Yanfen LUO，Chaozhou LU

Department of Business and Trade，Rongchang Campus，Southwest University，Chongqing 402460，China

1 Introduction

In the history of economics，there are four value theories：cost-ofproduction theory of value developed by Adam Smith；labor value theory advanced by Marx；marginal utility theory put forward by the Austrian School；equilibrium price theorymade by Marshall.From the individual's preferences and technology，equilibrium price theory，the combination of cost-of-production theory of value and marginal utility theory，analyzes the decentralized action of people seeking self-interestand guides the optimal allocation of resources（by perfect competition）.It becomes the mainstream thought of current economics.However，doubt is casted on the analysis of demand built based on subjective and unfathomable utility function.In this regard，from the labor value theory，this paper intends to use relative labor time to re-derive the demand and supply curve to explain the relationship between labor value and market equilibrium.

2 Relative labor time and reservation price

First，we consider a simple economy.The economy is constituted by two persons（A and B），each with eight hours of labor time.Both of them can produce two commodities（x and y）.The labor productivity of economic entity can be signified by the individual labor time consumed for the production of a unit of commodity.The larger the value is，the lower the labor productivity is.The labor productivity of the two persons is shown in Table 1.

2.1 Self-sufficient productionUnder the self-sufficient production，it is assumed that the economic entity evenly allocates the labor time on two commodities.The outputof economic entity and output of collective are shown in Table 2.

Table 1 Labor productivity（labor time consumed for the production of a unit of commodity）

Table 2 The output of individual and collectivewhen the self-sufficiency is achieved

2.2 Specialized division of laborThe division of labor is conducted between economic entities：A produces commodity x while B produces commodity y（Table 3）.After the division of labor，the labor productivity and total resources remain unchanged，while the total output increases，bringing additional income.However，if the fruits of labor are notexchanged and economic entity has only a single product，the situation isworse compared with diversification of productwhen there is self-sufficiency.

Table 3 Comparison of output of econom ic entity and collective before and after the division of labor

2.3 Division of labor and exchangeIt is assumed that the economic entity exchange products in accordancewith the propor-tion of one unit of commodity x＝four units of commodity y.What the economic entities get after exchange is better than what the economic entities get when there is self-sufficiency（Table 4）.Obviously，the commodity economicmechanism built on the basis of specialized division of labor and free exchange isbetter than the self-sufficiency economic mechanism.Those products for the exchange become commodities.

Table 4 Comparison of output of economic entity and collective before and after the division of labor and exchange

2.4 Available exchange price rangeThe exchange price of the above commodity：the price of one unit of commodity x＝the price of four units of commodity y.In fact，there is a price range between buyers'highest bid price and sellers'lowest asking price built based on relative labor time and derived opportunity cost，and the commodities are exchanged in this price range.If taking commodity x as object of exchange and commodity y as universal equivalent，then A is the supply side and B is the demand side.Assuming the opportunity cost（Cx）of producing one unitof commodity x is as follows：

Cx＝one unit of commodity x×labor time for one unit of commodity x／labor time for one unit of commodity y＝labor time for commodity x／labor time for commodity y＝relative labor time for commodity x.

The relative labor time and opportunity costs of both sides are as shown in Table 5.

Table 5 Opportunity cost

A is the supply side of commodity x，and the purpose of its economic behavior is to obtain commodity y，and exchange commodity x for y（Fig.1）.Only when the exchange proportion is one unit of commodity x≥two units of commodity y is A willing to become a professional producer and supplier of commodity x.

The reservation price of commodity x suppler is the lowest asking price for two units of commodity y，namely the relative labor time（opportunity cost）for producing one unit of commodity x.Similarly，the reservation price of buyer is the highestbid price for eightunitsof commodity y.The reservation price of commodity x supply and demand sides is summarized in Table 6.

Table 6 The reservation price of supp ly and demand sides

The exchange price range for one unit of commodity x is［2 units of y，8 unitsof y］.In the range，the transaction atany price is feasible，and it thus establishes the relations between payment willingness and objective relative labor time.There are numerous buyers and sellers，the expected exchange price is sole，and the market equilibrium will appear.

3 Market equilibrium model of relative labor time

In a large economic society，wemake the following hypotheses：

Hypothesis 1The economic society can produce two products（x，y）；the social basic economic system is private ownership of property；eachmarket is in a state of perfect competition；the economic entity has economic rationality.

Hypothesis3Each economic entity purchases or supplies one unit of commodity（if a natural entity purchases or supplies n units of commodity，it can be split into n economic entities in theory）.

3.2 Relative labor productivity and supply curveBy sequencing the reservation supply price for commodity x from low to high，the supply curve is obtained，as shown in Fig.3.Only those economic entities，with lower reservation purchase price for commodity x thanmarketprice，will choose to produce and supply commodity x.With the increase in themarketexchange price，the cumulative supply amountof commodity x increasesand the supply curve slopes upward on the right.

3.3 Relative labor productivity and market equilibriumIn a perfectly competitive market，the buying and selling of supply and demand sides will cause the adjustment of market exchange price to form a stable equilibrium exchange price，as shown in Fig.4.

4 Connotation of relative labor time and market equilibrium

4.1 Equilibrium exchange price reflects the exchange value

Equilibrium exchange pricemeanshowmany unitsof commodity y to be exchanged for one unit of commodity x when the market achieves a competitive equilibrium.The exchange price is the exchange value of commodity x measured by commodity y.In Fig.4，the whole society agrees that one unit of commodity x is exchanged for C*unitsof commodity y，so the exchange value ofone unit of commodity x measured by commodity y as general equivalent is C*.

4.2 Equilibrium exchange price reflects the labor value

4.3 Equilibrium exchange ratio guides the allocation of resourcesIn economic society，therearenumerouseconomic entitieswhich can produce commodity x.After the formation ofmarket equilibrium price，only those economic entities with the relative labor time for the production of commodity x lower thanmarket equilibrium price（OE segment in Fig.4），are voluntarily engaged in commodity production.In the economic society，there are numerous economic entities needing commodity x，and it relates to the distribution of a given commodity.After the formation ofmar-Itmakes the individual value contained in one unit of commodity x higher or lower than Cx*.Only for the production of one ket equilibrium price，only those economic entities with the relative labor time for the production of x higher thanmarketequilibrium price and the relative labor time for the production of other commodities lower than themarket equilibrium price of this commodity（AE segment in Fig.4），voluntarily first produce other commodities and then exchange them for commodity x.Equilibrium exchange price becomes the dividing line of comparative advantage.It guides the economic entities with comparative advantage higher than the dividing line to directly produce goods and guides the economic entities with comparative advantage lower than the dividing line to indirectly produce goods.Thewhole society produces the given amount of commodities needed with the minimum input，so the allocation of resources is optimized.

5 Conclusions

In this paper，based on the relative labor time，we reconstruct the demand and supply curves.Under ideal environment of perfect competition，the onlymarketequilibrium price is the ratio of labor value between two commodities，and commodity is sold according to its labor value.Compared with the traditional equilibrium price build based on subjective utility，the equilibrium price in this model can also play a role in guiding the allocation of resources，and it is based on objective quantifiable relative labor time.For a long time，it is difficult to calculate the labor value in the commodity，and this paper hopes to provide some ideas for the calculation of socially necessary labor time-the perfect competition equilibrium price in themodel is the ratio of socially necessary labor time between two commodities，and also the ratio of labor value between two commodities.

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