Introduction to Modern Economic Growth the more natural production function, which features capital and effective units of labor (with human capital augmenting the effective units of labor), as opposed to the production function used in the previous section with human capital as a third separate factor of production The economy is in discrete time and consists of a continuum of dynasties Each individual lives for two periods, childhood and adulthood Individual i of generation t works during their adulthood at time t, earns labor income equal to w (t) hi (t), where w (t) is the wage rate per unit of human capital and hi (t) is the individual’s human capital The individual also earns capital income equal to R (t) bi (t − 1), where R (t) is the gross rate of return on capital and bi (t − 1) is his asset holdings, inherited as bequest from his parent The human capital of the individual is determined at the beginning of his adulthood by an effort decision Labor is supply to the market after this effort decision At the end of adulthood, after labor and capital incomes are received, the individual decides his consumption and the level of bequest to his offspring Preferences of individual i (or of dynasty i) of generation t are given by η −η (1 − η)−(1−η) ci (t)η bi (t)1−η − γ (ei (t)) , where η ∈ (0, 1), ci (t) is own consumption, bi (t) is the bequest to the offspring, ei (t) is effort expended for human capital acquisition, and γ (·) is a strictly increasing, continuously differentiable and strictly convex cost of effort function The term η −η (1 − η)−(1−η) is included as a normalizing factor to simplify the algebra The human capital of individual i is given by (10.26) hi (t) = aei (t) , where a corresponds to “ability” and increases the effectiveness of effort in generating human capital for the individual Substituting for ei (t) in the above expression, the preferences of individual i of generation t can be written as ả hi (t) −(1−η) η 1−η −η ci (t) bi (t) −γ (10.27) η (1 − η) a The budget constraint of the individual is (10.28) ci (t) + bi (t) ≤ mi (t) = w (t) hi (t) + R (t) bi (t − 1) , 481