6. In the lectures, we considered a model of Chinese bureaucrats, where a bureaucrat could invest effort into two distinct activities: (i) political lobbying which increases his share of output and output growth, or (ii) productive legislation which can increase the level of local economic growth. Y = Y +(gGA*) 0.5 Y = Local output at time s g =productive legislation by the bureaucrat at time s G= aggregate legislation by all bureaucrats at time s A *= distance to technological frontier at time s cl=0.05, c2=0.1, Y=300 and A *=81, G=3600 with positive but decreasing returns to any input and positive cross-derivatives such that the marginal value of any input increases when the others are higher. What is the utility maximization problem for the bureaucrat and the ensuing first order conditions? (You do not have to show the second order conditions) (3) Suppose, the bureaucrat decides to invest in stealing from the general pie, how much will he invest and how much utility will he derive from it? (2) Now, how much will he invest if he chooses to invest in growth instead of stealing? What will be the value of g e, if G,=3600? What is his total utility? (3) Comparing the two utilities from (b) and (c) which of the two activities will the bureaucrat select given the parameter values and why? (2)