00:04
Now basically we have a consumer's utility function given by this, right? we have x1, x2 to know the number of items, so two goods, right? g1 and g2.
00:14
And the lagoonche multiplies to, you asked to use my like long multiplies to find the maximum value of you, right? if the consumer's income is 83, right? so obviously each item costs this much and for this goods and this much for this good, right? so 83, the constraint of course, 83 must be equal to x1 and times 1, right? and plus 2 times x2, right? so that would be, so i would say, or in other words, this can be really, re -reting as if x1 and x2, right, equals here, right, with f x1, x2, of course, is given by x1 plus 2x2 and minus 83, right? so the lagoonge method means that you need to construct a new function, which i'm going to call, let's say, g, right, gx1 and x2, right? and this is given by the arranging u function, you and then plus lambda, which is called like launch multiplier times if, right? now what you need to do is just to make sure, take the derivative of g which is worm, and that of course gives you, if you do that, you get 2x2 plus 3, right, and plus lambda and times the partial derivative of f with respect to x1, that's one, right? so this should be zero.
01:28
And similarly, you need to take partial g over partial x2, you do that, you will find this to be 2x1, right, and plus and plus lambda and times, you know, the times if you take the derivatives of every respect to x2, that's 2, right? so 2, and this is also been 0, right? so you have three equations, one, this, w, this, and of course, also this one, right? and you should be able to find out all the three unknowns, right? so what we need to do, of course, is to solve these three equations, right? so for example, what i'm going to do, first, what i'm going to do is multiply this equation by, for example, by two, right? then i will find that was to be 4x2 plus 6 plus 2 lambda, it was 0, right? and then you combine these two equations, if you subtract these two equations, obviously we get 4x2 minus 2x1, right, and plus 6, then, plus 0, right? so you combine that, you put this equation together with this one, right? so this one, let me rewrite it.
02:32
So that's actually given by 2x2, right? 2x2 plus 1 x1, right? and that should be equals, okay, and minus 83...