中級微觀試題-英文

I

True

or

false.（2points*10）

1.

If

Good

1

is

on

the

horizontal

axis

and

Good

2

is

on

the

vertical

axis,

then

an

increase

in

the

price

of

Good

1

will

not

change

the

horizontal

intercept

of

the

budget

line.

2.

Henrietta's

utility

function

is

U(x1,

x2)

=

x1x2.

She

has

diminishing

marginal

rate

of

substitution

between

goods

1

and

2.

3.

Other

things

being

equal,

a

lump

sum

tax

is

at

least

as

good

for

a

consumer

as

a

sales

tax

that

collects

the

same

revenue

from

him.

4.

Sharon

spends

all

of

her

income

on

peaches

and

strawberries.

Peaches

are

a

normal

good

for

her.

Her

income

increased

by

20

percent

and

prices

did

not

change.

Her

consumption

of

strawberries

could

not

have

increased

by

more

than

20

percent.

5.

Beatrice

has

the

utility

function

U(x

,y)=

min{x

,y}.

The

price

of

x

used

to

be

3,

but

rose

to

4.

The

price

of

y

remained

at

1.

Her

income

is

12.

The

price

increase

was

as

bad

for

her

as

a

loss

of

$3

in

income.

6.

Just

as

in

the

theory

of

utility

maximizing

consumers,

the

theory

of

profit

maximizing

firms

allows

the

possibility

of

"Giffen

factors".

These

are

factors

for

which

a

fall

in

price

leads

to

a

fall

in

demand.

7.

If

there

are

increasing

returns

to

scale,

then

average

costs

are

a

decreasing

function

of

output.

8.

Since

a

monopoly

makes

excess

profits

beyond

the

normal

rate

of

return

on

investment,

an

investor

is

likely

to

get

a

higher

rate

of

return

in

the

stock

market

by

investing

in

monopolistic

rather

than

competitive

industries.

9.

A

Stackelberg

leader

will

necessarily

make

at

least

as

much

profit

as

he

would

if

he

acted

as

a

Cournot

oligopolist.

10.

Dominant

strategy

equilibrium

is

a

set

of

choices

such

that

each

player's

choices

are

optimal

regardless

of

what

the

other

players

choose.

II

Fill

in

the

blanks

for

the

following

questions:（2points*10）

(1)

Your

budget

constraint

for

the

two

goods

A

and

B

is

12A+

4B

=

I

where

I

is

your

income.

You

are

currently

consuming

more

than

45

units

of

B.

In

order

to

get

5

more

units

of

A,

how

many

units

of

B

would

you

have

to

give

up?

___________

(2)

Matt's

utility

function

is

.

The

price

of

x

is

1,

the

price

of

y

is

4,

and

the

price

of

z

is

7.

Matt's

income

is

8.

How

many

units

of

x

does

Matt

demand?

__________

(3)

Daily

demand

for

gasoline

at

Billy-Bob's

Mobile

Station

is

described

by

where

Q

are

gallons

of

gasoline

sold

and

p

is

the

price

in

dollars.

Billy-Bob's

supply

is

.

Suppose

the

state

government

places

a

tax

of

20

cents

on

every

gallon

of

gasoline

sold.

What

is

the

deadweight

loss

resulting

from

this

tax?

______________

(4)

The

marginal

cost

curve

of

a

firm

is

MC

=

6y.

Total

variable

costs

to

produce

8

units

of

outputs

are____________

(5)

There

are

two

major

producers

of

corncob

pipes

in

the

world,

both

located

in

Herman,

Missouri.

Suppose

that

the

inverse

demand

function

for

corncob

pipes

is

described

by

where

q

is

total

industry

output

and

suppose

that

marginal

costs

are

zero.

What

is

the

Cournot

reaction

function

of

firm

1

to

the

output

q2

of

firm

2?

___________

III

Calculation

(25

points)

(1)

(10points)

Spence

and

Akerlof

are

the

only

two

owner

of

mineral

water

spring

of

equal

quality

in

an

isolated

economy.

It

costs

Spence

$2

per

gallon

to

get

his

water

bottled

and

costs

Akerlof

$6

per

gallon.

The

inverse

demand

curve

for

mineral

water

is

P

=

100

-

Q

/

6

,

where

P

is

the

price

per

gallon

and

Q

is

the

number

of

gallon

sold.

