Hello,
Do thatHowever I’m uncertain as to whether I have to multiply equation (1) which would give me
and then set this equal to equation 2 ?
But I must say... this is quite nasty
A consumers utility function is given by
The consumer has a budget of £480, the price of good X and good Y are £8 and £16 per unit.
Using the Lagrange multiplier method, identify the quantities of X and Y the consumer will purchase in order to maximise their utility?
This is what I have so far...
Px =8 Py=16 B=480
Maximise subject to constraint 8X + 16Y = 480
Partially differentiating gives
= (1)
= (2)
= 8X + 16Y – 480 (3)
I’ve then set these 3 equations equal to zero, in order to solve them.
However I’m uncertain as to whether I have to multiply equation (1) which would give me
and then set this equal to equation 2 ?
Or do I just divide equation (1) by equation (2) ?
Thank you,
After multiplying equation (1) by 2 I get that to be
Equation (2) is
Rearranging (1) and (2) gives,
(1)
(2)
I then set equation (1) equal to equation (2) which gives,
=
I guess I then have to try and rearrange that somehow to come up with a solution of Y ?
Hello, Apache!
Hello, Apache!
I solved it like this . . .A consumers utility function is given by:
The consumer has a budget of $480, the price of goods and are $8 and $16 per unit.
Using the Lagrange multiplier method, identify the quantities and
the consumer will purchase in order to maximise their utility.
This is what I have so far: .
Maximize subject to constraint
. .
Partially differentiating gives
. .
Multiply [1] by 5: .
Multiply [2] by 5: .
Equate [3] and [4]: .
Multiply by
Substitute into [3]: .
Substitute into [5]: .
I understand the method used however, I find I’m a little bit lacking in the manipulation of algebra, and I can’t get my head around how
becomes
And similarly when
I fail to see how that gets
I just can’t figure out how to rearrange, is there a simple way in which I’m just overlooking ?