(ECON198)[2010](s)midterm~ma_wxx^Sol_10233.pdf

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Department of Economics, HKUST

ECON 198

Microeconomic Theory I

Semester: Spring 2009/10

Tutor: John Cheng Office number: Room 2393 (ext.7597)

Email: ecjcheng@ust.hk Office hours: Tue 3:00p.m. C 5:00p.m.

Midterm Answer Key

1. Indifference curves will cross.

A ;B and B ~C but A ~ C It is not transitive and the indifference curves intersect.

2.

a.1 b

Vx = a(x +1) ( y +1)

ab.1

Vy = b(x +1) ( y +1)

vx a(y +1)

MRSv ==

vy b(x +1)

MRSu = ux = ay MRSv

uy bx

V is not a monotonic transformation of U.

4.

x2 x1 x

When one of them is a corner solution, then their MRS will not be equal.

5.

PxI PyI

Pxx + Py y =

+

P + PP P +

PP

x xyy xy

2PPI + PI

PP + PI

PP

xy xxyyxy

=

(P +

PP )(P +

PP )

x xyy xy

I

PP (

P +

P )2

xyx y

=

PP (

P +

P )2

xyx y

= I I

x(I, P , P ) = x yP + PP

x xy

x(tI,tP ,tP ) =

tI =

I = x(I, Px , Py )x ytP + tPtP P + PP

x xyx xy

I

y(I, P , P ) =

x yP + PP

y xy

y(tI,tP ,tP ) =

tI =

I = y(I, Px , Py )x ytP + tPtP P + PP

y xyy xy

Both x and y are homogenous function with degree 0

P

I(1+

y )

.x 2 Px

=.

< 0

.Px (P + PP )

2

x xy

Px

I(1+

)

.y 2 Py

=.

< 0

.Py (P + PP )

2

y xy

Both x and y are downward sloping, they are proper demand functions.

6. e + e + e = 0

x,px x,py x,I

ex,py = -(ex,px + ex,I )

e < 0, e > 0

x,px x,I

ex,py can be smaller than 0 or larger than 0

.x Py

When e=< 0

x,py .Py x

.x < 0 .Py

They are gross complements.

7.

Statement I shows that price and demand are negatively related. Statement II shows that price and demand are positively related, which contradicts statement I. The word demand in statement I is wrong, it should be quantity demanded. An increase in the price of apples will reduce the quantity demanded for apples. An increase in the demand for apples will increase the price of apples.

8.

AOC

y

There exists a quantity of BigMac that is between 0 and 1 which will give him a higher utility, however as the number of BigMac is discrete, he can either choose

0 or 1. We need to compare the utility when he consumes 0 BigMac and 1 BigMac. In the above diagram, it shows that he will consume 1 BigMac and he is indifferent before or after the increase in price.

AOC

y

1 BigMac

In the above diagram, it shows that he will not consume any BigMac and he is better off after the increase in price and income.

9

AOC

m m

W

w ICo IC1

1 Leisure

Suppose leisure is a normal good, then an increase in non-labor income will lead to an increase in the reservation wage rate.

AOC

m m-c

w

w ICo IC1

1 Leisure

Suppose the fixed monetary cost of work increases from 0 to c. Then the reservation wage rate will increase to w.

10. Since the family cannot change their consumption on electricity, it is a change in consumption bundle instead of a shift in the budget constraint.

f

y

e

When