ECO512 Lagrangean for the utility maximizing problem

) Suppose that a couple receives utility from their family’s consumption, c,
and their child’s private education, z (think of z as quality, not years of education).
The couple’s actual utility function is
u c z c z ( , ) ( ), 0
. The price of
consumption is $1/unit and that of z is p. The couple’s income is I. Consequently,
their budget constraint is given by:///////Let the utility function over two goods be given by the following:
0.5 0.5
1 2 1 2 u x x x x ( , ) =
State the Slutsky equation for the effect of a change in
1 p
on the amount demanded
of
1
x . Identify income and substitution effects