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The Sticky-Wage Model

In this model, economists pursue the sluggish adjustment of nominal wages path to explain why it is that the short-run aggregate supply curve is upward sloping. For sticky nominal wages, an increase in the price level lowers the real wage therefore making labor cheaper for firms. Cheaper labor means that firms will hire more labor, and the increased labor will in turn produce more output. The time period where the nominal wage cannot adjust to the changes in price level and output signifies the positive sloping aggregate supply curve.
•     The nominal wage is set by the workers and the firms based on the target real wage, which may or may not be the labor supply & demand equilibrium, and on price level expectation.

W =      ù       *           Pe
Nominal Wage = Target Real Wage * Expected Price Level

After the nominal wage has been set but before any hiring, firms learn the actual price level (P). From this the real wage is derived

W/P = ù * Pe/P
Real Wage = Target Real Wage * Expected Price Level/Actual Price Level

From the equation,
real wage = target real wage when expected price level = actual price level
real wage > target real wage when expected price level < actual price level
real wage < target real wage when expected price level > actual price level

The bargaining between workers and firms determine the nominal wage rate but not the actual level of employment. This is determined by the firms’ hiring decisions and the labor demand function

L = Ld(W/P)

Output is determined by the production function, Y = F(L). The aggregate supply curve, under the sticky-wage model, summarizes the two functions and the relationship between the price level and output. Any unexpected changes in the price level cause a deviation in the real wage, which in turn, affects the amount of labor and output.
•     The major weakness of the sticky-wage model however, is that in any model with an unchanging labor demand curve, unemployment falls when the real wage falls. Under this model the opposite happens, which means that the real wage should be countercyclical. Economic data over the past decades in the U.S. shows that the real wage in fact tends to rise along with output. This is evidence contrary to Keynes predictions in the General Theory.

The Imperfect-Information Model

Characteristics:
•     Assumes that the market is clear – all wages and prices are free to adjust in order to balance supply and demand – and that differences in the short-run and long-run aggregate supply curves are from misperceptions about prices

MLA Citation:
"Business Cycle Theory." 123HelpMe.com. 12 Dec 2018
<https://www.123helpme.com/view.asp?id=56755>.

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•     Built by Robert Lucas in the early 1970s.
•     Assumes that each supplier in the economy produces a single good and consumes many goods. Because of imperfect information, changes in overall price level may be confused with changes in relative prices. This confusion has a bearing on decisions about supply quantity and is responsible for the upward sloping aggregate supply curve. If a producer finds that prices are higher than expected, they might conclude that prices of all the goods have increased. In this case they might revise their estimate of general price level but they might not change their production/output. Alternatively, they might think that price of their product has increased so they might increase their production.
•     According to the model, the slope of the aggregate supply curve should depend on the volatility of aggregate demand. This was tested by Robert Lucas and he found that for countries where aggregate demand and prices were most stable, changes in aggregate demand had the biggest effect. As with the sticky-wage model, deviations in output from the natural rate occur when the price level also deviates from the expected level. Specifically, output rises when actual prices are greater than expected prices.

The Sticky Price Model

Characteristics:
•     Emphasizes that firms do not instantly adjust their prices when there are variances in demand. For example, some firms enter contracts with customers, some firms may not want to upset loyal customers with frequent price changes, and the way how some markets are structured make prices sticky.
•     Assumes that there is not perfect competition.
•     A firm’s desired price depends on the overall level of prices and the level of aggregate income. It is denoted as
_
p = P + a(Y – Y) _

Where ‘p’ is desired price, ‘P’ is overall level of prices, (Y – Y) is the level of aggregate output in respect to the natural rate, and ‘a’ is an number greater than zero which measures the sensitivity of the desired price to changes in the level of aggregate output.
•     There are two types of firms: (1) firms with flexible prices, and (2) firms with sticky prices. Those with flexible prices always set their prices according to the above desired equation while those with sticky prices set their prices in advance based on expectations such as economic conditions and what other firms will charge. These sticky-price firms use the formula:

p = Pe + a(Ye – Ye), where ‘e’ represents expected values.

•     With the help of the overall price level, the pricing rules of the flexible and sticky-price firms can be used to derive the aggregate supply equation Y = Y + á(P – Pe), which is the common end result for all three supply models. The overall price level depends on the expected price level and level of output.
•     One significant difference between the sticky-price model and the sticky-wage model is that a sticky-price firm responds to a drop in sales by reducing production and demand for labor – the firm does not move along a fixed labor demand curve.
•     The model also makes predictions about inflation and the short-run supply curve – a higher average inflation rate results in a steeper curve. This prediction is supported by international data; countries with high average inflation have steep short-run aggregate supply curves and low-inflation countries have relatively flat aggregate supply curves.

Mutual Characteristic Of All Three Models
•     The basic short-run aggregate supply equation that all three theories share is
_
Y = Y + á(P – Pe),     á > 0
_
Where Y is output, Y is the natural rate of output, P is the price level, Pe is the expected price level, and á is some number greater than zero which indicates how sensitive output is with regards to changes in the price level. Seeing that 1/ á is the gradient of the aggregate supply curve, if á = 0, then the supply curve is vertical. But as á moves away from zero and becomes very large, the curve grows almost horizontal. This basic common equation says that output will deviate from the natural rate when the price level also deviates from the expected level.
•     Countries with variable aggregate demand have steep aggregate supply curves – if the price level is highly variable then few firms will commit to prices in advance.
•     In all three theories, output rises above the natural rate when the price level exceeds the expected price level, and output falls below the natural rate when the price level is less than the expected price level.

Conclusions & Considerations

Unemployment and inflation are two very important measures of economic performance. Lowering, maintaining, and controlling these rates are targets of economic policymakers. There is short-run tradeoff between inflation and unemployment however, as a lower rate in one measurement means a higher rate in the other. This tradeoff between the two is called the Phillips curve – a reflection of the short-run aggregate supply curve – and is often used to express aggregate supply by economists. The modern form of the curve states that the inflation rate depends on expected inflation, the deviation of unemployment from the natural rate or cyclical unemployment, and supply shocks.

As all three models have weaknesses in their arguments and assumptions, it’s not hard to see why economists disagree on which is the best to explain aggregate supply. However, the theories and information that each model consists of collectively communicate a better understanding of the short-run aggregate supply than any single model could.