The key answers to the midterm exam of intermediate
microeconomics
1, E ; buy 20 cans apple juice using 20 coupons and 4 cans orange juice is
the optimal choice for Lin. So choose E.
2, D; denote x as the amount of strawberries Walt consumes, y is the
amount of creams. The utility function for Walt is min｛2x,3y｝,subject to
10x+10y=200. The optimal amount is (12,8). So choose D.
24
3, B; △CS= 15 (15  p / 3)dp =-76.5 so change in consumer’s surplus is
closet to -76.so choose B.
4, B; q(p)=30-p/3; p(q)=90-3q.so choose B.
5, D; since the preference is unchanged under a positive monotonic
transformation,
U ( x, y)  x 2 y8  x0.2 y 0.8
. x* ( p , m) 
m
p1
 0.2 105  21
.so
choose D.
6, C; the utility function for Ella is min｛5x,y｝. When x=10,y=25.the
utility for Ella is 25.now the problem is min 10x + 15y . subject to min
｛5x,y｝=25. the optimal choice is (5,25).so the least amount money is
425.choose C.
p dq
，when changed the measure from bushels to pecks. The
q dp
7, E;   
budget constraint and the price enlarge four times. However demand
function is unchanged. So the price elasticity of demand will be
unchanged.
8.
(a):
P
r(1)
r(2)
r(3)
r(4)
Q
1
2
3
4
(b) r(1)=v(1)-v(0)=v(1); r(2)=v(2)-v(1); … r(n)=v(n)-v(n-1)
(c) the area under the demand curve S=∑r(i)=∑v(k)-v(k-1)=v(n), it just
is the utility when consume n units of good.
(d) GCS=∑v(k)-v(k-1)=v(n); NCS=v(n)-np
max U ( x A , xB )  x A xB
9. (a) s.txA  2 xB  40
,
we get x A* =20, xB* =10. so before the
price changed, Tom consumes 20 units of A and 10 units of B.
(b) the price of B falls to﹩1, Tom consumes the old bundle (20,10),
only pays $30. The new income is﹩30,and the price of A,B is (1,1). Then
the optimal choice for Tom is (15,15). Tom would consume 15 units of A
and 15 units of B.
(c) from (b),we know that the substitution effect makes Tom buy more B,
and the more amount is 15-10=5.
(d) the price changed to (1,1),and the income is 40﹩everyday, so
max U ( xA , xB )  xA xB
s.txA  xB  40
, we solve it , get x A* =20, xB* =20. so Tom consumes
20 of units A and 20 units of B.
(e) the income effect makes Tom consume more B. and the more amount
is 20-15=5.