Here is a question that is more a test of logic and organization than math.I provide it as an opportunity to 'mess around' some more with utility functions, indifference curves, and utility maximization. Approach it as in assignment 1. The first big problem here is to figure out what the indifference map might look like. Then this question requires you to combine 'diagramatic' techniques and logic in order to characterize solutions in the diagram, which you then need to translate into some equations you can solve to get a general answer. The math here is not hard in the least, it is more a question of what math to do, and keeping track of a bunch of cases.

Consider preferences represented by the utility function

u(x) = min{(x1 + 5x2), (2x1 + 2x2), (5x1 + x2)}

Derive Walrasian demand. [Hint: this is a function of income and price ratio. So one straight forward way to get demand is to pick some point on the vertical axis (which is the point m/p2, and then in your mind's eye rotate a budget from very steep to quite flat from that point. As you do so, you are effectively varying p1 from high to low. Take note of the optimal bundle. You can then characterize it by (a) being on the budget and (b) being on some ray from the origin, or on a region of budget. Solve the resulting two equations.]

Draw representations of the Engel Curves, Income Expansion path, Demand Curves, and Price Offer curve for some endowment. (Yes - some of these 'curves' are actual 'regions/sets'for some parameter values. Nothing wrong with multi-valued mappings, unless you insist on only ever doing calculus!)