ارتباط انحنا و قيمت كالاي مستهلك.

In a vast sense, economy is a medium of products distribution and exchange of goods or services by different agents. Demand and supply issues for goods and services lead societies to plan market-based economics. The main goal of marketbased economics is to balance demand and supply, known as the general equilibrium. Mathematical economy paves the way to verify the existence, uniqueness, and algorithms for computing the equilibria. Differential geometries prefer to visualize the shape of the equilibrium manifold, i.e., the set of pairs of prices and endowments such that the aggregate excess demand function is equal to zero. Balasko had shown if the equilibrium price is unique for every economy, the price is constant, and the curvature is zero. Moreover, Loi and Matta generalized it in the form that for two commodities and an arbitrary number of agents, if the curvature of E (r), which is equilibrium manifold with fixed total resources r, is zero, there is the uniqueness of equilibrium for every economy. The general equilibrium condition is also must be held in a flea market, in which all kinds of goods are in their depreciated form. By definition, depreciation is the decline in the value of an asset over time due to different factors such as usage, wear, and tear and obsolescence, which is a significant concept that must be considered when pricing an item for sale. One reason why depreciation must be considered is that, if it is not, businesses would have an unrealistic and distorted estimation of their assets. Consequently, their estimation of the depreciation period net profit in the book value (B.V) will be inaccurate. In turn, the amount of tax a company needs to pay may exceed the original amount as the losses are not considered accurately. Here, to calculate the incurred losses due to depreciation, we consider the current value of the original price paid for the item, considering the interest rate and different depreciation periods. This matter yields the current value of the item to be sold and, comparing it with the current value of its original price lets us understand whether selling the price is to the benefit of the seller or not. Parametrization of depreciation and curvature Imagine in the flea market there are rfixed total depreciated resources and m consumers, and according to equilibrium theory, the supply and demand in this market must be equal. So by assuming l = m = 2 we have, B(r) = {(s(t), w₁ (t), w₂(t)) | f₁(s(t), w₁(t)) + f₂(s(t), w₂(t)) = r(t)}, and the equilibrium manifold be formed as below E(r) = {(s(t), w₁¹ w₁²) | f₁¹(s(t), s(t)w₁¹+w₁²) = f₂¹ (s(t), s(t) (r₁-w₁²) + r₂ - w₁²) = r₁}. The monetary value of an asset decreases over time due to use, wear, and tear, or obsolescence and straight-line depreciation is formulated as follows, D_J = J/N (p - s) where Nis the expected life of the equipment, sis the salvage value of the equipment at the end of each depreciation period, and pis the price of equipment at the early stage when it had been bought. The B.V of good is the difference between the initial cost and the depreciation cost at the end of depreciation periods which is formulated as follow, (1).B.V_J = p - J/N (p - s) The significant matter to focus on is that we must find the present value of the money that is paid for that equipment J periods of depreciation ago and compare it with a salvage value of the equipment at the moment t. To do that, we must make use of the compound amount formula, w = p(1+i)^J, (2) which iis the interest rate. Now we rewrite Eq. (2) as, w(t) = w(t-J)(1 + i)^J, (3) and at the end, by having Eq. (3) as an assumption, we can reform Eq. (1) as follows, B.V_J = w(t) - J/W(w(t) – s(t)). Here we construct a parametrization by using time and depreciation periods. ∅(t,J) = (s(t),J,w(t) - J/N (w(t) - s(t))). We assume the salvage value of equipment at the end of depreciation periods must be vanished, s(t)_t=N = 0, and the depreciation periods which has passed must be less than total life of equipment, J < N, thus, w(t) - J/N (w(t) - s(t)) = 0, w(t) = λs(t), whichλ > 1 and λ = J/N-J. The goal of this paper is to realize whether selling a used item is to benefit. We need to compare the current value of the original price paid for the product, due to the interest rate, with its price in a flea market as a used item and also the uniqueness of the price of depreciated goods by using the zero curvature in a flea market in general equilibrium conditions. Here also, we have calculated Ricci and Gaussian curvature by using the relation between these curvatures in the second fundamental form that we have constructed. We collect the mathematical economy aspect of general equilibrium in its differential geometry and topological view. Moreover we have parametrized the depreciation due to general equilibrium condition assumptions. In order to show the uniqueness of price of depreciated good s(t), by using that if 1 = 2, a necessary and sufficient condition for q unique equilibrium price is that the curvature of E (r) must be vanished. Results and discussion We consider the unit tangent sphere bundle of a Riemannian manifold (M. g) as a (2n+1) dimensional manifold, and then we equip that to the g-natural metric. Considering the associated metric of this metric, we define an almost contact B-metric structure on the unit tangent sphere bundle, and by using the coefficients of the structural tensors and the relevant classification for such structures, we attempt to classify the unit tangent sphere bundle equipped to this structure, and we prove that the non-zero coefficients of structure tensor F belong to the class F₁⊕F₄. Conclusion The following conclusions are obtained from this research. In this paper, using the initial definitions and assumptions of general equilibrium theory, and differential geometry, we have provided a new parametrization for depreciation, based on equilibrium condition and the book value formula. Therefore, in equilibrium condition, the curvature vanishes, and thus we obtain w(t) = s(t) + c. We know that w(t)is present value of the amount originally paid for the item and s(t) is the current price of depreciated item in flea market. Comparing these two values, considering the equilibrium conditions, if w(t) > s(t), c must be less than zero, which means we have lost money by selling this item. And if w(t) < s(t), cmust be greater than zero, which means we have profited. [ABSTRACT FROM AUTHOR]