The mayor of Albuquerque is worried about the increase in meth consumption in her district. There is a new product in town called "Blue Sky", which is of a higher quality, and the mayor wants to do something about it. On the other hand, the mayor is interested in being re-elected and she knows that the best predictor for re-election is GDP per worker in the current year, and the prediction for GDP per capita in the long run. Therefore, she wants to get tough with meth dealers only if this does not have negative effects on the GDP per worker. The mayor hires Saul Goodman, a respected lawyer/economist, to produce some estimates of the effect of this policy on the living standards for Albuquerque in the long and short run. Saul uses the Solow growth model for his analysis, adding the government spending to it. His proposal is to hire new policemen and put them in the streets, so drug dealers won't be able to work. Saul tells the mayor she needs to spend g per worker, i.e. she will spend a total of G = gL, where L is the constant number of workers. The mayor should finance this spending with lump-sum taxes T on consumers, and, given that the council has a no-debt rule, we have G = T. Consumers will consume a fraction 1 - s of their disposable income, as they must pay taxes, i.e. C = (1- s)(YT) while the rest of the disposable income will be saved and therefore become investment It = s(Yt - T). The production function is given by Yt = AF (Kt, L), where A is the constant total factor productivity and F (Kt, L) is a constant return to scale function with positive but decreasing marginal product for labour and capital (for example, Ko L-a). The mayor wants to see the details of the proposal before any decision. a. b. C. Derive the equation for the evolution of capital per worker k = K+, and the equation characterizing the steady state for capital per worker. Show that the steady state can be computed as the solution of this equation: SAf (k) =sg+dk* where f(k) = F (, 1), and d is depreciation rate. [Hint: remember that G = T] (10 marks) Use a diagram to show that, depending on the value of g, there may be two steady states, one with high capital per worker and one with low capital per worker. (10 marks) Assume the value of g is such that there are two steady states, and ignore the one with low capital per worker. What are the long-run consequences of this policy with respect to the case with no government spending? What is the policy recommendation given to the mayor? Explain your reasoning using a diagram. (10 marks)