Final answer:
The equation for the marginal utility with respect to x is - (y + 1) / ((x + 2y + 1)^2).
Step-by-step explanation:
The marginal utility with respect to x in the context of the utility function u(x, y) = - (1 / (x + 2y + 1))⁻¹ can be found by taking the partial derivative of the function with respect to x. To find the marginal utility with respect to x, we differentiate the utility function with respect to x, treating y as a constant. The equation for the marginal utility with respect to x is:
MUx = - (y + 1) / ((x + 2y + 1)2)