General Equilibrium Modeling for Economic Policy Analysis

This paper explores the value concept for explaining the relationship between price and value in the market. This relationship is important in determining market equilibrium and general equilibrium of the economy. Based on theoretical base, the GDP formula is built upon the value added method, and the general equilibrium model is developed upon market equilibriums and macro balances. In addition, the conceptual framework is proposed with macro closures for the context of the policy analysis. The simulation experiment is to conduct changes in target sector structure and macro balances on economic growth and transition. The paper contributes an insight on the general equilibrium of the economy and changes in economic policy on economic growth and transition.


Introduction
Economic growth is always the most important topic in economic literature. Many researchers attempt to identify driven factors on the economic growth that forms the base of economic growth theories. To deal with this problem, economists must understand general equilibrium and GDP measurement of the economy. In addition, it also requires a standard tool to analysis economic policy or economic shock on the economic growth and transition.
Value concept plays a crucial role in determining relationship between demand and supply in markets, and resource allocation between firms and customers. Leon Walras (1874) and Alfred Marshall (1890) argued that both supply (cost of production) and demand (utility) are interdependent and mutually determinant of each other's values. While Alfred Marshall (1890) developed his analysis to explain value in terms of supply and demand. Leon Walras (1874) created his theoretical model of general equilibrium as a means of integrating both the effects of the demand and supply side forces in the whole country. Based on theoretical base, Arrow and Debreu (1954) developed computable general equilibrium (CGE) model to study how an economy react to changes in economic policy. The general equilibrium model is built upon institutions (households, firms, governments, and rest of world), markets (commodity market, factor market, and capital market), and macro balances (saving investment balance, government balance, and external balance). By changing in economic policy or economic shock, new macro balances and market equilibriums will be established for the economy.
However, the traditional general equilibrium models use econometric techniques to estimate parameters that ignore inherent linkage of economic data and macro balances.
For that reason, this paper explores value concepts of price, utility and value, in which the utility function is formed with incorporation of price and value. From value creation perspective, the value added method is used for GDP measurement. The GDP formula not 3 only presents driven factors for economic growth, but also is used for the general equilibrium model with constraints of market equilibriums and macro balances. The simulation experiment is to conduct changes in target sector structure and macro balances on the economic growth and transition.

Value concept
The concept of value has a very long history in economic and philosophical thought that attempt to explain two meanings of value: value-in-use (value) and value-in-exchange (price). The difference between value-in-use and value-in-exchange is important because it forms the base of value theories. Most economists tried to make a clear distinction between value and price of a good or service. Baier (1966) offered a broader definition such as "value is the capacity of a good, service, or activity to satisfy a need or provide a benefit to a person or legal entity". Value is something which is perceived and evaluated at the time of consumption (Wikström, 1996;Woodruff and Gardial, 1996;Vargo and Lusch, 2004;Grӧnroos, 2008). There is a common understanding that value is created in the users' processes as value-in-use (Grönroos, 2011). Since value-in-use (value) is more appreciate guide to well-being than value-in-exchange (price), should economists use the law of diminishing marginal utility to explain demand curve. Thus, the value concept needs to redefine and theory of value should be constructed upon a law of diminishing marginal value (Trinh, 2014a). The theory of value not only interprets relationship between value and price, but also redefines the utility concept in this relationship. Based on this theoretical base, the utility function is formed with the incorporation of value, price (Trinh et al., 2014) as follows.
(1) Where,v,p,and u are unit value,unit price,and unit utility,respectively. TV,TR,and TU are total value,total revenue,and total utility,respectively. 4 From the value creation perspective, the value creation system involves three processes of production, exchange, and consumption as in Figure 1.

