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
= 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) ?