original_docstring: 
      Finds total utitilty for a set of years with a savingsrate for each year
      
docstring: Finds total utitilty for a set of years with a savingsrate for each year
docstring_tokens: Finds total utitilty for a set of years with a savingsrate for each year
code: def tot_ut_multiple_sks_quick(sks, k0, l0, n, b, weight, theta, alpha, delta):
      '''
      Finds total utitilty for a set of years with a savingsrate for each year
      '''
      t = len(sks)
      k_short = np.empty(t)
      k_short[0] = k0
      l_short = np.array([l0*(1+n)**i for i in range(t)])
      
      for i in range(1,t):    
          k_short[i]=sks[i-1]*prod(k_short[i-1],l_short[i-1],alpha,b)+(1-delta)*k_short[i-1]
      
      y_short = prod(k_short,l_short,alpha,b)
      
      return total_utility(y_short*(1-sks)/l_short, weight, theta)
code_tokens: def tot_ut_multiple_sks_quick ( sks , k0 , l0 , n , b , weight , theta , alpha , delta ) : t = len ( sks ) k_short = np . empty ( t ) k_short [ 0 ] = k0 l_short = np . array ( [ l0 * ( 1 + n ) ** i for i in range ( t ) ] ) for i in range ( 1 , t ) : k_short [ i ] = sks [ i - 1 ] * prod ( k_short [ i - 1 ] , l_short [ i - 1 ] , alpha , b ) + ( 1 - delta ) * k_short [ i - 1 ] y_short = prod ( k_short , l_short , alpha , b ) return total_utility ( y_short * ( 1 - sks ) / l_short , weight , theta )
short_docstring: Finds total utitilty for a set of years with a savingsrate for each year
short_docstring_tokens: Finds total utitilty for a set of years with a savingsrate for each year
comment: '''
      Finds total utitilty for a set of years with a savingsrate for each year
      '''