Lucas aggregate supply function

New classical made its first attempt to model aggregate supply in Lucas and Leonard Rapping (1969).[2] In this earlier model, supply (specifically labor supply) is a direct function of real wages: more work will be done when real wages are high and less when they are low. Under this model, unemployment is "voluntary".[3] In 1972 Lucas made a second attempt at modelling aggregate supply.[3] This attempt drew from Milton Friedman's natural rate hypothesis that challenged the Phillips curve.[4] Lucas supported his original, theoretical paper that outlined the surprise based supply curve with an empirical paper that demonstrated that countries with a history of stable price levels exhibit larger effects in response to monetary policy than countries where prices have been volatile.[4]

On the basis of Lucas' 1973 paper,[5] Thomas Sargent and Neil Wallace introduced their 'surprise' supply function in which there was a white noise error term introduced that cannot be predicted in any way.[6] Lucas introduced the effects of nominal and real shocks affecting a macro-economy into his system through price expectations: if expectations are true, output in any given period is at its natural level. However, the well-known and widely accepted aggregate production function described by Sargent and Wallace also provides leeway for the white-noise shocks independent of price expectations–resulting in the accidental nature of equilibrium and in the inefficacy of countercyclical efforts of monetary policy.[7]

Lucas's model dominated new classical economic business cycle theory until 1982 when real business cycle theory, starting with Finn E. Kydland and Edward C. Prescott,[8] replaced Lucas's theory of a money driven business cycle with a strictly supply based model that used technology and other real shocks to explain fluctuations in output.[9]

The rationale behind Lucas's supply theory centers on how suppliers get information. Lucas claimed that suppliers had to respond to a "signal extraction" problem when making decisions based on prices; the firms had to determine what portion of price changes in their respective industries reflected a general change in nominal prices (inflation) and what portion reflected a change in real prices for inputs and outputs.[10] Lucas hypothesized that suppliers know their own industries better than the general economy. Given this imbalance in information, a supplier could perceive a general increase in prices due to inflation as an increase the relative price for its output, reflecting a better, real price for its output and encouraging more production. The surprise leads to an increase in production and employment throughout the economy.[10]

The function can be represented simply as:

${\displaystyle Y_{s}=f(P-P_{expected})}$

The simple version models aggregate output as a function of the price surprise. A more complicated expression of the Lucas supply curve adds expectations to the model. Aggregate supply is a function of the “natural” level of output (${\displaystyle Y_{N_{t}}}$) and the difference between actual prices (${\displaystyle P_{t}}$) and the expected price level given past information ${\displaystyle \Omega _{t-1}}$ times a coefficient based on an economy's sensitivity to price surprises (${\displaystyle \alpha }$):[11]

${\displaystyle Y_{s}=Y_{N_{t}}+\alpha [P_{t}-E\left(P_{t}|\Omega _{t-1}\right)]}$

By invoking Okun's law to express the function in terms of unemployment, Lucas's supply function can be viewed as an expression of the expectations-augmented Phillips curve.[12]

• Lucas islands model

• Snowdon, Brian; Vane, Howard R. (2002). An Encyclopedia of Macroeconomics. Aldershot: E. Elgar. ISBN 978-1-84542-180-9.
• Snowdon, Brian; Vane, Howard R. (2005). Modern Macroeconomics. Cheltenham: E. Elgar. ISBN 978-1-84542-208-0.
• Turnovsky, Stephen J. (2000). Methods of Macroeconomic Dynamics (Second ed.). MIT Press. pp. 97–104. ISBN 978-0-262-20123-0.