Microeconomics Questions: Perfect Competition, Asymmetric Information, and Price Discrimination

Question 1) Perfect Competition and Trade

Question 1) Perfect Competition and Trade
Consider the perfectly competitive market of quinoa (a type of grain), in the country of Peru. 

Peru is currently close to trade to the rest of the world. In the domestic market for quinoa in Peru, the equilibrium price is 5 per kilo, customers purchase 5 million kilos, and the elasticity of demand and supply are -6 and 2 respectively.

a) Suppose that the government of Peru imposes a tax of 1 per kilo on quinoa. What is the percentage of the tax born by consumers? How much is the reduction in quantity traded as a result of the tax?

b) Peru is thinking of opening to trading with the rest of the world. Suppose that as a result of opening trade, exports amount to 2 million units. What is the reduction in local consumption by Peruvian customers as a result of opening trade?

c) Suppose that the government is considering one of the two options to increase revenue (either a tax, or opening trade). If the government cannot subsidize (or compensate) Peruvian consumers, which option do Peruvian consumers prefer?

Question 2) Asymmetric Information
Consider a market for consulting services where clients differ in the difficulty for consultants of the consulting jobs. In particular, there are three types of consulting jobs ranked by their difficulty and expected costs (T1, T2, and T3) according to the figure below. For example, a T3 job is an “easy” job that generates value of 25 to the client and consultants incur a cost of 20 when performing it. Suppose that clients know the difficulty of the job, but consultants do not know it at the time at which they agree to accept the job.

a) Can there be a competitive market equilibrium allocation where all three types of clients/jobs (under the assumption of asymmetric information) are active in the market? In an equilibrium with asymmetric information, which type of clients will be active in the market hiring consultants?

b) Suppose that Type T3 customers value consulting services more. In particular, they value consulting services at 31. Can there be a competitive market equilibrium allocation where all three types of clients/jobs (under the assumption of asymmetric information) are active in the market?

c) Suppose that consultants learn that all firms in a particular industry (say fashion) are type T3, and, moreover, type T3 clients can only be found in that industry. As a result of this insight, can there be a competitive market equilibrium allocation where all three types of clients/jobs purchase consulting services?

Question 2) Asymmetric Information

Question 3) Price Discrimination
The Beverly Hills Hotel is undergoing a change of management. You are the new CEO and you are considering a new design for the hotel and refurbishing of the rooms. There are 1000 consumers, which can be of two types (High and Low) with different valuations for a room. There are three different types of rooms: Royal, Aristocratic and Economy. Each consumer would purchase at most one room and their valuations are given by

                                 Royal                 Aristocratic           Economy
High Type                1,200                     900                        850
Low Type                  800                       700                        650

The marginal cost of production is zero, irrespective of the type of room (so effectively the hotel is seeking to maximize revenues). 

a) The mayor of Beverly Hills (where the Beverly Hills Hotel is located) forbids Hotels from having different types of rooms. Suppose that the Hotel cannot tell whether a customer is High Type or Low Type. Which room would they choose (and what price will they charge for that room)? What if the hotel can tell whether a customer is High or Low, which room would they choose then?

b) Social pressure on the mayor of Beverly Hills leads to a repeal of the law imposing a unique type of room, so that now the Hotel could offer different types of rooms to its guests. If you can offer different rooms to different customers, but you cannot tell the customer’s type (High or Low), what type of rooms would you offer and at which price? What if you can actually observe the type of customer, what would you then offer and at what price? 

c) Customers suffer from a particular form of “social status”: As in Edwardian times, any excessive display of wealth is frowned upon. This means in our case that if the hotel guests’ choice of room is disclosed (let’s say on the Twitter feed of the Hotel) High Types now value an Aristocratic room at 1100, while Low Types value it at 750 (with other valuations unchanged). If the hotel announces each hotel’s choice on their Twitter feed, which options will they offer? The hotel is deciding whether to announce the customer’s choices on their Twitter feed. Should they do it? How much do they stand to gain (or lose) by disclosing customer choices?