Problem Set 2
1) Using the bundles (1,1), (2,1), (3,3), and (2,3), graph the Indifference Curves through
these bundles for a person whose preferences are characterized by
a) u(x,y) = 2x+2y
7
6
5
4
4
6
3
12
10
2
1
0
0
1
2
3
4
b) u(x,y) = min(x,y)
5
4.5
4
3.5
3
1
2.5
3
2
2
1.5
1
0.5
0
0
1
2
3
4
c) u(x,y) = xy
12
10
8
1
2
6
9
6
4
2
0
0
1
2
3
4
d) u(x,y) =xy2
18
16
14
12
1
10
2
8
27
6
18
4
2
0
0
1
2
3
4
2) Four other people have the following preferences. For each person, calculate Marginal
Utility of good x and Marginal Utility of good y.
a) u(x,y) = 2x+2y
b) u(x,y) = 5x+3y
c) u(x,y) = xy2
d) u(x,y) = x3y2
e) u(x,y) = x.5y.3
You were not asked to calculate the MRS, but you should be able to by now.
a) MUx=2, MUy=2, MRS = 1
b) MUx=5, MUy=3, MRS = 5/3
c) MUx= y2, MUy= 2xy, MRS = y / 2x
d) MUx= 3x2y2, MUy= 2x3y, MRS = 3y / 2x
e) MUx= .5x-.5y.3, MUy= .3x.5y-.7, MRS = 5y / 3x
3) For each of the four bundles, (2,3), (3,2), (4,4), and (9,0), calculate the cost associated
with buying each bundle for the given prices.
Px=2 and Py=4
Px=3 and Py=3
Px=1 and Py=5
Px=2,Py=4
Px=3,Py=3
Px=1, Py=5
(2,3)
2*2+4*3=16
3*2+3*3=15
1*2+5*3=17
(3,2)
2*3+4*2=14
3*3+3*2=15
1*3+5*2=13
(4,4)
2*4+4*4=24
3*4+3*4=24
1*4+5*4=24
(9,0)
2*9+4*0=18
3*9+3*0=27
1*9+5*0=9