Exercise 23.12. Consider the model in Section 23.3, starting with (0) = 1 and an oligarchic

Exercise 23.12. Consider the model in Section 23.3, starting with μ (0) = 1 and an oligarchic regime. Suppose that at some time t 0 < ∞ a new technology arises, which is ψ > 1 as productive as the old technology. However, entrepreneurial skills with this new technology are uncorrelated with entrepreneurial skills relevant for the old technology. In particular, suppose that entrepreneurial skills for new technology are given by aˆi (t + 1) = ⎧ ⎪⎪⎨ ⎪⎪⎩ AH with probability σˆH if aˆi (t) = AH AH with probability σˆL if aˆi (t) = AL AL with probability 1 − σˆH if aˆi (t) = AH AL with probability 1 − σˆL if aˆi (t) = AL . (1) Show that there exists ψ¯ such that if ψ > ψ¯, all existing entrepreneurs will increase entry barriers and switch to the new technology. (2) Show that if ψ < ψ¯, then again entry barriers will be increased and now only entrepreneurs who have low skills with the old technology will switch to the new technology. (3) Now analyze the response of democracy to the arrival of the same technology. (4) Compare output per capita in democracy and oligarchy after the arrival of new technology, and explain why democracy is more “flexible” in dealing with the arrival of new technologies.