So we were discussing a utility function in class today and I'm not sure how my teacher arrived at the First Order Necessary Condition that he did (using substitution)
We want to maximise the function $$U(a, b)$$ where $$a = y - pb$$
a is good 1 and b is good 2, whereas y is your income and p is price of good 2 (he got rid of p1 by stating that the price of good 1 = 1, so we just have p (no subscript as "it would be trivial now")
The FONC (with respect to b) that he arrived at is $$U_{1}(a, b) \frac{∂a,b}{∂b} + U_{2}(a, b) = 0$$
I'm completely at a loss to how he arrived there. I think my differentiation is rusty and I'm differentiating U(a, b) with respect to b, wrong.
Apologies if this is a bit vague, he rushed through this in the last 3 minutes of class and I might not have caught it all.
Thanks!