Given the utility function
Determine the value of marginal utilities 
1at the point (25,8). Hence
(a) estimate the change in utility when both x1 and x2 increase by 1 unit
(b) find MRCS at this point.
Homework Answers
Q1) We have U = X11/2X21/3
(a) dU/dX1 = 1/2 X11/2-1X21/3 = 1/2X1-1/2X21/3
(at 25,8) = 1/2 (1/5) *2 = 2/10 = 1/5
dU/dX2 = 1/3 X11/2 X2-2/3
(at 25,8) = 1/3 * 5 *1/4 = 5/12
Thus, chnage in utilities are 1/5 and 5/12 as X1 and X2 change by one unit respectively
(b) MRCS = marginal utility of X1 / Marginal utility of X2
= (1/5)/(5/12) = 12/25
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