Trump and Biden share a Rental Apartment with a very old Bathroom: Economics Assignment, SMU, Singapore

Question I Trump and Biden share a rental apartment with a very old bathroom. Suppose in a particular week, they have to decide whether to clean the bathroom. Their payoffs in this scenario can be represented by the below payoff matrix, where X > 0 represents how much cleaner the bathroom becomes when they both work together.

(a) If X = 3, solve for all Nash Equilibria in this game. Comment on the social efficiency of the Nash equilibria.

(b) If X = 0, solve for all Nash Equilibria in this game. Are the outcome(s) for this scenario socially efficient? Discuss how playing this game repeatedly every week will affect the possibility of reaching a socially efficient outcome.

Suppose now Trump and Biden decided to approach the apartment owner for help in deciding on upgrading the bathroom. Upgrading the bathroom would cost $400. If the bathroom is upgraded, they will both enjoy the benefits of being able to use it. The value to Trump of upgrading the bathroom is $180 and the value to Biden of upgrading the bathroom is $370.

The apartment owner recently read Hal Varian’s textbook and decided to use the VGC mechanism to determine whether to upgrade the bathroom.

Assume that Trump and Biden can either choose to report their own true value or report a value of 0.

(c) In each of the 4 combinations of reports, will the bathroom be provided and what will be the additional VCG tax paid by each of Trump and Biden? Use this to fill up the payoff matrix below.

(d) Suppose we iteratively eliminate weakly dominated strategies for each player. Is this game dominance solvable? Discuss the role of the VCG mechanism in implementing socially efficient outcomes.

(Note: For player I, a strategy s1 is weakly dominated if its payoff is S the payoff of another strategy s11, no matter what the other player j does)

There are two types o produce very good cases that consume less good ones that are valued at $14.

Customers can order a mobile phone purchase, customers cannot distinOlii’l manufacturer. However, they can date High-quality manufacturers can many quality manufacturers can manufacture the pro Consumers can be assumed to have similar risk

(a) For a lottery L, how does i) the risk premium and ii) the certainty equivalent of the lottery differ for risk-averse, risk-loving, and risk-neutral consumers?

(b) State a possible utility function for the consumers, u(x), defined on monetary value x. Given this utility function, what is their expected utility of getting a high-quality case with probability p and getting a low-quality case with probability 1 p?

(c) Suppose that the proportion of high-quality manufacturers is -1. What will be the equilibrium outcome(s) — i.e. who is in the market and what are prices — in the following 2 cases: i) cH = $12 and ii) CH = $17?

(d) Suppose the proportion of high-quality manufacturers is 1/2. For what values of cH is there an equilibrium in which both types of phone manufacturers are in the market?

Suppose now, there is only one type of mobile phone case manufacturer. Consider the mobile phone case industry as a whole. Suppose the production of phone cases can only be done in a way that pollutes the surrounding environment. Denote the market output by Q.

Suppose the inverse market demand function for phone cases is P = 500 — 2Q. There are 20 identical phone case manufacturers in the industry. The marginal private cost of an individual manufacturer is MCP(q) = 20 + 3q.  The marginal external cost, resulting from the industry’s pollution, is MC’ (Q) =

(e) Derive the number of phone cases produced in i) the competitive equilibrium and ii) the social optimum.

(f) Discuss the reason(s) for any differences between the competitive equilibrium and the social optimum and solutions to the inefficiencies (if any).