ns = xs + x2 (w − pe) Assuming equilibrium in the labour market, we solve for the market-clearing nominal wage (w∗). so because demand equals the supply, so we get, xd + x1(p − w∗) = xs + x2(w∗ − pe), then we can get w∗, after substituting w∗ into demand function, we get n=n*+(x1x2/x1+x2)[p-pe], where n*=xd-x1(xd-xs/x1+x2) which is also the level of employment when expectations are correct, the nature level of employment, then adding time subscripts, and assume a simply production, Setting aggregate supply equal to aggregate demand and we can get the equilibrium price level :
where,is the aggregate excess demand shock, new classical economists assumed that agents have rational expectations. After running the conditional expectations operator Et-1 through the equation, we can get the final solution for output represented as: where. This equation shows that it is only the random component of the money supply that can effect output when agents from rational expectations, the growth rate of economy which we call it g does not affect output, this result is called the policy ineffectiveness proposition. Even we try to use the method of undermined coefficients, we can get the same result.
More precisely, an unanticipated change in u affects real out put but anticipated g will anyway have no effect. In addition, if expectation initially correct, output is at its natural level, if money supply rises unexpectedly, agent’s price expectation will not change but both the output and price level will rise, in other words, the rise in output is a result due the fact of a price surprise. At the same time, if there is an unexpected or anticipated rise in the money supply, rational agents will realize that prices will change. As a result, their expectation price will change; the price level does change but output not. However, we just cannot ever ignore money, another factor that could have real effects on output.
Let us now look at new Keynesian model upon aggregate supply. New Keynesian models show the effectiveness on macroeconomics policies once it was recognized that wages and prices were not fully flexible. In other words, new Keynesians argued that in some market prices were sticky or slow to adjust. In particular they stressed that wage contracts were frequently negotiated to cover one, two or even three years. The aim of this section is to explain how the existence of such overlapping wage contracts restores policy effectiveness. The model is based on optimizing micro-foundations and rational expectations. From a simply
Non-overlapping wage contract model, assuming labour market is not perfectly competitive, we can get the aggregate supply equation:
The graph on the left shows the basic idea of Keynesian’s model, wage is set for two periods and has achieved the full employment, workers expected money supply of Em in both periods, in first period, actual money supply is lower, so output falls below full employment, so an expansion of m to m1 will restore full employment. As a matter of fact, monetary policy shows effectiveness. Also, we can look at Keynesian’s model algebraly; just simply look at the solutions of output, we can actually get two answers, in different condition. If there is a constant monetary growth, we can get , if we assume there is contingent monetary policy, we cannot get , it is obvious to find out that contingent policy has lower variance than constant growth policy. But any of these models has proved the effectiveness of monetary policy.
Now I have talked about both theories, I believe that supposing in a modelWhich the market is imperfect and subject to menu costs, with the objective of maximizing profits. It was believed that the real effects of a nominal shock depend on how often adjust their prices; the greater the speed of adjustment of individual prices, the smallerthe real effects of a nominal shock, and the steeper the Phillips curve. This approach makes the following statements: There is a negative correlation between the variance of aggregate demand and output. Although in new classical model, prices and wages are perfectly fit. But I think Keynesian’s model is more realistic. And monetary policy is playing an important role in world economy. Any model contains expectation is a risky model, it always contains uncertainty. So I am in favor of new Keynesian’s theory.
In conclusion, it is not possible to say which model is right and wrong. The new classical theory and new Keynesian theory are actually assuming the model from different view. One thing in common for sure is that they both try to offer rational behavior form the rational expectations though theoretical point of view. Personally I would strongly consider the model which is more practical. In other words, I believe that new Keynesians’ theory is better explained the question.