Editing Classical general equilibrium model

{{Short description|Economic model}}
The '''classical general equilibrium model''' aims to describe the economy by aggregating the behavior of individuals and firms.<ref>{{Cite journal |last=Burgstaller |first=André |date=1989 |title=A Classical Model of Growth, Expectations and General Equilibrium |url=https://www.jstor.org/stable/2554284 |journal=Economica |volume=56 |issue=223 |pages=373–393 |doi=10.2307/2554284 |jstor=2554284 |issn=0013-0427|url-access=subscription }}</ref> Note that the classical [[general equilibrium]] model is unrelated to [[classical economics]], and was instead developed within [[neoclassical economics]] beginning in the late 19th century.<ref>{{Cite book |last=McKenzie |first=Lionel W. |url=https://www.worldcat.org/oclc/49226070 |title=Classical general equilibrium theory |date=2002 |publisher=MIT Press |isbn=0-262-13413-6 |location=Cambridge, Mass. |oclc=49226070}}</ref>

In the model, the [[individual]] is assumed to be the basic unit of analysis and these individuals, both workers and employers, will make choices that reflect their unique tastes, objectives, and preferences. It is assumed that individuals' wants typically exceed their ability to satisfy them (hence scarcity of [[good (economics)|goods]] and time). It is further assumed that individuals will eventually experience diminishing [[marginal utility]]. Finally, [[wages]] and [[prices]] are assumed to be elastic (they move up and down freely). The classical model assumes that traditional [[supply and demand]] analysis is the best approach to understanding the [[labor market]]. The functions that follow are aggregate functions that can be thought of as the summation of all the individual participants in the market.

==Aggregate supply==
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==Labor demand==
The consumers of the labor market are firms. The demand for labor services is a derived demand, derived from the supply and demand for the firm's products in the goods market. It is assumed that a firm's objective is to maximize [[Profit (economics)|profit]] given the demand for its products, and given the production technology that is available to it.

Some notation:
 Let <math>p</math> be price level of commodities
 Let <math>w</math> be nominal wage
 Let <math>\omega</math> be real wage (w/p)
 Let <math>\pi</math> be profit of firms
 Let <math>L^{D}</math> be labor demand
 Let <math>Y^{S}</math> be the firms output of commodities that it will supply to the goods market.

===Output function===
Let us specify this output (commodity supply) function as:
:<math>Y^{S}(L^{D})</math>
It is an increasing concave function with respect to L<sup>D</sup> because of the [[Production theory basics|Diminishing Marginal Product]] of Labor. Note that in this simplified model, labour is the only factor of production. If we were analysing the goods market, this simplification could cause problems, but because we are looking at the labor market, this simplification is worthwhile.

===Firms' profit function===
Generally a firm's profit is calculated as:
 profit = revenue - cost<br>
In ''nominal terms'' the profit function is:
 <math>p \cdot \pi = p \cdot Y^{S} - w \cdot L^{D}</math><br>
In ''real terms'' this becomes:
 <math>\pi = Y^{S} - \frac{w}{p} \cdot L^{D} = Y^{S} - \omega \cdot L^{D}</math>

===Firms' optimal (profit maximizing) condition===
In an attempt to achieve an optimal situation, firms can maximize profits with this ''Maximized profit function'':
 <math>\frac{dY^{S}(L^{D})}{dL^{D}} = \omega</math><br>
When functions are given, Labor Demand (L<sup>D</sup>) can be derived from this equation.

==Labour supply==
The suppliers of the labor market are [[household]]s. A household can be thought of as the summation of all the individuals within the household. Each household offers an amount of labour services to the market. The supply of labour can be thought of as the summation of the labour services offered by all the households. The amount of service that each household offers depends on the consumption requirements of the household, and the individuals relative preference for consumption verses free time.

Some notation:
 Let U be total utility
 Let Y<sup>D</sup> be commodity demand (consumption)
 Let L<sup>S</sup> be labor supply (hours worked)
 Let D(L<sup>S</sup>) be disutility from working, an increasing convex function with respect to L<sup>S</sup>.

===Households' consumption constraint===
Consumption constraint = profit income + wage income<br>
 <math>Y^{D} = \pi + \omega \cdot L^{S}</math>

===Households' utility function===
total utility = utility from consumption - disutility from work <br>
<math>U = Y^{D} - D(L^{S})</math><br>
'''substitute consumption''': <br>
<math>U = \pi + \omega \cdot L^{S} - D(L^{S})</math>

===Households' optimal condition===
'''Maximized utility function''': <br>
<math>\frac{dD(L^{S})}{dL^{S}} = \omega</math><br>
When functions are given, Labor Supply (L<sup>S</sup>) can be derived from this equation.

==Aggregate demand==
Y = C + I + G
whereby Y is output, C is consumption, I is investment and G is government spending

==Monetary market==

MV=PY(Fisher's Equation of Exchange)

==References==
{{Reflist}}
[[Category:Economics models]]
[[Category:Utility]]