Figure 1: Value creation perspective
Source: Adapted from Grӧnroos andVoima (2012), Trinh (2014b;Trinh, 2014a) In firm perspective, the firm takes on the role of value facilitator, and also joins the customer's value creation as a value co-creator. Firm's production function is defined under the form of Cobb Douglas production function as follows: Where, Q is total output of production. A1 is firm's total factor productivity. K1 and L1 are firm capital and firm labor, respectively. α1, β1, are the output elasticities of production input factors.
By using the least-cost combination of production inputs, firm's cost function (TC1) can be determined as a function of output, depending on input prices and the parameters of the firm's production function as follows: Firm's profit function is determined by the following formula.
Where,  is firm profit and TR is total revenue ( Q p TR   ).
In customer perspective, the customer is always a value creator. The customer also takes part in the firm's production process as a co-producer. Since the value is created in the consumption process, customer capital (K2) and customer labor (L2) are added in the consumption function as follows: Where, Q is total output of consumption. A2 is customer's total factor productivity. α2, β2, are the output elasticities of consumption input factors.
By using the least-cost combination of consumption inputs, customer's cost function (TC2) can be determined as a function of output, depending on input prices and the parameters of the customer's consumption function as follows: Where, 2 TC is customer's total cost, 2 K w and 2 L w are unit costs of customer capital and customer labor.
Customer's utility function is determined by the following formula.
Where, U is customer utility and TU is total utility ( From the value creation perspective, value is created in the consumption process, both firm cost and customer cost have to consider in value creation. The joint cost function and the joint value function are determined as follows: ) and TC is total joint cost.  U are determined as follows: Customer then plays a role of the firm in the next exchange. The customer utility   1 i U in the initial exchange is also the firm profit   2 i Π in the next exchange.
For the final exchange, customers are the final consumers that buy the final commodities from the last firms in the exchange processes. Firm profit   im Π is given as follows: Total joint value (value added) of industry i is determined by the following formula.
is defined as a sum of production value of intermediate , total production value of industry i can be expressed as follows: Total production value (GDP) of the economy with n industries is determined as follows:  (18) can be rewritten as follows: From Equation (17) From Equation (19), setting , GDP measurement under the income approach can be expressed as follows: GDP is measured through total income that includes capital interest (KWK), labor wage (LWL), firm savings (SF), capital depreciation (D), tax and subside (T). 9

General Equilibrium Modeling
Understanding the economy requires a basic knowledge of key flows that influence economic activity. How does government policy influence GDP? It requires some knowledge of economy's structure that includes three main elements: markets, institutions, and macro balances. Figure 3 illustrates a basic structure of the economy that shows how institutions (households, enterprises, governments, and rest of world) interact in markets (commodity market, factor market, and capital market) under macro balances (saving investment balance, government balance, and external balance).  The economy contains four institutions: households, enterprises, governments, and rest of world.
Households receive income from factor markets in form of wages, profit, interest, and rent fees. Households spend for buying goods and services from commodity markets.
Households may send their saving or borrow money for their spending from capital markets.
Enterprises receive revenue from providing goods or services for households, governments, rest of world (ROW) on commodity markets. Enterprises also spend on costs of capital and labor on factor markets. Enterprises also need a required capital for their investment. Enterprises may send their profits to capital market or make loans from capital market.
Government collects tax from enterprises and households imposing on goods and services from commodity markets. Government may borrow money for their deficit from capital market or send their surplus to capital market. In addition, government returns a portion of the money it collect from tax in form of subsides that supports for enterprises and households.
A social accounting matrix (SAM) is an economywide data framework that presents the real economy of a country. SAM is an accounting framework that assigns numbers to the inflow (income) and outflow (outflow) in the circular flow diagram. A SAM is laid out as a square matrix in which each row and column is called an "account". Table 1 shows the SAM that corresponds to the circular flow diagram in Figure 3. Each of the boxes in the diagram is an account in the SAM. Each cell in matrix presents by convention, a flow of funds from a column account to a row account. The underlying principle of double-entry accounting requires that for each account in the SAM, total revenue equals total expenditure. This means that an account's row and column totals must be equal. The economy is constructed under macro balances including government balance, external balance, and saving-investment balance.