Determine

the

Cournot

duopoly

equilibrium.

(2)

John

Henry,

an

avid

gardener,

has

found

that

the

number

of

happy

plants,

h,

depends

on

the

amount

of

light,

l,

and

water,

w.

The

production

function

is

as

follows:

h

=

min

{l,

2w}.

a.

Suppose

John

wants

to

produce

4

happy

plants,

what

are

the

minimum

amounts

of

light

and

water

required?

(10points)

b.

If

each

unit

of

light

costs

w1,

and

each

unit

of

water

costs

w

2,

derive

John’s

cost

function

c

(w1,

w2,

h).

(15points)

IV

Graphing

and

Analysis

(35

points)

(1)

In

the

two-commodity

case,

derive

the

price

offer

curve

if

the

two

goods

are

perfect

complements

for

the

consumer.

(10points)

(2)

Graph

to

present

roughly

the

Heckscher-Ohlin

theory

on

international

trade,

showing

how

trade

leads

to

production

specialization

and

to

welfare

improvements.(10

points)

(3)Suppose

individuals

derive

utility

from

two

goods,

housing

and

all

other

consumption.

a.

Graph

to

show

that

if

the

government

requires

individuals

to

buy

more

housing

than

they

would

freely

choose

(say,

by

setting

minimum

housing

standards),

such

a

policy

may

reduce

utility.

(10

points)

b.

Could

you

imagine

such

a

situation?

(2

points)

c.

Which

group

would

you

expect

to

suffer

the

greatest

losses

of

utility

from

such

a

policy?

(3

points)

I

True

or

false.（2points*10）

1.

A

consumer’s

preference

is

directly

related

to

his

income

and

prices

of

goods.

2.

The

relation

“strictly

preferred

to”

satisfies

completeness,

reflexivity

and

transitivity.

3.

A

consumer

has

a

von

Neumann-Morgenstern

utility

function

of

the

form

U(cA,cB,pA,pB)=pAv(cA)+pBv(cB)

where

pA

and

pB

are

the

probabilities

of

events

A

and

B

where

cA

and

cB

are

consumptions

contingent

on

events

A

and

B

respectively.

This

consumer

must

be

a

risk

lover

if

v

is

an

increasing

function.

4.

Suppose

a

consumer

has

strictly

convex

preferences

and

her

Engel

curve

for

a

good

is

a

vertical

line

for

some

range

of

income.

In

that

same

income

range,

her

demand

curve

for

the

good

slopes

down.

5.

If

the

supply

is

perfectly

elastic,

then

an

upward

shift

of

the

demand

curve

will

lead

to

a

higher

price

and

quantity

in

equilibrium.

6.

If

a

competitive

firm

uses

two

inputs

and

it

has

the

production

function

F(x1;x2)

=

x11/2+x21/2

,

then

its

marginal

cost

curve

is

horizontal.

7.

A

general

has

the

two

possible

pure

strategies,

sending

all

of

his

troops

by

land

or

all

of

his

troops

by

sea.

An

example

of

a

mixed

strategy

is

where

he

sends

1/4

of

his

troops

by

land

and

3/4

of

his

troops

by

sea.

8.

If

two

people

have

identical

homothetic

preferences

and

if

their

indifference

curves

have

diminishing

marginal

rate

of

substitution,

then

in

an

Edgeworth

box,

the

locus

of

Pareto

optimal

allocations

between

them

is

a

diagonal

straight

line.

9.

When

there

is

production,

a

competitive

equilibrium

is

not

Pareto

optimal

unless

there

are

increasing

returns

to

scale.

10.A

firm

produces

one

input

with

one

output

and

has

decreasing

returns

to

scale.

The

price

that

it

pays

per

unit

of

input

and

the

price

it

gets

per

unit

of

output

are

independent

of

the

amount

that

this

firm

buys

or

sells.

If

the

government

taxes

its

net

profits

at

some

percentage

rate

and

subsidizes

its

inputs

at

the

same

percentage

rate,

the

firm's

profit

maximizing

output

will

not

change.

II

Fill

in

the

blanks

for

the

following

questions:（2points*10）

11.If

good

1

is

measured

on

the

horizontal

axis

and

good

2

is

measured

on

the

vertical

axis,

and

if

the

price

of

good

1

is

p1

and

the

price

of

good

2

is

p2;

then

the

slope

of

the

budget

line

is______________.

