Professor’s extra explanation and hints: How do I solve for the Expenditure Fun

Too Tired? Too Anxious? Need More Time? We’ve got your back.

Professor’s extra explanation and hints:
How do I solve for the Expenditure Function for those dang calculus-unfriendly utility functions in Question 1 ?
Recall what the Expenditure Function, E(p1, p2, U), is supposed to represent: the minimum expenditure necessary for a consumer to be able to achieve consumption worth U utility given prices (p1, p2). For the perfect complement and perfect substitute case, you should be able to solve for that Expenditure Function without using calculus …
1(a): For the above preferences, the profit maximizing bundle always involves equal amounts of the two goods: x1 = x2. Having more of any one of the goods is a waste as having more of that good does NOT increase utility.
Compare bundle A = {x1 = 4, x2 = 4} with bundle B = ({x1 = 4, x2 = 10}. For both bundles, the utility you get is 4. But bundle B will be much more expensive.
So, you have some income Y to spend on the two goods. And you want the two goods to be the same quantity … how much would you get of each? Note that Y = p1 x1 + p2 x2. But x1 = x2. So Y = p1 x1 + p2 x1 = (p1 + p2) x1 … so x1 = ? And therefore x2 = ?
As for indirect utility, if x1 = x2 for profit maximizing bundle then U(x1, x2) = min{x1, x2} = x1 = x2 (for profit maximizing bundle) … Similarly, if U = 2, then you need x1 = x2 = 2 … which costs you p1 * 2 + p2 * 2 = (p1 + p2) * 2 …
1(c): use Shephard’s Lemma to derive the Hicksian demand from the Expenditure Function ..

Too Tired? Too Anxious? Need More Time? We’ve got your back.