I. Find the MRS for the following utility functions at the point (x, y) = (1. 2). i. u(x, y) = x?y. ii. u(x, y) = square root (x.y) iii. u(x, y) = x^2?y. iv. u(x, y) = x + y. v. u(x, y) = min{x, y}.
Solution
Ans 1) MRS = MU x /MU y
u(x,y) = x.y
We differentiate the above equation with respect to (wrt) x , we get
MUx = y ;
We then differentiate the utility equation wrt , we get
MUy = x
MRS = y/x at the point (1,2) WE HAVE MRS = 2/1 = 2
Ans 2) U = Sq rt of (x.y)
MUx = sq rt ( y/x) and MUy = Sq rt (x/y)
MRS = y/x = 2/1 = 2
ans 3)
MUx = 2xy
MUy = x 2
MRS = 2y/x = 2.2/1 = 4
Ans 4) MUx = 1 and MUy = 1
MRS = 1
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I- Find the MRS for the following utility functions at the point (x- y.docx
1. I. Find the MRS for the following utility functions at the point (x, y) = (1. 2). i. u(x, y) = x?y. ii.
u(x, y) = square root (x.y) iii. u(x, y) = x^2?y. iv. u(x, y) = x + y. v. u(x, y) = min{x, y}.
Solution
Ans 1) MRS = MU x /MU y
u(x,y) = x.y
We differentiate the above equation with respect to (wrt) x , we get
MUx = y ;
We then differentiate the utility equation wrt , we get
MUy = x
MRS = y/x at the point (1,2) WE HAVE MRS = 2/1 = 2
Ans 2) U = Sq rt of (x.y)
MUx = sq rt ( y/x) and MUy = Sq rt (x/y)
MRS = y/x = 2/1 = 2
ans 3)
MUx = 2xy
MUy = x 2
MRS = 2y/x = 2.2/1 = 4
Ans 4) MUx = 1 and MUy = 1
MRS = 1
