Which mathematics are required for fully understanding the theories of the firm? When I say &quot;theories of the firm&quot;, I'm referring, in particular, to the theories exposed in the next works: 1) Transaction Cost Economics exposed in &quot;Transaction Cost Economics&quot; by Tadelis and Williamson (2013) (chapter 4 of &quot;The Handbook of Organizational Economics&quot; by Gibbons and Roberts); 2) Property Rights Theories exposed in &quot;The Costs and Benefits of Ownership&quot; by Grossman and Hart (1986), &quot;Property Rights and The Nature of The Firm&quot; by Hart and Moore (1990), and &quot;Firms, Contracts, and Financial Structure&quot; by Hart (1995); and 3) Incentive System Theories exposed in &quot;The Firm as an Incentive System&quot; by Holmstrom and Milgrom (1994), and &quot;Multitask Principal-Agent Analyses: Incentive Contracts, Asset Ownership, and Job Design&quot; by Holmström and Milgrom (1991).
When I say &quot;Which mathematics&quot;, I would appreciate if a list of chapters of a highly recommended math book is given, due to I need to be prepared for analyzing those theories as soon as possible. In this regard, it should be noted that I have studied the first eight chapters of the first volume of Apostol's Calculus. In advance, thanks so much.
I haven't gone through all the papers so I just sampled 'The Firm as an Incentive System'. Browsing through it, it relies on Linear Algebra and Real Analysis. Again, I warn that I have not gone through the entire paper but seeing some of the terminology used there, I could guess that these two a clearly involved (maybe they use some bit of topology as well). They use a concept of sublattice somewhere and that pertains to group theory.
A good starting place for real analysis could be Steven R. Lay's 'Analysis'. There you can learn some of the basic terminologies that they have used like supremum and infimum. For Linear Algebra, it has got to be Gilbert Strang's text 'Introduction to Linear Algebra'. Linear Algebra is used extensively in Econometrics as well. You can find his lectures at: https://ocw.mit.edu/courses/mathematics/18-06-linear-algebra-spring-2010/ .
Hope this helps!