Imagine the one-country model of technological change. There are two things produced; knowledge A and consumption good Y. The production functions are given as Y = A LY ?A = 3 LA A LY and LA denote the numbers of workers allocated to Y production and A production, respectively. In this economy, there are 10 million workers in total: LY + LA = 10 (Hint: The growth rate of variable x is defined as in x = ?x / x.) - Suppose that 2 workers are assigned to the knowledge production. What is GDP per worker (y) equal to? - What is the growth rate ? of knowledge equal to? - What is the growth rate ? of GDP per worker equal to? - Suppose that there was an improvement in knowledge production such that ?A = 5 LA A. What should this economy do to keep the growth rates unchanged?
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The production function for \( Y \) is \( Y = A L_Y \). Assuming \( A \) is the current level of knowledge, GDP (\( Y \)) is \( A \times 8 \). GDP per worker (\( y \)) is then given by: \[ y = \frac{Y}{L_Y + L_A} = \frac{A \times 8}{10} = 0.8A \] Show more…
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