Mathematically explain Permanent income theory
The permanent income theory is based on the idea that people's consumption patterns are influenced by their expectations of future income rather than their current income levels. According to this theory, individuals will adjust their consumption levels based on their expected permanent income, which is considered to be the average level of income that an individual expects to receive over an extended period of time.
Mathematically, the permanent income theory can be modeled using the following equation:
Ct = PIt + εt
Where:
Ct = Consumption in period t
PIt = Permanent income in period t
εt = Transitory income in period t
The theory suggests that individuals will consume a fraction of their permanent income, rather than their current income. This is because people are more likely to base their consumption decisions on their long-term income expectations rather than short-term fluctuations in income. Transitory income, represented by εt, reflects temporary changes in income that may impact consumption levels in the short term, but do not have a lasting effect on overall consumption patterns.
Overall, the permanent income theory suggests that individuals will smooth out their consumption over time to maintain a consistent standard of living, even in the face of temporary fluctuations in income. This theory helps to explain why people may continue to spend and consume even during periods of economic downturn or uncertainty.