Hi!

I've got the following utility function:

$\displaystyle U = (y_1 - 2) (y_2 - 4) = y_1y_2 - 4y_1-2y_2-8$

prices are

$\displaystyle p_1 = 2 , p_2=4$

$\displaystyle p_1$ is the price of good 1

$\displaystyle p_2$ is the price of good 2

$\displaystyle y_1$ is the quantity of good 1

$\displaystyle y_2$ is the quantity of good 2

The budget costraint is:

$\displaystyle 100 = 2y_1 + 4y_2$

Now, we know that we have equilibrium when we have

$\displaystyle \frac { \delta U / \delta y_1} {p_1} = \frac { \delta U / \delta y_2} {p_2}$

because weighted marginal utilities are equal.

Ok, now this is where i get stuck! The book "says" that

My question is: why are $\displaystyle \delta U / \delta y_1$ equal to $\displaystyle y_2 - 4$ and $\displaystyle \delta U / \delta y_2$ equal to equal to $\displaystyle y_1 - 2$ ?with our data, we have:

$\displaystyle \frac { \delta U / \delta y_1} {p_1} = \frac {y_2 - 4} {2}$ and $\displaystyle \frac { \delta U / \delta y_2} {p_2} = \frac {y_1 - 2} {4}$

Thank you in advance!