In this model, the society allocates a fraction "gamma" of workforce to innovation and the remaining fraction to production. Suppose that, for simplicity, total workforce is normalized to unity: L = 1. If the productivity growth rate is defined by d A_t / d t = "theta" * "gamma" * A_t and real GDP per worker by  y_t = A_t * ( 1 - "gamma" ), what is the long-run growth rate of y_t ?

Exploring Economics
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Chapter20: Economic Growth In The Global Economy
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Consider the simple innovation model.

In this model, the society allocates a fraction "gamma" of workforce to innovation and the remaining fraction to production. Suppose that, for simplicity, total workforce is normalized to unity: L = 1.

If the productivity growth rate is defined by

d A_t / d t = "theta" * "gamma" * A_t

and real GDP per worker by 

y_t = A_t * ( 1 - "gamma" ),

what is the long-run growth rate of y_t ? 

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