Wednesday, March 25, 2015

Oligopolistic producer behavior or why airline tickets are not cheaper


Small example from the literature:
image 
Note: John Nash just won the Abel prize (http://www.nature.com/news/beautiful-mind-john-nash-adds-abel-prize-to-his-nobel-1.17179).
image
We implement different behaviors with a GAMS model:
Behavior Equations
Oligopolistic (MCP)

Nash-Cournot Equilibrium
image
image
Monopolistic (NLP)

Think of this as firms are merged.
image
image
Competitive (NLP)

Technique:
Optimize Social Welfare Objective.

Check solution by: Price= Marginal Cost.
image
image

image
Here q(i) is quantity supplied by firm i. We see most profit is to be made by merging firms and reducing capacity, just as happened in the US airline industry (Europe is a very different story). See also: https://www.nytimes.com/2015/03/24/business/dealbook/as-oil-prices-fall-air-fares-still-stay-high.html.
Another small example from energy markets: https://yetanothermathprogrammingconsultant.blogspot.com/2013/07/microeconomic-principles.html