اقتصاد خرد آماری
|کد مقاله||سال انتشار||مقاله انگلیسی||ترجمه فارسی||تعداد کلمات|
|5876||2013||17 صفحه PDF||سفارش دهید||10604 کلمه|
Publisher : Elsevier - Science Direct (الزویر - ساینس دایرکت)
Journal : Physica A: Statistical Mechanics and its Applications, Available online 17 May 2013
A statistical generalization is made of microeconomics in the spirit of going from classical to statistical mechanics. The price and quantity of every commodity1 traded in the market, at each instant of time, is considered to be an independent random variable: all prices and quantities are considered to be stochastic processes, with the observed market prices being a random sample of the stochastic prices. The dynamics of market prices is determined by an action functional and, for concreteness, a specific model is proposed. The model can be calibrated from the unequal time correlation of the market commodity prices. A perturbation expansion for the correlation functions is defined in powers of the inverse of the total budget of the aggregate consumer and the propagator for the market prices is evaluated.
In most studies of microeconomics, at a given instant, the quantity and price of a commodity are taken to be a determinate quantity. Microeconomics studies the (deterministic) equilibrium value of the quantities and prices of commodities as well their time evolution. A statistical generalization is made in microeconomics by considering quantities qi(t)qi(t) and price pi(t)pi(t) to be independent random variables for each instant of time, namely stochastic variables. A possible reason for prices to be random is that, similar to the price of equities, the prices of commodities incorporate all the market information and result in the traded prices. In the absence of new information, any departures from the traded prices, hence, should be indeterminate, random and uncertain. Furthermore, market prices are not in equilibrium, but rather have a (random) evolution in time tt that can have an overall drift reflecting market sentiment. Market prices may not contain all the market information and the source of randomness of market prices may have other explanations such as due to the existence of ‘sticky’ prices . In statistical microeconomics, the supply View the MathML sourceS[p] and demand View the MathML sourceD[p] of commodities at market prices View the MathML sourcep is the starting point for analyzing the behavior of the producers and consumers of commodities. The competing tendency of demand and supply, namely demand increases when prices fall whereas supply increases when prices rise is reflected in the traded prices. In fact, in most microeconomics texts, the market commodity price is taken to be the value for which supply is equal to demand. Supply and demand are inseparable, with one determining the other and vice versa. The view taken in this paper is that supply and demand are two facets of the same entity, namely a microeconomic potential functionView the MathML sourceV[p]. Using the analogy from mechanics, a potential function View the MathML sourceV[p] is postulated that combines supply and demand into a single entity and embodies the competing effects of both supply and demand. As will be discussed later, both the supply and demand functions are dimensionless and hence can be consistently added together. The potential is chosen to be the sum of supply and demand, namely
نتیجه گیری انگلیسی
A statistical generalization of microeconomic modeling is proposed in this paper by considering all commodity prices to be stochastic processes. The demand and supply function are interpreted as being components of a single underlying microeconomic potential and the average market price, to lowest order is given by minimizing the microeconomic potential. A simple model for both the demand and supply functions has been proposed so that a concrete analysis could be carried out. The utility function was evaluated from the demand function using the principle of duality. A Feynman path integral was defined for the random evolution of commodity prices and provides a theoretical framework for the study of commodity prices considered as stochastic processes. The choice for the microeconomic kinetic term View the MathML sourceT[p] is based on a detailed empirical study of equity markets; the form chosen for View the MathML sourceT[p] has been shown by empirical evidence to be very accurate for a wide range of equities . The kinetic term driving the time dependence of commodity prices was proposed, in analogy with the behavior of equity prices, to be determined by the velocity and acceleration of commodity prices. This form of the kinetic energy leads to many new features not present in quantum mechanics. Furthermore, since commodities undergo a classical random evolution, many of the problems related to the lack of unitarity due to the acceleration term in the Lagrangian do not appear in microeconomics. The microeconomic potential term View the MathML sourceV[p] combines the demand and supply of commodities into a single entity and provides an entirely new perspective on the mode of competition between supply and demand. One needs to study all the major commodities; as mentioned earlier, the empirical study of gasoline prices  supports the form of the microeconomic potential chosen in this paper. The Lagrangian that combines the kinetic and potential terms for commodity prices shows the central role being played by the kinetic term; this term is absent in the standard treatments of microeconomic analysis that are focused almost solely on supply and demand. Of course, whether the kinetic term in fact is important in the dynamics of commodity prices is an empirical question and needs to be further studied. A well defined perturbation expansion about the minimum of the potential was defined and the propagator was explicitly evaluated. The expansion of the path integral in terms of the inverse of the budget constraint is valid only for a large budget; if the budget becomes small, the statistical fluctuations become large and numerical methods are then necessary for evaluating the path integral. The expansion of market prices and its correlators in a power series in the inverse of the total budget, which has been introduced in this paper, needs to be studied empirically to ascertain whether in fact market data provides evidence of such an expansion. The calibration and testing of the proposed statistical model of microeconomics is based on comparing the model’s prediction with the empirical values of market prices as well as by comparing the model’s propagator (unequal time correlation function) of market prices with the empirical propagator obtained from market data.