed the basis of the competing hypothesis of rational expectations. Besides, value of the expectation/ coefficient may differ for various group of economic agents, individual and over time. In addition, expectation may lag actual when there change in trend. Changes in trend of a variable of interest may emanate from the behavior of related variable that affected by broader factors such as recent global financial crisis. Those, expected value not only depend on its own past values but also together with past, present and expected values of others related variable.
2. Compare the effect of expansionary monetary policy between the new Classical and Keynesian on output and employment.

In Keynesian view, it is assuming that money wage is flexible, and labor supply (Ns) is assuming to depend on the expected real wage (W/Pe).

Expansionary monetary policy such as increase in money supply shift AD curve to the right from (AD to AD1 and AD2). These cause output rise from (Y0 to Y1 to Y2) and rise in employment from (N0 to N1 to N2) as well as price level rise from (P0 to P1 to P2). As employment increase, the unemployment rate will reduce. This induce the increase in money wage from (W0 to W1 to W2)
As increase in Ad cause rise in price level then other variable remain equal, the fasters the growth in Ad cause higher rate in inflation. Keynesian model implies that their trade-off between inflation and unemployment.

As Philip curve explain that the more quickly AD growth, the large rightward shift in AD, and other variable being equal, the faster rate of growth in output and employment. For given labor force, unemployment rate will be lower the as the fasters rate of growth in AD.
Increase in the money supply leads to an increase in employment and output in the short- run, until labor supplier correctly perceives the increase in price level that result from expansionary monetary policy action. Keynesian view that expectation about price are backward-looking so increase in money supply will affect output and employment.
In the new classical model, it is assuming that people are behave on rational expectation. Rational expectations imply that the workings of the economy are understood, and that fiscal and monetary policy will be anticipated rendering the policy ineffective. Where there is adequate information, people form beliefs about the economic future that are reasonably accurate. Based on their judgments, people adjust their economic behavior accordingly. As labor market were very competitive, new information is quickly absorbed. These variables expected include level on money supply, (Me), government spending (Ge), tax collection (Te), autonomous investment (Ie) and other possible variables.

Initially, assume aggregate demand (AD), aggregate supply (AS), labor demand (Nd) and labor supply (Ns) with actual and expected variable is zero with output (Y0), employment (N0), money wage (W0) and price level (P0).

When there is expansionary in monetary policy, there will be an increase in money supply and shift the AD to the right from AD(M0) to AD(M1). These changes also cause output rise from Y0 to Y’1 and rise in price level from P0 to P’1. With the rise in price, labor demand (Nd) would shift to the right from Nd(P0) to Nd(P’1). Increase in price also will increase money wage from W0 to W’1. New equilibrium moves from point A to B.

However, because the increase in money supply was anticipated, there would also increase in the expected money supply because of rational expectation. Labor supplier know that the inflationary effect occurs because of the increase in money supply. This instance cause labor supply (Ns) and AS shifting to the left to Ns (Me 1) and AS (Me1).
As decline in AS, it put further upward pressure on the price level and labor demand shift to Nd (P’1). The new equilibrium at point C where output and employment return to their initial level at Y0, N0 respectively with price level permanently higher at P1 and money wage W1.
New Classical believed that anticipated changes in the money supply do not affect real output and employment in the labor market because people assume have perfect information. With these information, people form rational expectation on upcoming events in the future so economic agents will adjust quickly to eliminate shortages and surpluses in the market.

When increase in the money supply is unanticipated due to monetary surprise, increase in money supply shift AD from Ad (M0) to AD(M1). As price level rises to P’1, labor demand also shifts to the right to Nd(P’1). As money supply is unanticipated, it does not affect the labor supplier’s expectation. Price level will take place in current period, so the labor supply does not shift. These cause changes in output and employment which output rise from Y0 to Y1 and employment will also rise from N0 to N1 and money wage rise to W’1. New equilibrium moves from A to B.