Introduction to Modern Economic Growth Exercise 15.23 Derive equation (15.47) Exercise 15.24 Derive equation (15.49) Exercise 15.25 Complete the proof of Proposition 15.14 and show that there cannot exist any other constant growth path equilibrium Exercise 15.26 * Show that if σ < 1, the constant growth path equilibrium in Proposition 15.14 is globally stable Show that if σ > 1, it is unstable Relate your results to Proposition 15.7 Exercise 15.27 Now let us use the results of Proposition 15.14 to revisit the discussion of the experiences of continental European economies provided in Blanchard (1997) Consider the model of Section 15.6 Discuss how a wage push, in the form of a wage floor above the market clearing level will first cause unemployment and then if σ < 1, it will cause capital-biased technological change Can this model shed light on the persistent unemployment dynamics in continental Europe? [Hint: distinguish two cases: (i) the minimum wage floor is constant; (ii) the minimum wage floor increases at the same rate as the growth of the economy] Exercise 15.28 * The analysis in the text has treated the supply of the two factors as endogenous and looked at the impact of relative supplies on factor prices Clearly, factor prices can also affect relative supplies In this exercise, we look at the joint determination of relative supplies and technologies Let us focus on a model with the two factors corresponding to skilled and unskilled labor Suppose a continuum υ of unskilled agents are born every period, and each faces a flow rate of death equal to υ, so that population is constant at (as in Section 9.8 above) Each agent chooses upon birth whether to acquire education to become a skilled worker For agent x it takes Kx periods to become skilled, and during this time, he earns no labor income The distribution of Kx is given by the distribution function Γ(K) which is the only source of heterogeneity in this economy The rest of the setup is the same as in the text Suppose that Γ(K) has no mass points Define a BGP as a situation in which H/L and the skill premium remain constant (1) Show first that in BGP, there is a single-crossing property: if an individual with cost of education Kx chooses schooling, another with Kx0 < Kx must 702