Intertemporal budget constraint

In <a href="/facts/Economics/HYctA2Dn">economics</a> and <a href="/facts/Finance/fLh1GgN8">finance</a>, an intertemporal budget constraint is a <a href="/facts/Constrained_optimization/tJuCmQ4b">constraint</a> faced by a <a href="/facts/Decision_theory/TbXcQX0v">decision maker</a> who is making choices for both the present and the future. The term intertemporal is used to describe any relationship between past, present and future events or conditions. In its general form, the intertemporal budget constraint says that the <a href="/facts/Present_value/1Ea8bdC2">present value</a> of current and future cash outflows cannot exceed the present value of currently available funds and future cash inflows. Typically this is expressed as

∑
          
            t
            =
            0
          
          
            T
          
        
        
          
            
              x
              
                t
              
            
            
              (
              1
              +
              r
              
                )
                
                  t
                
              
            
          
        
        ≤
        
          ∑
          
            t
            =
            0
          
          
            T
          
        
        
          
            
              w
              
                t
              
            
            
              (
              1
              +
              r
              
                )
                
                  t
                
              
            
          
        
        ,
      
    
    {\displaystyle \sum _{t=0}^{T}{\frac {x_{t}}{(1+r)^{t}}}\leq \sum _{t=0}^{T}{\frac {w_{t}}{(1+r)^{t}}},}

where 
 
 
 
 
 x
 
 t
 
 
 
 
 {\displaystyle x_{t}}
 
 is expenditure at time t, 
 
 
 
 
 w
 
 t
 
 
 
 
 {\displaystyle w_{t}}
 
 is the cash that becomes available at time t, T is the most distant relevant time period, 0 is the current time period, and 
 
 
 
 
 
 1
 
 1
 +
 r
 
 
 
 
 
 {\displaystyle {\frac {1}{1+r}}}
 
 is the <a href="/facts/Discount_factor/90o5yEkL">discount factor</a> computed from the interest rate r.
Complications are possible in various circumstances. For example, the <a href="/facts/Interest_rate/Nb4JN7gR">interest rate</a> for discounting cash receipts might be greater than the interest rate for discounting expenditures, because future inflows may be borrowed against while currently available funds may be invested temporarily pending use for future expenditures, and borrowing rates may exceed <a href="/facts/Investment_return/CldGgD1f">investment returns</a>.

Intertemporal budget constraint open-in-new

Intertemporal budget constraint