Use Solow model to analyze the effect of immigration. Assume the originalcase where population growth rate is n1, depreciation rate d, savings rate s, TFP A, and production function per person is Af(k).

1. Please draw the law of motion for capital per person in the space below. Clearly mark the axes and the curves. Find where the steady state level of capital per person is, and mark the steady state point E and level of capital per person k*
2. Please draw the capital "depreciation" and investment graph that describes the steady state capital per person k*. Clearly mark the axes, what each curve represents and the steady state point.
3. Suppose there is a sudden increase of immigrants to the country. This means that all in a sudden, the total population N increased. But it does NOT change the population growth rate. Everything else in the economy stays the same too. In the space below, redraw part (b) as a point of comparison, and illustrate how the sudden increase of immigrants change the economy. AND, describe in less than two sentences, what's the impact to the capital per person?
4. Please use less than two sentences to describe the long-run impact of the sudden increase of immigration (the impact on steady state point and steady state capital per person).
5. Can you draw the transition path from this sudden (and temporary) increase of immigration? (I am looking for one graph describing the vertical axis as the aggregate output and horizontal axis being time.)
6. Suppose, instead of a sudden increase of immigration, there is a permanent change of immigration law that makes it easier for immigrants to come. As a result, the growth rate of population increases to n2, a higher level than the original n1. Please draw in the space below, how does the steady state change? (you may want to redraw part (b) again for comparison.) Clearly mark everything so I know the difference and what you are drawing.
7. Can you draw the transition path for aggregate output (just like how you did for Part e)?