# Thread: Suppose a consumer's utility function is U(x,y) = 4xy

1. ## Suppose a consumer's utility function is U(x,y) = 4xy

a) Partially differentiate the utility function to find expressions for the marginal utility of x and y.
b) What is the marginal rate of substitution when x = 2 and y = 16
c) The consumer has a budget of $96 to spend. The price of x is$12 and the price of y is \$6. Write the equation for the budget constraint.
d) What is the slope of the budget line, dy/dx?

2. Originally Posted by brumby_3
a) Partially differentiate the utility function to find expressions for the marginal utility of x and y.
To find a partial derivative, differentiate with respect to the variable required and hold all other variables constant.

$\frac{\partial U}{\partial x} = 4y$

Have a go at finding $\frac{\partial U}{\partial y}$

3. Hi Pickslides,
The answer I got is 4x.
I've actually figured out how to do the remaining questions, but now I have some extension questions I could use some help with.

e) Set up the Lagrangian function.
f) Partially differentiate the Lagrangian function with respect to first x, then y and λ. Set each of the partial differentials you obtain equal to zero.
g) Solve the three simultaneous equations you got in f) to find the consumer's optimal bundle of x and y, and to find the marginal utility of an extra dollar of income, λ.