Question

Suppose a consumer spend all of her income on only two goods, x and y. Her preferences over these two goods are represented by the utility function u(x,y)=2x^1/2+3y. Find the mrs_{xy. Is it diminishing or not? (In the solution of this problem our teachers prefers to solve this via MUx/ MUy this ratio. But in other schools they prefer to solve this MUx/ MUy . Which one is true ? Why they use minus sign ?}

Answer 1

Answer:

Given the utility function,

u(z,y) = 2x1/2 +34

Thus,

MU, = u(x, y) = (2x1/2 + 3y) = 2** *23-1 + 0 = 2-}

Similarly,

MU, = u(x, y) = (2x1/2 + 3y) = 0+3 = 3

And we know that,

MU, MRSTY MUY

Now plugging the values, we get,

MRS., "

Thus this is the slope of the indifference curve i.e. MRS. But if find the slope of this MRS (i.e. slope of slope) then we will know it is diminishing or rising. To be diminishing the new slope should be less than zero. i.e.

д(M RSy). дх

Therefore,

a(MRSTy) a = - - -$2 < 0 ar 3*27-1/2-1 6

Thus the utility function is diminishing.

We use minus sign because MRSxy=Change in Y/Change in X (i.e. )and the Change in Y is always negative. To express MRS as a positive value we multiply by -1 only to use it for comparison of two MRS value.

MRSy =