An individuals utility depends upon the consumption of goods x and y,
I have to find the utility maximisation of x and y,
(1)
(2)
Multiply (1) by 2 = (3)
(4)
(3)-(4), after rearranging and substitution,
x = 8, y = 8
To check these are the maximum points,
Find cross partial derivitives,
= 16 > 0
3 conditions meet = maximum
I then have to use the total differential of the function to find an expression for the slope of any curve.
Slope of curve =
This is where i become a little stuck as to what I should do next.