00:01
Let's go over this question.
00:10
So we need to find marginal utility of good x, y, and the marginal rate of substitution.
00:16
Marginal rate of substitution is going to be the negative of marginal utility of x over marginal utility of y.
00:33
So marginal utility of x is going to be the partial derivative in terms of x.
00:40
So y is a constant.
00:50
So we have 4 and then following the power rule it's negative 2 square root of x for marginal utility.
01:24
And then for y since x is a constant, it's just going to be 2.
01:46
So then the absolute value is just going to be 1 over square root of x.
02:06
Then for the next one i'm going to just leave the negative sign out.
02:24
So we have ln of x plus ln of y.
02:34
So we know that the derivative of ln x is 1 over x.
02:42
And since y is a constant, ln of a constant is going to just be another constant.
02:48
So we have 1 over x and then for ln of y, it's 1 over y.
03:04
So that's y over x.
03:15
So let's go on to the next one.
03:31
So here we have x raised to the a, y raised to the b.
03:43
So we need to follow the power rule as usual and because y has a variable the exponent, we need to keep it when we have marginal utility of x...