Consider the endogenous growth model that is a simplified version of a model developed by Robert Lucas, where the representative consumer has 1 unit of time in each period, they cannot save and can only allocate their time between supplying labour to produce output and accumulating human capital. Human capital, denoted as H, is the accumulated stock of skills and education that a worker has at a point in time, and b is a parameter that captures the efficiency of the human capital accumulation technology, with b 0. The number of units of labour that the consumer effectively supplies is the number of units of time spent working multiplied by the consumer's quantity of human capital. The representative firm produces output using only efficiency units of labour, using a technology that is linear in total factor productivity and efficiency units of labour. i) Derive the competitive equilibrium.
Consider the endogenous growth model that is a simplified version of a model developed by Robert Lucas, where the representative consumer has 1 unit of time in each period, they cannot save and can only allocate their time between supplying labour to produce output and accumulating human capital. Human capital, denoted as H, is the accumulated stock of skills and education that a worker has at a point in time, and b is a parameter that captures the efficiency of the human capital accumulation technology, with b 0. The number of units of labour that the consumer effectively supplies is the number of units of time spent working multiplied by the consumer's quantity of human capital. The representative firm produces output using only efficiency units of labour, using a technology that is linear in total factor productivity and efficiency units of labour. i) Derive the competitive equilibrium.
Chapter1: Making Economics Decisions
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Transcribed Image Text:Consider the endogenous growth model that is a simplified version of a model developed by Robert
Lucas, where the representative consumer has 1 unit of time in each period, they cannot save and can
only allocate their time between supplying labour to produce output and accumulating human capital.
Human capital, denoted as H, is the accumulated stock of skills and education that a worker has at a point
in time, and b is a parameter that captures the efficiency of the human capital accumulation technology,
with b 0. The number of units of labour that the consumer effectively supplies is the number of units
of time spent working multiplied by the consumer's quantity of human capital. The representative firm
produces output using only efficiency units of labour, using a technology that is linear in total factor
productivity and efficiency units of labour.
i) Derive the competitive equilibrium.
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