Model Answer
0 min readIntroduction
The short-run aggregate supply (SRAS) curve illustrates the relationship between the price level and the quantity of output supplied by firms in the short run. Robert Lucas, a Nobel laureate, developed a model to explain the SRAS curve based on rational expectations and the assumption of a perfectly competitive labour market. His model highlights how unexpected changes in the price level can influence output, while fulfilled expectations have no real effect. This is because workers base their labour supply decisions on expected, not actual, real wages. Understanding this framework is crucial for comprehending macroeconomic fluctuations and the effectiveness of monetary policy.
Derivation of the SRAS Curve with Unfulfilled Expectations
Lucas’s model assumes a small island economy with a large number of identical firms and workers. Workers maximize utility by choosing the amount of leisure to consume, and firms maximize profits by choosing the amount of labour to hire. The labour market clears, meaning that the real wage rate adjusts to equate labour supply and labour demand. The key assumption is that workers form expectations about the future price level and base their labour supply decisions on the expected real wage.
Let:
- W = nominal wage
- P = price level
- Pe = expected price level
- L = labour supplied
- Y = output
The real wage (w) is perceived by workers as W/Pe. Workers choose labour supply (L) based on this perceived real wage. Firms, however, observe the actual price level (P) and determine the actual real wage as W/P. The production function is assumed to be linear in labour, i.e., Y = AL, where A is a constant representing productivity.
If the actual price level (P) differs from the expected price level (Pe), firms experience an unexpected change in the real wage. If P > Pe, the actual real wage is lower than expected, and firms will hire more labour because labour is relatively cheaper. This leads to an increase in output. Conversely, if P < Pe, the actual real wage is higher than expected, and firms will hire less labour, leading to a decrease in output.
The SRAS curve is therefore upward sloping when expectations are not realised. It shows the positive relationship between the price level and the quantity of output supplied, given a specific level of expected inflation. Mathematically, the SRAS curve can be represented as:
Y = A L(W/Pe). Since L is a function of W/Pe, changes in P (when P ≠ Pe) affect Y.
Shape of the SRAS Curve when Expectations are Fulfilled
When expectations are fulfilled, i.e., P = Pe, the actual real wage equals the expected real wage (W/P = W/Pe). In this case, firms are operating at their planned level of output, and there is no incentive to change the quantity of labour hired. The SRAS curve becomes vertical at the level of potential output (Yn). This is because changes in the price level do not affect the real wage, and therefore do not affect labour supply or output.
The vertical SRAS curve implies that monetary policy can only affect the price level in the long run, but cannot permanently affect output. Any attempt to increase output through monetary expansion will only lead to inflation, as the economy is already operating at its potential.
The SRAS curve when expectations are fulfilled can be represented as:
Y = Yn, regardless of the price level P, when P = Pe.
Diagrammatic Representation
A diagram showing two SRAS curves would be ideal here. One curve, upward sloping, representing the case where expectations are not fulfilled. The other, vertical, representing the case where expectations are fulfilled. The x-axis would represent output (Y), and the y-axis would represent the price level (P).
Conclusion
Lucas’s model provides a powerful framework for understanding the short-run aggregate supply curve and the role of expectations in macroeconomic fluctuations. The shape of the SRAS curve depends crucially on whether expectations are fulfilled. When expectations are not realised, the SRAS curve is upward sloping, allowing for short-run output fluctuations. However, when expectations are fulfilled, the SRAS curve becomes vertical, indicating that output is determined by real factors and monetary policy can only affect the price level. This model underscores the importance of credible monetary policy and the management of expectations for macroeconomic stability.
Answer Length
This is a comprehensive model answer for learning purposes and may exceed the word limit. In the exam, always adhere to the prescribed word count.