Greenwood–Hercowitz–Huffman preferences | Wikipedia audio article
Channel: wikipedia tts
Date: 2019-06-04

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Greenwood%E2%80%93Hercowitz%E2%80%93Huffman_preferences


00:04:58 Generalization: Jaimovich–Rebelo preferences



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SUMMARY
=======
Greenwood–Hercowitz–Huffman preferences are a particular functional form of utility developed by Jeremy Greenwood, Zvi Hercowitz, and Gregory Huffman, in their 1988 paper Investment, Capacity Utilization, and the Real Business Cycle. It describes the macroeconomic impact of technological changes that affect the productivity of new capital goods. The paper also introduced the notions of investment-specific technological progress and capacity utilization into modern macroeconomics.
GHH preferences have Gorman form.
Often macroeconomic models assume that agents' utility is additively separable in consumption and labor.  I.e., frequently the period utility function is something like

  
    
      
        u
        (
        c
        ,
        l
        )
        =
        
          
            
              c
              
                1
                −
                γ
              
            
            
              1
              −
              γ
            
          
        
        −
        ψ
        
          
            
              l
              
                1
                +
                θ
              
            
            
              1
              +
              θ
            
          
        
      
    
    {\displaystyle u(c,l)={\frac {c^{1-\gamma }}{1-\gamma }}-\psi {\frac {l^{1+\theta }}{1+\theta }}}
  where 
  
    
      
        c
      
    
    {\displaystyle c}
   is consumption and 
  
    
      
        l
      
    
    {\displaystyle l}
   is labor (e.g., hours worked).  Note that this is separable in that the utility (loss) from working does not directly affect the utility (gain or loss) from consumption, i.e. the cross-derivative of utility with respect to consumption and labor is 0.
GHH preferences might instead have a form like:

  
    
      
        u
        (
        c
        ,
        l
        )
        =
        
          
            1
            
              1
              −
              γ
            
          
        
        
          
            (
            
              c
              −
              ψ
              
                
                  
                    l
                    
                      1
                      +
                      θ
                    
                  
                  
                    1
                    +
                    θ
                  
                
              
            
            )
          
          
            1
            −
            γ
          
        
      
    
    {\displaystyle u(c,l)={\frac {1}{1-\gamma }}\left(c-\psi {\frac {l^{1+\theta }}{1+\theta }}\right)^{1-\gamma }}
  where now consumption and labor are not additively separable in the same way.  For an agent with this utility function, the amount she/he works will actually affect the amount of utility she/he receives from consumption,  i.e. the cross-derivative of utility with respect to consumption and labor is unequal to 0.
More generally, the preferences are of the form

  
    
      
        u
        (
        c
        ,
        l
        )
        =
        U
        
          (
          
            c
            −
            G
            (
            l
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          )
        
        ,
        
          U
          ′
        
        
        0
        ,
        
          U
          ″
        
        
        0
        ,
        
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        0
        ,
        
          G
          ″
        
      ...