[tabako]

I'm surprised you are doing this in intermediate micro... where do you go to school?

It should be clear that p and x* should both be vectors, and p.x* is that dot product of them. For (2): you didn't define what y is, but I assume its the consumer's budget or something like that. p.x* is a scalar, and it's how much the consumer spends on goods, so having y - p.x* >= 0 fits with y being the budget.

From this, we can look at the fourth statement and see that one of two things are 0.

either lambda = 0, or y - p.x* = 0.

This says that either the consumer exhausts all of his budget (i.e. y = p.x*), or the marginal utility of income is 0 (i.e. lambda = 0). This should make intuitive sense, as marginal utility of income can't be positive if you aren't using all of your income.

As for the other two statements, I don't have a good grasp of what they intuitively represent, though I might be able to figure out how to solve a problem with them.


I haven't actually done this stuff before, but I am fairly confident that what I said about (2) and (4) is correct.