MU and MRS?

Question

can you help me figure this out? i'm having trouble

u(x1, x2) = (x1 +a)(x2 +b)

how do i find MU1, MU2 and therefore MRS?

i know you do partial deriv but i'm unsure of how to proceed

please help!!

Answer 1

Now see, we apply product rule of derivates while taking the partial derivative, because both functions are multiplying.

du/dx1 = MUx1 = (x2 + b)(1) + (X1 + a)(0) = X2 + b

du/dx2 = MUx2 = (x1 + a)(1) + (X2 + b)(0) = X1 + a

Now MRS = MUx1/MUx2

MRS = (x2 + b)/(x1 + a)

I hope it will work.

Answer 2

I'll start by multiplying it out, but that's just me lol

U = x1x2 + x1b + x2a + ab

Find MU1 by taking the partial derivative in terms of x1

dU/d(x1)=x2 + b

Then find MU2 by taking the partial derivative in terms of x2

dU/d(x2)=x1 + a

Now that you have both of them, you can find MRS

Does that make sense?