Suppose for a Solow Model Y=K^2/3(LE)^1/3. The population growth rate is n and technological progress rate is g. And K is capital, LE is effective worker, L is just worker.

1: Find the growth rates of output, capital, output per effective worker and output per worker in the long run.

2: What is f(k)? Find the Golden rule of capital stock. Show your derivation

3:Suppose the Cobb-Douglas production function:Y = AK^aL^1-aand a is equal to 2/3.If the labor force increased by 5 percent, what would happen to the measured output of the economy? Does labor productivity defined as Y/Ldefined as output per worker increase, decrease, or stay the same? Does total factor productivity increase, decrease, or stay the same