Q. This problem uses the Solow model to analyze the e?ects of immigration. Suppose that the economy is initiallyin steady state.
1. Suppose that there is a one-time increasein labor force from immigration, but n (the population growth rate) remains constant. Analyze the short-run and long-run effects of this change for the levels of per-capita output, and the growth rates of (total) output and per-capita output.

2. Suppose that immigration is a continuing process so that n increases to a higher value n>n ˜ . Analyze the short-run and long-run e?ects of this change for the levels of per-capita output, and the growth rates of (total) output and per-capita output. Consider the Solow model. Suppose an economy begins in steady state and is characterized by the following parameter values: s = 0.2, d = 0.1, z = 1, N = 100, n = 0 and with the production function Y = zK^1/3N^2/3 Calculate the growth rate of per capita GDPin period immediately following each of the changes listed below:
1. The investment rate doubles.
2. The productivity level rises by 10%
3. An earthquake destroys 75% of the capital stock