Leontief utilities

<p>In <a href="/facts/Economics/HYctA2Dn">economics</a>, especially in <a href="/facts/Consumer_theory/Yrpoc6fI">consumer theory</a>, a Leontief utility function is a function of the form:

u
        (
        
          x
          
            1
          
        
        ,
        …
        ,
        
          x
          
            m
          
        
        )
        =
        min
        
          {
          
            
              
                
                  x
                  
                    1
                  
                
                
                  w
                  
                    1
                  
                
              
            
            ,
            …
            ,
            
              
                
                  x
                  
                    m
                  
                
                
                  w
                  
                    m
                  
                
              
            
          
          }
        
        .
      
    
    {\displaystyle u(x_{1},\ldots ,x_{m})=\min \left\{{\frac {x_{1}}{w_{1}}},\ldots ,{\frac {x_{m}}{w_{m}}}\right\}.}

where:
</p>
<ul><li>
  
    
      
        m
      
    
    {\displaystyle m}
  
 is the number of different <a href="/facts/Good_(economics)/AtK6gQh2">goods</a> in the economy.</li>
<li>
  
    
      
        
          x
          
            i
          
        
      
    
    {\displaystyle x_{i}}
  
 (for 
  
    
      
        i
        ∈
        1
        ,
        …
        ,
        m
      
    
    {\displaystyle i\in 1,\dots ,m}
  
) is the amount of good 
  
    
      
        i
      
    
    {\displaystyle i}
  
 in the bundle.</li>
<li>
  
    
      
        
          w
          
            i
          
        
      
    
    {\displaystyle w_{i}}
  
 (for 
  
    
      
        i
        ∈
        1
        ,
        …
        ,
        m
      
    
    {\displaystyle i\in 1,\dots ,m}
  
) is the weight of good 
  
    
      
        i
      
    
    {\displaystyle i}
  
 for the consumer.</li></ul>
<p>This form of utility function was first conceptualized by <a href="/facts/Wassily_Leontief/f0LrLYVU">Wassily Leontief</a>.
</p>

Leontief utilities open-in-new

Leontief utilities