Explain why this situation could be considered a principal-agent problem. (5 marks)

• Gregory
• December 14, 2021

Math/Physic/Economic/Statistic Problems

1. In two-car automobile accidents, passengers in the larger vehicle are significantly more likely to survive than are passengers in the smaller vehicle. In fact, death probabilities are decreasing in the size of the vehicle you are driving, and death probabilities are increasing in the size of the vehicle you collide with. Some politicians and lobbyists have argued that this provides a rationale for encouraging the sale of larger vehicles and discouraging legislation that would induce automobile manufacturers to make smaller cars. Discuss this argument in light of our course. (5 marks)

2. Michael wants to rent out a flat from Susan. Michael has a big passion for art and enjoys drawing, so much that he often draws on any surface he can find, including walls.

Michael’s receives £400 in utility from being able to draw on the walls of the flat, whereas Susan would like the walls to remain clean.

If Michael draws on the walls, it will cost Susan £700 to have the walls repainted. Thus, Susan is considering charging Michael a damage deposit of £700. (10 marks)

a) Explain why this situation could be considered a principal-agent problem. (5 marks)

b) Draw the extensive form of this principal-agent problem and use backward induction to solve for the Nash Equilibrium. (5 marks)

3. Answer the following question for each of the following examples: (i) smoking by individuals; (ii) toxic waste production by firms; (iii) research and development by a high-tech firm; and (iv) individual vaccination against communicable illness. (10 marks)

a) Is there an externality? If so, describe it, including references to whether it is positive or negative, and whether it is a consumption or production externality. (4 marks)

b) If there is an externality, does it seem likely that private markets will arise that allow this externality to be internalized? In other words, do you believe any potential inefficiencies can be removed without policy changes by the government? Why or why not? (6 marks)

Consider a free market with demand equal to Q = 72 – 2P and supply equal to Q = 24 + 4P. (10 marks)

1. a) What is the value of consumer surplus? What is the value of producer surplus? (2 marks)
2. b) Now the government imposes a £3 per unit subsidy on the production of the good. Why is there a dead weight loss associated with the subsidy, and what it the size of this loss? (4 marks)
3. c) Explain how a subsidy might help reduce inefficiencies in the presence of externalities. In your answer, provide an example for when the use of subsidies might be appropriate and discuss what the optimal amount of the subsidy should be. (4 marks)

Find the Bayesian Nash Equilibrium. Briefly explain the intuition behind each of the steps you are taking to get the answer. (15 marks)

Using the extensive form below, draw the Bayesian Normal form of the game and find all the Bayesian Nash Equilibrium of the game. Explain the intuition behind the steps you are taking to get the answer. (15 marks)