Introduction to Modern Economic Growth Using these observations, we obtain Z Z a¯ a RH (R) + dH (a) V (a) dH (a) = 1−β a≥R − β Combining this equation with (6.46), we have ∙ ¸ Z RH (R) R a =β + dH (a) (6.47) 1−β 1−β a≥R − β Manipulating this equation, we obtain β R= − βH (R) Z a ¯ adH (a) , which is a convenient way of expressing the cutoff rule R Equation (6.47) can be rewritten in a more useful way as follows: ∙Z ¸ Z R a R =β dH (a) + dH (a) 1−β a