12.Manuel

consumes

only

apples

and

bananas.

He

prefers

more

apples

to

less,

but

he

gets

tired

of

bananas.

If

he

consumes

fewer

than

17

bananas

per

week,

he

thinks

that

one

banana

is

a

perfect

substitute

for

one

apple.

But

you

would

have

to

pay

him

one

apple

for

each

banana

beyond

17

that

he

consumes.

The

indifference

curve

that

passes

through

the

consumption

bundle

with

25

apples

and

26

bananas

also

passes

through

the

bundle

with

A

apples

and

11

bananas,

where

A

equals____________.

13.Rabelaisian

Restaurants

has

a

monopoly

in

the

town

of

Upper

Glutton.

Its

production

function

is

where

L

is

the

amount

of

labor

it

uses

and

Q

is

the

number

of

meals

produced.

Rabelaisian

Restaurants

finds

that

in

order

to

hire

L

units

of

labor,

it

must

pay

a

wage

of

per

unit

of

labor.

The

demand

curve

for

meals

at

Rabelaisian

Restaurants

is

given

by

.

The

profit

maximizing

output

for

Rabelaisian

Restaurants

is______________.

14.An

airline

has

exclusive

landing

rights

at

the

local

airport.

The

airline

flies

one

flight

per

day

to

New

York

with

a

plane

that

has

a

seating

capacity

of

100.

The

cost

of

flying

the

plane

per

day

is

$(4,000

+10q)

where

q

is

the

number

of

passengers.

The

number

of

flights

to

New

York

demanded

is

.

If

the

airline

maximizes

its

monopoly

profits,

the

difference

between

the

marginal

cost

of

flying

an

extra

passenger

and

the

amount

the

marginal

passenger

is

willing

to

pay

to

y

to

New

York

is_____________.

15.Socrates

owns

just

one

ship.

The

ship

is

worth

$200

million

dollars.

If

the

ship

sinks,

Socrates

loses

$200

million.

The

probability

that

it

will

sink

is

.02.

Socrates'

total

wealth,

including

the

value

of

the

ship

is

$225

million.

He

is

an

expected

utility

maximizer

with

von

Neuman

Morgenstern

utility

U(W)

equal

to

the

square

root

of

W.

What

is

the

maximum

amount

that

Socrates

would

be

willing

to

pay

in

order

to

be

fully

insured

against

the

risk

of

losing

his

ship?_____________

III

Calculation

(25

points)

1.

Derive

the

basic

equation

for

choice

of

consumption.(10

points)

2.

(15

points)

D&P,

a

computer

company,

monopolizes

the

domestic

market

which

inverse

demand

curve

is

pd

=

30

000－20

qd

.

D&P

sells

computers

also

to

foreign

market

at

constant

price

pf

=

20

000.

D&P’s

cost

is

C

=

20

020

124

+

10

000

Q

+

5

Q2

.

3-1

If

D&P

is

maximizing

its

profit,

how

many

computers

it

would

sell

in

each

market

and

at

what

price?

Provide

also

the

corresponding

price

elasticities

of

demand.

3-2

Graph

to

show

your

price-quantity

solutions.

IV

Graphing

and

Analysis

(35

points)

1.

(10

points)

Suppose

that

airlines

fares

are

reduced

by

50%

after

one

flies

25

000

miles

a

year.

Graph

to

show

that

a

typical

flyer-customer

with

well-behaved

preferences

will

not

choose

to

fly

exactly

25

000

miles.

(

Graphing

is

enough.)

2.

Draw

a

typical

Edgeworth

Box

of

pure

exchange

showing

also

a

disequilibrium

budget

line.

Tell

which

good

is

too

cheap

in

the

case.

Then

draw

another

Edgeworth

Box

to

show

very

clearly

in

the

box

how

to

determine

the

final

equilibrium.

(10

points)

3.

Draw

to

show

a

(8

points)

How

does

a

change

in

the

price

of

a

good

shift

the

Income

Expansion

Path;

b

(7

points)

How

does

a

change

in

income

shift

the

Price

Offer

Curve.

I

True

or

false.（2points*10）

1.

