Working Through Mas-Colell When the Problems Won't Yield
The graduate micro sequence at most schools runs on Mas-Colell, Whinston, and Green. It covers everything from consumer theory to general equilibrium to game theory in roughly 1,100 pages of dense notation. The exercises are where the actual learning happens, and that is also where people get stuck repeatedly. The solutions manual for MWG was published alongside the textbook. The official version contains worked solutions for a large number of the exercises, though not every single one. People who teach from this book often compile additional notes or supplementary solution sets because the book itself does not cover every problem in full detail. Those unofficial compilations circulate widely in PDF form on university course websites and academic forums. Here is what I have found over the years about using these materials without undermining your own work.
The first thing to understand is that the problems in MWG are not routine calculus exercises. They require you to set up definitions, invoke theorems correctly, and handle edge cases involving boundary solutions or non-strict preferences. When you look at a solution before doing the work yourself, you miss the part where the setup matters. I worked through Chapter 3 on consumer preferences on my own before consulting any solution. The envelope theorem and Roy's identity derivations in the back are clean when presented cleanly, but trying to reproduce them from memory after reading the answer first leaves you with no real ability to handle a slight variation in the problem statement. One specific issue I ran into involved Exercise 17.C.1, which deals with the relationship between expenditure minimization and utility maximization under non-convex preferences. The official solution assumes standard differentiability conditions without calling them out explicitly in the exercise text. I spent about forty minutes chasing a sign error because the problem setup in the book omits a boundary condition that the solution relies on. The workaround was to compare the result against the corresponding discussion in the main text around page 320 and verify that the Hicksian demand was being derived under the assumption that the utility function is quasi-concave. Once I confirmed that assumption held in my version of the problem, the algebra matched. When you are checking your work against a solution manual, the most useful approach is to treat it as a verification step, not a teaching tool. Write out the full proof or computation on paper first. Then open the manual and compare line by line. This takes longer than skipping ahead, but it actually builds the skill the course is supposed to develop.
The unofficial solution sets that circulate online vary significantly in quality. Some are accurate and well-written. Others contain errors in the more advanced chapters, particularly in general equilibrium and mechanism design. I learned this the hard way in a doctoral qualifying exam when I had relied on a particular online solution for the Gibbard-Satterthwaite characterization. The exercise was slightly different from the standard version, and the solution I consulted did not account for the modification. I had to reconstruct the argument from the first principles of strategy-proofness during the exam. After that, I stopped trusting any single source without cross-referencing. If you are using a solutions manual, cross-reference against at least two sources when possible. Compare your derivation with the main text, then check the manual. For exercises that involve fixed-point theorems, pay attention to whether the solution properly establishes compactness and convexity of the relevant correspondence before applying Kakutani. Several online solutions skip that step and just assert the result. That shortcut works for passing a homework check, but it fails under exam conditions where the grader expects the full topological justification. The biggest limitation of working through MWG with any solution manual is that the material assumes a level of mathematical maturity that most students do not possess when they start. Measure theory, point-set topology, and functional analysis appear throughout without much hand-holding. If you encounter a proof that relies on a result you have not seen, stopping to look it up is necessary rather than optional. The manual will not teach you the underlying mathematics.
Get the Full Details
For the exercises in the later chapters on game theory and information economics, I recommend pairing the solutions manual with lecture notes from a course that covers the same material. The notation in the book can be dense, and seeing the same concepts explained with different notation often clarifies the structure better than reading the solution directly. Most university libraries carry the hardcopy of the official solutions manual. If your institution does not, checking with the economics department is usually faster than searching online repositories, where the files tend to be outdated or incompletely scanned. The exercises are numbered consistently across editions, so the 1995 first edition manual is largely usable even if you are working from a later printing.