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Government balance is a constraint choice between government savings (the difference between government revenue and government expenditure) and tax rates. Closure (GOV-1) is that government savings is a flexible residual while all tax rates are fixed. Under another closure (GOV-2), tax rates are adjusted endogenously to generate a fixed level of government saving.
External balance is a constraint choice between net export (the difference between export and import) and exchange rates. Closure (ROW-1) is that net export is a flexible, while the exchange rate is fixed. Under another closure (ROW-2), the exchange rate is fixed to generate a fixed level of trade balance (net export).
Saving-investing balance is a constraint choice between investment drivers or saving drivers. Closure (SI-1) is that investment quantities are flexible, while savings is fixed. For another closure (SI-2), investment is fixed to generate a fixed level of saving.    In order to conduct changes in economic policy, the simulation experiment is carried out on the hypothetical economy with m sectors, each sector produce an offering (j = 1..m) by using total capital ( j K ) and total labor ( j L ).The demand function of offering j is defined as follows: Price demand: Market equilibrium: Production function   j Q of offering j are given as follows: Production function: Total profit function   Π of all offerings in the economy are determined as follows: Profit function: Where, Tj is tax or subside of the offering j (j = 1..m).
The following general equilibrium model is to maximize gross domestic product (GDP) under market equilibrium and macro balances.
The basic general equilibrium model: The basic general equilibrium model is developed with the objective function of GDP. GDP formula is built upon the value added method. The model is based on equilibrium of total supply and total demand (constraints of (27) and (28), target sector structure (constraint (29), and macro balances (constraints of (30) to (32)). The simulation experiment is carried out on the hypothetical economy with m sectors. Each sector j (j = 1..m) produces one offering (product or service) with total production output of Qj (j = 1..m) by using total capital (Kj) and total labor (Lj). The domestic price for offering j is given by the demand function . Net export price is adjusted with a ratio of EXj (ratio of export price and import price), which depends on exchange rate, export price and import price for the offering j.
In order conduct changes in economic policy on the economy, policy constraints of (29), (30), (31), and (32) are added to the general equilibrium model. Constraint (5)  . From these constraints and combinations of macro closures from Table 2, the model provides optimal solutions for the transformation from the current economy policy to the new economic policy with target sector structure of the economy.

Economic Policy Analysis
The simulation experiment assumes that the hypothetical economy has only three sectors (Industry, Agriculture, Service) (j = 3). Parameters of the economy are given in Table   3 and Table 4.  In order to evaluate changes in sector structure and macro policy, the experiment assumes the same macro closures (GOV-1, ROW-1, SI-1), policy parameters and macro constraints, in which government balance is less than or equal to 100, external balance is less than or equal to 500, and saving-investment balance is greater than or equal to 300. There are three 3 experimental models of the economy as follows: Model 1: The economy has the current sector structure of 30% Industry, 35% Agriculture, and 30% Service.
Model 2: The economy has the target sector structure of 35% Industry, 30% Agriculture, and 30% Service.
Model 3: The economy has the target sector structure of 35% Industry, 25% Agriculture, and 35% Service.
In order to conduct how the economy allocates resources under macro balances,   The expenditure approach measure GDP by using data on personal expenditure, capital investment, government expenditure, and net export. GDP using in the expenditure approach is the sum of personal expenditure (C), capital investment (I), government expenditure (G), and net export (NX). Table 6 shows the expenditure approach for GDP measurement of the economy. The income approach measures GDP by summing up the incomes that firms pay households for the resources they hire such as labor wage (L×WL), capital interest (K×WK), firm saving (SF), capital depreciation (D), tax and subside (T). GDP using the income approach is the sum of personal expenditure (C), capital depreciation (D), total saving (S), tax and subside (T). Table 7 shows the expenditure approach for GDP measurement of the economy.    Customer saving (SC = 462.05) and firm profit (П = 24.57) would lend in the financial market, where government and the rest of the world would borrow to finance their deficits.

Conclusions
Theory of value encompasses all the theories within economics that attempt to explain meanings of value and price. Neoclassical economists argue that the value has origins in exchanged and used process and price is depended on its utility. However, the utility is still a conceptual that economist is used to explain demand curves. In fact, the utility concept has also the same meaning with the value concept in modern economies, in which the value is created in consumption. Since the value concept is more appreciate guide to well being than the price concept, the theory of value refines the relationship between value and price. In addition, the utility function is formed with incorporation of value and price that is also used for GDP measurement. The GDP formula is important to not only explain endogenous and exogenous variables, but also analyze economic growth and transition in the general equilibrium model.
In order to analyze how economic policy or economic shock has influence on the economy, the general equilibrium model is developed with the objective function of GDP, and constraints of market equilibriums and macro balances. A framework of economic policy analysis is proposed with the different macro closures that depend on the context of the policy analysis. The simulation experiment is carried out on the hypothetical economy with three typical sectors (Industry, Agriculture, and Service). The experiment is to conduct changes in economic policy (target sector structure, government balance, external balance, saving-investment balance) on the economic growth and transition. The paper contributes an insight on general equilibrium of the economy, conceptual framework for policy analysis on economic growth and transition. 23 However, the study has some limitations that also suggest for further researches: (1) since the general equilibrium model is developed upon economic data from SAM, linkage of national accounts and SAM should be studied in future; (2) the demand function is assumed in the general equilibrium model, the further researches need to analyze determinants of demand and forecast market price; (3) it also assumes market equilibriums, in which total production output are totally consumed by households, governments, and rest of world; (4) the research should expand with multiple sectors and with SAM data for the economy.