Introduction to Modern Economic Growth H denotes the efficiency units of labor (human capital), given by H = P i∈N hi , where N is the set of all individuals in the population and hi is the human capital of individual i Assume that H is fixed Suppose there are no human capital externalities and factor markets are competitive (1) Calculate the steady-state equilibrium of this economy (2) Prove that if 10% higher h at the individual level is associated with a% higher earnings, then a 10% increase in the country’s stock of human capital H will lead to a% increase in steady-state output Compare this to the immediate impact of an unanticipated 10% increase in H (i.e., with the stock of capital unchanged) Exercise 3.10 Consider a constant returns to scale production function for country j Yj = F (Kj , Aj Hj ), where Kj is physical capital, Hj denotes the efficiency units of labor and Aj is labor-augmenting technology Prove that if Kj /Yj = Kj /Yj in two different countries j and j , than the rental rates of capital in the two countries, Rj and Rj will also be equal Exercise 3.11 Imagine you have a cross-section of countries, i = 1, , N , and for each country, at a single point in time, you observe labor Li , capital Ki , total output Yi and the share of capital in national income, αK i Assume that all countries have access to a production technology of the following form F (L, K, A) where A is technology Assume that F exhibits constant returns to scale in L and K, and all markets are competitive (1) Explain how you would estimate relative differences in technology/productivity across countries due to the term A without making any further assumptions Write down the equations that are involved in estimating the contribution of A to cross-country income differences explicitly (2) Suppose that the exercise in part leads to large differences in productivity due to the A term How would you interpret this? Does it imply that countries have access to different production possibility sets? (3) Now suppose that the true production function is F (H, K, A) where H denotes efficiency units of labor What other types of data would you 153