Question: Consider the Solow growth model with population growth and growth in the efficiency of labor. Suppose that 2 countries A and B have the same production function given by \({{Y}_{t}}=K_{t}^{\alpha }{{\left( {{L}_{t}}{{E}_{t}} \right)}^{1-\alpha }}\) the same rate of growth of E (g), the same depreciation rate of physical capital (and the same saving rate s. The initial level of E, Eo, is lower in country A than in country B.

1. Compare the steady-state levels of output per effective worker of these two countries.
2. Assume now that at time 0 both countries are below the steady state and that \(k_{0}^{A}>k_{0}^{B}\) (i.e., country B starts o↵ with a lower level of capital per effective worker than does country A) and continue to assume that the initial level of E is higher in country B than in country A. Draw log of output per capita for these two countries as a function of time (have time on the x-axis) starting in period 0 and show how they both converge to their respective balanced growth paths.
3. Do these countries converge to each other in output per capita? Defend your answer.

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