Questions

Consider an overlapping generation economy in which each individual lives

two periods: young and old. Individual born at period t has the following utility

function.

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 H*p*(t) denotes human capital used in production. The human capital accumulation equation is:

where H*E*(t) is human capital devoted to education. In total we have H*E*(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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