Question: Consider the Solow growth model with population growth and growth in the efficiency of labor. The production function is given by \({{Y}_{t}}=K_{t}^{\alpha }{{\left( {{L}_{t}}{{E}_{t}} \right)}^{1-\alpha }}\). Suppose that the rate of growth of E is constant at 3% and that population grows at a constant rate of 2%. Suppose that the rate of growth of GDP per capita between periods 0 and 1 is 1%.

1. Draw a graph of GDP per capita (in logs) as a function of time starting in period 0. On the same graph draw the balanced growth path.
2. Draw a graph of capital per effective worker (in logs) as a function of time in period 0.
3. What is the rate of growth of total output between periods 0 and 1? What is the rate of growth of total output once the economy reaches the balanced growth path?

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