Consumption Smoothing - Model

Model

Robert Hall (1978) formalized Friedman's idea. By taking into account the diminishing returns to consumption, and therefore, assuming a concave utility function, he showed that agents optimally would choose to keep a stable path of consumption.

With (cf. Hall's paper)

being the mathematical expectation conditional on all information available in
being the agent's rate of time preference
being the real rate of interest in
being the strictly concave one-period utility function
being the consumption in
being the earnings in
being the assets, apart from human capital, in .

agents choose the consumption path that maximizes:

Subject to a sequence of budget constraints:

The first order necessary condition in this case will be:

By assuming that we obtain, for the previous equation:

Which, due to the concavity of the utility function, implies:

Thus, rational agents would expect to achieve the same consumption in every period.

Hall also showed that for a quadratic utility function, the optimal consumption is equal to:

c_{t}=\left \left[ E_{t}\sum_{i=0}^{\infty }\left( \frac{1}{1+r}\right) ^{i}y_{t+i}+A_{t}\right]

This expression shows that agents choose to consume a fraction of their present discounted value of their human and financial wealth.


Read more about this topic:  Consumption Smoothing

Famous quotes containing the word model:

    “It has to be acknowledged that in capitalist society, with its herds of hippies, originality has become a sort of fringe benefit, a mere convention, accepted obsolescence, the Beatnik model being turned in for the Hippie model, as though strangely obedient to capitalist laws of marketing.”
    —Mary McCarthy (1912–1989)

    “The Battle of Waterloo is a work of art with tension and drama with its unceasing change from hope to fear and back again, change which suddenly dissolves into a moment of extreme catastrophe, a model tragedy because the fate of Europe was determined within this individual fate.”
    —Stefan Zweig (18811942)

    “... if we look around us in social life and note down who are the faithful wives, the most patient and careful mothers, the most exemplary housekeepers, the model sisters, the wisest philanthropists, and the women of the most social influence, we will have to admit that most frequently they are women of cultivated minds, without which even warm hearts and good intentions are but partial influences.”
    —Mrs. H. O. Ward (1824–1899)