Classical general equilibrium model

<h2 id="aggregate-supply">Aggregate supply</h2>

<h2 id="labor-demand">Labor demand</h2>
<p>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 <a href="/facts/Profit_(economics)/kfPA9rfB">profit</a> given the demand for its products, and given the production technology that is available to it.
</p><p>Some notation:
</p>
Let 
  
    
      
        p
      
    
    {\displaystyle p}
  
 be price level of commodities
Let 
  
    
      
        w
      
    
    {\displaystyle w}
  
 be nominal wage
Let 
  
    
      
        ω
      
    
    {\displaystyle \omega }
  
 be real wage (w/p)
Let 
  
    
      
        π
      
    
    {\displaystyle \pi }
  
 be profit of firms
Let 
  
    
      
        
          L
          
            D
          
        
      
    
    {\displaystyle L^{D}}
  
 be labor demand
Let 
  
    
      
        
          Y
          
            S
          
        
      
    
    {\displaystyle Y^{S}}
  
 be the firms output of commodities that it will supply to the goods market.

<h3>Output function</h3>
<p>Let us specify this output (commodity supply) function as:
</p>

Y
          
            S
          
        
        (
        
          L
          
            D
          
        
        )
      
    
    {\displaystyle Y^{S}(L^{D})}

<p>It is an increasing concave function with respect to LD because of the <a href="/facts/Production_theory_basics/G5mF3WkI">Diminishing Marginal Product</a> 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.
</p>
<h3>Firms' profit function</h3>
<p>Generally a firm's profit is calculated as:
</p>
profit = revenue - cost

<p>In <i>nominal terms</i> the profit function is:
</p>

p
        ⋅
        π
        =
        p
        ⋅
        
          Y
          
            S
          
        
        −
        w
        ⋅
        
          L
          
            D
          
        
      
    
    {\displaystyle p\cdot \pi =p\cdot Y^{S}-w\cdot L^{D}}

<p>In <i>real terms</i> this becomes:
</p>

π
        =
        
          Y
          
            S
          
        
        −
        
          
            w
            p
          
        
        ⋅
        
          L
          
            D
          
        
        =
        
          Y
          
            S
          
        
        −
        ω
        ⋅
        
          L
          
            D
          
        
      
    
    {\displaystyle \pi =Y^{S}-{\frac {w}{p}}\cdot L^{D}=Y^{S}-\omega \cdot L^{D}}

<h3>Firms' optimal (profit maximizing) condition</h3>
<p>In an attempt to achieve an optimal situation, firms can maximize profits with this <i>Maximized profit function</i>:
</p>

d
              
                Y
                
                  S
                
              
              (
              
                L
                
                  D
                
              
              )
            
            
              d
              
                L
                
                  D
                
              
            
          
        
        =
        ω
      
    
    {\displaystyle {\frac {dY^{S}(L^{D})}{dL^{D}}}=\omega }

<p>When functions are given, Labor Demand (LD) can be derived from this equation.
</p>
<h2 id="labour-supply">Labour supply</h2>
<p>The suppliers of the labor market are <a href="/facts/Household/snEgg9vP">households</a>. 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.
</p><p>Some notation:
</p>
Let U be total utility
Let YD be commodity demand (consumption)
Let LS be labor supply (hours worked)
Let D(LS) be disutility from working, an increasing convex function with respect to LS.

<h3>Households' consumption constraint</h3>
<p>Consumption constraint = profit income + wage income
</p>

Y
          
            D
          
        
        =
        π
        +
        ω
        ⋅
        
          L
          
            S
          
        
      
    
    {\displaystyle Y^{D}=\pi +\omega \cdot L^{S}}

<h3>Households' utility function</h3>
<p>total utility = utility from consumption - disutility from work

U
        =
        
          Y
          
            D
          
        
        −
        D
        (
        
          L
          
            S
          
        
        )
      
    
    {\displaystyle U=Y^{D}-D(L^{S})}

substitute consumption:

U
        =
        π
        +
        ω
        ⋅
        
          L
          
            S
          
        
        −
        D
        (
        
          L
          
            S
          
        
        )
      
    
    {\displaystyle U=\pi +\omega \cdot L^{S}-D(L^{S})}

</p>
<h3>Households' optimal condition</h3>
<p>Maximized utility function:

d
              D
              (
              
                L
                
                  S
                
              
              )
            
            
              d
              
                L
                
                  S
                
              
            
          
        
        =
        ω
      
    
    {\displaystyle {\frac {dD(L^{S})}{dL^{S}}}=\omega }

When functions are given, Labor Supply (LS) can be derived from this equation.
</p>
<h2 id="aggregate-demand">Aggregate demand</h2>
<p>Y = C + I + G
whereby Y is output, C is consumption, I is investment and G is government spending
</p>
<h2 id="monetary-market">Monetary market</h2>
<p>MV=PY(Fisher's Equation of Exchange)
</p>

<h2 id="references">References</h2>

<ol>
<li id="fn:1"><p>Burgstaller, André (1989). "A Classical Model of Growth, Expectations and General Equilibrium". Economica. 56 (223): 373–393. doi:10.2307/2554284. ISSN 0013-0427. JSTOR 2554284. <a href="https://www.jstor.org/stable/2554284" target="_blank">https://www.jstor.org/stable/2554284</a> <a href="#fnref:1" class="footnote-back-ref">↩</a></p></li>
<li id="fn:2"><p>McKenzie, Lionel W. (2002). Classical general equilibrium theory. Cambridge, Mass.: MIT Press. ISBN 0-262-13413-6. OCLC 49226070. <a href="0-262-13413-6" target="_blank">0-262-13413-6</a> <a href="#fnref:2" class="footnote-back-ref">↩</a></p></li>
</ol>

Classical general equilibrium model open-in-new

Classical general equilibrium model