2) GrowingChina. This problem discusses the Malthusian trap that has worried China for centuries and that the country has now escaped (Note: A Malthusian trap is a decline in output per worker after an increase in population; this results from returns to labor eventually decreasing with more workers). Let there be Ls = 1000 Chinese workers who inelastically supply labor and who spend all of their income on rice. These workers own the Chinese rice firms which have aggregate production function: Q = F(L, K) = AK1/3 (hL)2/3 ("aggregate" meaning F(.) is a hypothetical production function for society as a whole). Let A = 3.33, K = 729, h = 1, and p = 1, where A is a technology parameter, K is the level of physical capital, and h is a human capital parameter (Recall: these three factors drive growth in output per worker). a) Calculate and graph the equilibrium wage and quantity of labor in the labor market (Hint: this is analogous to the producer's profit maximization problem, but now we are solving for the level of production and labor for society as a whole directly). b) Graph the production function and show total output (Q") at the optimal level of labor, L*. What is output per worker at that point? c) Suppose that over several years, the Chinese workforce rises to L's = 1,728 workers. If nothing else changes, what is the new equilibrium wage and output per worker? Why don't these new workers produce enough to keep the output per worker at least as high as before? d) Consider the following changes to the production function: an increase in A, an increase in K, and an increase h. How would each of these help China escape the Malthusian trap