00:01
So for a, our individual spends 70 % on goods x1 and x2.
00:06
So if they have to work 40 hours a week, their total income is 40 hours.
00:10
Therefore, the amount they spend, we want to take 0 .7 times 40, which is equal to 28 hours.
00:19
Given that they need to work for one hour to afford two units of x1 and one hour for three units of x2, we can write our constraint as 2x plus 1 plus 3x plus 2 is equal to 28.
00:35
To find our optimal consumption bundle we can use our lagrangian function.
00:39
This is going to be 1 half ln of x1 plus 1 half ln of x2 plus lambda times 28 minus 2x1 minus 3x2.
00:58
Then we want to take this derivative with respect to x1 and x2 and set them equal to 0.
01:04
So we're going to get 1 over 2x1 minus 2 lambda is equal to 0.
01:10
We're going to get 1 over 2x2 minus 3 lambda is equal to 0.
01:17
And we are going to get 28 minus 2x1 minus 3x squared is equal to 0.
01:27
Solving these, we're going to get that x1 is equal to 8, x2 is equal to 4, and our lambda is equal to 1 over 16...