Richard

has

utility

function

U(x,y)

=

x

+2y.

If

the

price

of

x

is

1

and

the

price

of

y

is

1/2;

then

Richard

must

consume

equal

amounts

of

both

goods

in

order

to

maximize

his

utility.

2.

A

consumer’s

utility

function

is

U(x1,

x2)

=

min{x1,

2x2}.

If

Good

2

has

a

price

of

zero,

the

consumer

will

always

prefer

more

of

Good

2

to

less.

3.

A

consumer’s

utility

function

is

U(x

,y)=min{x

,2y

}.

If

the

price

of

good

x

is

zero

and

the

price

of

good

y

is

p,

then

the

consumer's

demand

function

for

good

y

is

m/2p.

4.

If

a

person

is

a

net

supplier

of

a

normal

good

and

its

price

increases

while

all

other

prices

stay

the

same,

then

his

demand

for

the

good

must

decrease.

5.

Market

demand

curve

is

simply

the

horizontal

summation

of

individual

demand

curves.

6.

The

economist's

distinction

between

long

and

short

run

captures

the

idea

that

quantities

of

some

factor

inputs

can

be

varied

in

the

short

run

but

not

in

the

long

run.

7.

A

firm

uses

a

single

variable

input

x

to

produce

outputs

according

to

the

production

function

f

(x)

=

300x-5x2.This

firm

has

fixed

costs

of

$300.

This

firm's

short

run

marginal

cost

curve

lies

below

its

short

run

average

variable

cost

curve

for

all

positive

values

of

x.

8.

Third

degree

price

discrimination

occurs

when

a

monopolist

sells

output

to

different

people

at

different

prices,

but

every

unit

that

an

individual

buys

costs

the

same

amount.

9.

In

the

Bertrand

model

of

duopoly,

each

firm

sets

its

price,

believing

that

the

other's

price

will

not

change.

When

both

firms

have

identical

production

functions

and

produce

with

constant

returns

to

scale,

the

Bertrand

equilibrium

price

is

equal

to

marginal

cost.

10.

While

game

theory

predicts

non-cooperative

behavior

for

a

single

play

of

prisoners'

dilemma,

it

would

predict

cooperative

tit-for-tat

behavior

if

the

same

people

play

prisoners'

dilemma

together

for,

say,

20

rounds.

II

Fill

in

the

blanks

for

the

following

questions（2points*10）:

11.

Charlie's

utility

function

is

.

If

Charlie's

income

were

40,

the

price

of

apples

were

3

and

the

price

of

bananas

were

7,

how

many

apples

would

there

be

in

the

best

bundle

that

Charlie

could

afford?

_____________

12.

In

Problem

12.9,

Billy

has

a

von

Neumann-Morgenstern

utility

function

.

If

Billy

is

not

injured

this

season,

he

will

receive

an

income

of

4

million

dollars.

If

he

is

injured,

his

income

will

be

only

$10,000.

The

probability

that

he

will

be

injured

is

0.1

and

the

probability

that

he

will

not

be

injured

is

0.9.

His

expected

utility

is____________.

13.

Suppose

that

Dent

Carr's

long

run

total

cost

of

repairing

s

cars

per

week

is

.If

the

price

he

receives

for

repairing

a

car

is

16,

then

in

the

long

run,

how

many

cars

will

he

fix

per

week

if

he

maximizes

profits?________________

14.

A

situation

where

everyone

is

playing

a

dominant

strategy

must

be

a

______________equilibrium.

15.

A

firm

has

the

long

run

cost

function

.

In

the

long

run,

it

will

supply

a

positive

amount

of

output,

so

long

as

the

price

is

greater

than_____________.

III.

Calculation

(25

points)

1.

A

monopolist

can

sell

outputs

Q1

and

Q2

in

two

markets

that

are

effectively

isolated

from

one

another.

His

cost

function

is

C

=

1988

+

29Q

+

Q2

/

40,

where

Q

=

Q1

+

Q2

.

The

demand

in

the

two

markets

are

given

by

Q1

=

480

-

4

P1

and

Q2

=

200

-

2

P2

respectively.

a.

How

much

does

he

sell

in

each

market?

Compare

the

prices

and

the

price

elasticities

of

demand

in

the

two

markets;

(10

points)

b.

If

the

market