Consider an overlapping generation economy in which each individual lives
two periods: young and old. Individual born at period t has the following utility
c1t and c2,t+1 denotes the young-age and old-age consumption, respectively. Each individual gives birth to one child at the end of her old age and also decides on a bequest level bt+1 for her child. An Individual’s utility is assumed to be increasing with bt+1 to capture altruism.
The young individual inelastically provides 1 unit of labor and earns a wage accordingly. At the end of young age, each individual decides how much to consume and save given her wage income and bequest received from her parents. The old-age individual does not work and lives on her savings. The production function is given as:
Additionally, assume the capital depreciation rate is δ ∈ (0, 1). The size of young-age individuals is normalized to be 1. Derive the capital accumulation equation and discuss the steady state of this economy.
Consider the following endogenous growth model: a representative household’s lifetime utility function is given as:
The production function is:
where Hp(t) denotes human capital used in production. The human capital accumulation equation is:
where HE(t) is human capital devoted to education. In total we have HE(t) +
HP (t) = H(t). Workers can allocate the 1 unit of time between production
(u(t))and human capital accumulation (1 − u(t)). Denote the fraction of human
capital allocated to production by φ(t), please do the following:
(a) calculate the GDP growth rate on BGP.
(b) Discuss how φ(t) and u(t) are determined on BGP
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