Reference no: EM132324460
Assignment
1. Consider a market with a linear demand function P = 100 -Q. There are 2 firms in the market with identical marginal costs of production c = 20, no fixed costs, and no capacity constraints. Both firms discount future payoffs with the discount factor δ ∈ [0,1]. Let p1 and p2 be the prices charged by firm 1 and firm 2, respectively. The two firms decide to the collude at the monopoly price and follow a trigger strategy: after one firm has deviated, both firms play the static Bertrand equilibrium forever.
(a) Suppose that prices are observed N periods after they are chosen. Write the constraint that must hold for collusion to be sustainable and derive the critical discount factor δ0, where δ ≥ δ0.
(b) How does δ0 vary with N? Explain intuitively how increases in N make it easier or harder to sustain collusion.
(c) Now suppose that with probability α ∈[0,1], a new innovation takes place, allowing more efficient firms to enter the market and charge p= c. Write the constraint that must hold for collusion to be sustainable and derive the critical discount factor δ0, where δ > δ0.
(d) How does δ0 vary with α? Explain intuitively how changes in value of a make it easier or harder to sustain collusion.
2. You have been hired by Kabletown, a small local cable television provider in Mountainville, as a consultant to advise the firm on pricing strategies. Due to the rough terrain and perpetual fog, no satellite television company can serve customers in Mountainville. As a result, Kabletown is the sole provider of cable television service in Mountainville. You find out that there are only two types of customers for Kabletown's service: residential households and restaurants.
Total Residential Household Demand is given by QH = 200 - 2P.
Total Restaurant Demand is given by QR = 100 - P.
Kabletown's total cost of production is given by TC(Q) = 10Q, where Q is the number of customers that subscribe to Kabletown's service. Assume that Kabletown cannot discern whether a particular subscriber is a household or a restaurant, and thus, can only charge a single price in the entire market.
(a) Calculate Kabletown's total market demand. Find Kabletown's profit-maximizing price, quantity sold in each market, and total profits.
(b) What is the consumer surplus in the restaurant sub-market?
You propose that Kabletown develop a new technology that allows it to identify what type of customer sub- scribes to its service. This would also allow the firm to charge different types of customer separate prices. Arbitrage across sub-markets is not possible.
(a) If Kabletown had access to this technology, what would be the profit-maximizing price in the household sub-market and what would be the profit-maximizing price in the restaurant sub-market? How much would Kabletown be willing to pay for this technology?
(b) You hear from a friend in the industry that the Restaurant Owners' Association is planning = to lobby the local government about cable TV pricing policy. Do you think they are likely to lobby for or against a bill that prohibits separate pricing for separate segments? Justify your answer. Up to how much would the association be willing to spend on such lobbying activity?
3. Consider a Cournot market with linear demand p = a - Q, a > 0 and zero marginal costs for all the firms. Recall that in Problem Set 2, we derived the expressions for the equilibrium quantities, prices, and profits in an industry with N firms. Assume that there is a fixed cost of entry F into the market.
(a) Calculate the price elasticity of demand ∈D at the equilibrium market price. Verify that L = (HHI/∈D)by calculating the Lerner Index L and the Herfindahl-Hirschman Index HHI separately.
(b) If firms continue to enter the market as long as they earn a non-negative profit, how many firms will enter this industry?
(c) If a regulator, seeking to maximize social surplus (the sum of consumer surplus and producer surplus), can control the number of firms N in the industry, but cannot influence the (Cournot) competition once the industry is formed, what N will she pick? Assume again that there is a fixed cost of entry F.
(d) What is the socially optimal price? Denote this price by p. Suppose that in addition to setting the number of firms, the same regulator can also dictate the price in this industry. Is p feasible? Explain
your answer.
4. In a two-period lived economy, one consumer wishes to buy a TV set in period 1. The consumer lives for two periods and is willing to pay a maximum price of $100 per period of TV usage. In period 2, two consumers (who live in period 2 only) are born. Each of the newly born consumers is willing to pay a maximum of $50 for TV usage in period 2.
Suppose that in this market, there is only one firm producing TV sets, that TV sets are durable, that production is costless, and that there is no discounting between periods. The monopolist cannot discriminate between consumers within the same time period.
The monopolist and the first-period consumer know that two more consumers will be born in the second period and know what their valuations will be. Finally, assume that a consumer purchases if he or she is indifferent between purchasing and not purchasing.
(a) Calculate the prices that the monopolist charges for TV sets in each period.
(b) What if in the first period, a consumer who lives for two periods is now only willing to pay no more than $20 per period for TV usage? Recalculate the prices that the monopolist charges for TV sets in each period.