Consider the Cobb-Douglas production function with labor-augmenting technology used in class: Y = F(K,L) = K\"(EL)1_' with 1 > a > 0 a) In the economy of Springfield, the capital share of income is 50 percent, the population grows by 4 percent per year, depreciation is 3 percent per year, and technological growth is 5 percent per year. If Springfield is at steady state, what is the growth rate of: i) Capital per effective worker ii) Capital per worker iii) Output per worker iv) Aggregate capital v) Aggregate output b) Suppose Ogdenville (the country next to Springfield) has the exact same economic funda- mentals as Springfield (i.e. all the same parameters). Ogdenville is struck by an earthquake which destroys half the capital stock. i) Show graphically (using a Solow Growth Model) the dynamic path of Ogdenville from the starting point with lower capital stock back to st.st. equilibrium. ii) On the transition path to st.st. equilibrium, will output per worker grow faster in Ogdenville or in Springfield? Why? iii) Once Ogdenville reaches st.st., will output per worker grow faster in Ogdenville or Springfield? Why