13. Suppose Paul\'s aility function is U -SxY, where U is mesured in usils (leve
ID: 1141805 • Letter: 1
Question
13. Suppose Paul's aility function is U -SxY, where U is mesured in usils (level of happiness). X'is consumption hors-d is consumption of swimming hoursFor this utility fa ton, tho a Suppose Y-2. Calculace Paul's utility for X-2,3,9, and 10. For given level of Y, does good X display diminishing marpimal utility of X is given by MUs -SY; the marginal utility - to see this, calculate the MU between X-2 and X-3 and then again between X-9 and X-10 10 b. Suppose X-4. Calculate Paul's utility for y-2,3, 9, and 10. For a given level of X, does good Y display diminishing marginal utility to see this, calculate the MU between Y-2 and Y-3 and then again between Y-9 and Y-10 MU 10 Find three different bundles containing rand y that give Paul500 utils ofsatisfaction. It would help to solve the Utility function for Yand see what values orx you need: e. S00-$XY 500 100 Check... MRS 100 U-SPT-100-500 500 500 500 500 d. In your table above calculate the MRS at each point. What happens to the marginal rae of substitution between x and Yas consumption of X increases? e. Does the principle of diminishing MRS depend on the diminishing marginal utility of X and )?Explanation / Answer
Solution 13. a.
X
U = 5X*2
MU=U/X
2
20
10
3
30
9
90
10
10
100
Thus marginal utility is not diminishing. It is constant.
b.
Y
U = 5*4Y
MU=U/X
2
40
20
3
60
9
180
20
10
200
Thus marginal utility is not diminishing. It is constant.
c.
U=5XY
X
Y
Check
MRS=MUx/MUy = 5Y/5X
500
If X=1
Y=100/1 = 100
U=5*1*100 =500
100/1 = 100
500
If X=2
Y= 100/2 = 50
U=5*2*50=500
50/2 = 25
500
If X=5
Y = 100/5 = 20
U=5*5*20=500
20/5 = 4
500
If X=10
Y = 100/10 =10
U=5*10*10=500
10/10 =1
d. We can see that as X increases, MRS decreases.
e. The principle of diminishing MRS between X and Y depends on diminishing marginal utility of X and increasing marginal utility of Y.
X
U = 5X*2
MU=U/X
2
20
10
3
30
9
90
10
10
100
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