dorsal/arxiv
View SchemaEconomics from a Physicist's point of view: Stochastic Dynamics of Supply and Demand in a Single Market. Part I
| Authors | V. Granik, A. Granik |
|---|---|
| Categories | |
| ArXiv ID | physics/0207118 |
| URL | https://arxiv.org/abs/physics/0207118 |
Abstract
Proceeding from the concept of rational expectations, a new dynamic model of supply and demand in a single market with one supplier, one buyer, and one kind of commodity is developed. Unlike the cob-web dynamic theories with adaptive expectations that are made up of deterministic difference equations, the new model is cast in the form of stochastic differential equations. The stochasticity is due to random disturbances ("input") to endogenous variables. The disturbances are assumed to be stationary to the second order with zero means and given covariance functions. Two particular versions of the model with different endogenous variables are considered. The first version involves supply, demand, and price. In the second version the stock of commodity is added. Covariance functions and variances of the endogenous variables ("output") are obtained in terms of the spectral theory of stochastic stationary processes. The impact of both deterministic parameters of the model and the random input on the stochastic output is analyzed and new conditions of chaotic instability are found. If these conditions are met, the endogenous variables undergo unbounded chaotic oscillations. As a result, the market that would be stable if undisturbed loses stability and collapses. This phenomenon cannot be discovered even in principle in terms of any cobweb deterministic model.
{
"annotation_id": "67712b6d-2e8a-44e6-9f39-69d558283e93",
"date_created": "2026-03-02T18:00:39.897000Z",
"date_modified": "2026-03-02T18:00:39.897000Z",
"file_hash": "8f3197fad4375669f9fb254eb40f82d83801984ae7524a2c4e4f3af6cd86c1ce",
"private": false,
"record": {
"abstract": "Proceeding from the concept of rational expectations, a new dynamic model of\nsupply and demand in a single market with one supplier, one buyer, and one kind\nof commodity is developed. Unlike the cob-web dynamic theories with adaptive\nexpectations that are made up of deterministic difference equations, the new\nmodel is cast in the form of stochastic differential equations. The\nstochasticity is due to random disturbances (\"input\") to endogenous variables.\nThe disturbances are assumed to be stationary to the second order with zero\nmeans and given covariance functions. Two particular versions of the model with\ndifferent endogenous variables are considered. The first version involves\nsupply, demand, and price. In the second version the stock of commodity is\nadded. Covariance functions and variances of the endogenous variables\n(\"output\") are obtained in terms of the spectral theory of stochastic\nstationary processes. The impact of both deterministic parameters of the model\nand the random input on the stochastic output is analyzed and new conditions of\nchaotic instability are found. If these conditions are met, the endogenous\nvariables undergo unbounded chaotic oscillations. As a result, the market that\nwould be stable if undisturbed loses stability and collapses. This phenomenon\ncannot be discovered even in principle in terms of any cobweb deterministic\nmodel.",
"arxiv_id": "physics/0207118",
"authors": [
"V. Granik",
"A. Granik"
],
"categories": [
"physics.gen-ph"
],
"title": "Economics from a Physicist\u0027s point of view: Stochastic Dynamics of Supply and Demand in a Single Market. Part I",
"url": "https://arxiv.org/abs/physics/0207118"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "33c59f61-aadd-4879-a1e8-7eaeec9acf74",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}