ECON GU 4251: Problem set 2
Spring 2024
Problem sets are graded (check/check minus) based on effort, this includes the formatting of your work (typesetting is strongly encouraged). You can work in groups, but each student must upload an individual solution. Submissions need to be in pdf format and submitted via Canvas. We will not accept other formats.
Second Degree Price Discrimination
There are two music streaming services, NO ADS and ADS. The marginal cost per-user of NO ADS is $0.5, the marginal cost per-user of ADS is $0.2. There are 10 million consumers who value NO ADS $2, and ADS $0.7. There are 10 million consumers who value NO ADS $0.7, and ADS $0.5.
a. The two streaming services are supplied by a perfectly competitive industry. What is the price of NO ADS, and what is the price of ADS?
How many users choose NO ADS, and how many users choose ADS? What are the industry profit? What is total consumer surplus?
b. Due to a change in the licensing system, the marginal cost of NO ADS increases by $0.01, while the marginal cost of ADS increases by $0.115.
What happens to the perfect competitive prices?
What happens to the number of consumers choosing each product?
c. The costs are nowas in part a.
However, instead of being supplied by a perfectly competitive industry, the two streaming services are offered by a monopolist. The firm knows the composition of consumers, and their preferences, but it cannot set prices individually to each buyer.
(The firm chooses one price for NO ADS and one price for ADS, and the consumers self-select freely between the two options).
Compute the optimal prices set by the firm, consumer surplus, and welfare.
d. How much money would the monopolist pay to obtain a technology allowing them to distinguish and price discriminate between differen types of buyers?
Nash Equilibrim in Simple Games
Solve for the Nash equilibria of the following (normal-form) game. (Ignore mixed strategies; if you do not know what this means, nevermind.)
Wasteful Races?
Consider a country with 10 million individuals. In a semi-public service (think about education, healthcare, transportations) individuals use non-redeemable vouchers. If a firmi enters the market, and they charge any price Pi ≤ 5, individuals can pay with the voucher. If there are more than one firm, say N firms, individuals choose randomly (in equal share) between the firms with a price lower than 5. Entering implies a fixed cost of $10 million dollars, marginal costs are zero.
a. Argue that, upon entering, any firm will select a price Pi = 5. Formally, you can argue that taking entry as given, Pi = 5 is a dominant strategy. (Hint: the profit of a firm after entering is surely -10(million), to which we must add revenues. These are equal to...)
b. Consider the case of N = 2 and “fill in” the following normal form game, where firms are only choosing whether or not to enter, and upon entering they surely set Pi = 5.
c. Find the Nash equilibrium of this game.
d. Can you argue (in less than 20 words) that Nash equilibrium leads to lower welfare than a case in which the government only allows one firm to enter the market?