What are the answers and how to go about it?

4. The government has hired an economics expert to inform them about the optimal tax level, which depends on a number of underlying economic factors that they government is unsure about. Based on these factors, the optimal tax level is a number t between 0 and 100%. The expert observes this level, but the government does not. The expert, after observing t, makes a report to the government about the tax level r. After receiving the report, the government sets the actual tax level T. The payoffs for both players depend both on t and T (but not r directly). . The payoffs for the government are UG(t, T) = -(t - T)? . The payoffs for the expert are UE(t, T) = -(t - T + 0)? where 0 > 0. (a) (5 points) Sketch this game using a game tree. (b) (5 points) If the true level is t, what level of T does the government most prefer? The expert? (Hint: sketch their utility functions) (c) (5 points) Suppose the government believes that the expert is truthful; that is, they always report the true optimal level. What will the government set T' if the observe a report R? What is the expert's best response to this? Is this an equilibrium? (d) (5 points) Suppose now 0 = 0. Repeat (b) and (c), with this assumption. (e) (5 points) What is the key difference in your results between (c) and (d)? Explain. Total for Question 4