Exercise 22.17. * Prove Proposition 22.19. Exercise 22.18. Consider an environment with concave preferences as in Section 22.5. Assume that there is full depreciation (i.e., δ = 1), citizens are yeoman-producers only using their own labor and have access to a production technology for producing the unique final good given by Yi (t) = AKi (t) α, where Ki (t) is the capital holding of producer i. Both citizens and elites have logarithmic preferences. Characterize the MPE in this environment. [Hint: conjecture a policy rule that depends only on the current (average) net output, so that the tax rate for next period is τ (t + 1) = τ ¡ Y N (t) ¢ , where Y N (t) = (1 − τ (t)) AK (t) α, where K (t) is the common capital stock of all producers].