(Solution) 11/23/2014 Concourse | Advanced Corporate Finance W EBSTER UNIVERSITY W EBSTER GROVES, MO GEORGE HERBERT W ALKER SCHOOL OF BUSINESS &... | Snapessays.com


(Solution) 11/23/2014 Concourse | Advanced Corporate Finance W EBSTER UNIVERSITY W EBSTER GROVES, MO GEORGE HERBERT W ALKER SCHOOL OF BUSINESS &...


Need help with an assignment.Homework 1 - Economics 312

 

Due Date: January 27, 2015

 

Varian: Ch. 2 (Review Questions) - 1, 2, 3, 6; Ch. 3 (Review Questions) - 2, 3, 5.

 

I. Find the MRS for the following utility functions at the point (

 

x,y

 

) = (1

 

,

 

2).

 

i.

 

u

 

(

 

x,y

 

) =

 

x

 

·

 

y

 

.

 

ii.

 

u

 

(

 

x,y

 

) =

 

?

 

x

 

·

 

y

 

.

 

iii.

 

u

 

(

 

x,y

 

) =

 

x

 

2

 

·

 

y

 

.

 

iv.

 

u

 

(

 

x,y

 

) =

 

x

 

+

 

y

 

.

 

v.

 

u

 

(

 

x,y

 

) = min

 

{

 

x,y

 

}

 

.

 

II. Let

 

u

 

(

 

x,y

 

) =

 

x

 

1

 

/

 

3

 

y

 

2

 

/

 

3

 

and let

 

I

 

= 100,

 

p

 

x

 

=

 

p

 

y

 

= 1. Explicitly write out the

 

FOC (?rst-order condition) for the consumer’s UMP (utility maximization prob-

 

lem). Now, compute the consumer’s demand function.

 

III. Let

 

u

 

(

 

x,y

 

) = 5

 

x

 

+4

 

y

 

and let

 

I

 

denote income and

 

p

 

x

 

,p

 

y

 

the prices of the goods.

 

Compute the demand functions for goods

 

x

 

and

 

y

 

when

 

I

 

= 100 and

 

p

 

x

 

= 1 =

 

p

 

y

 

.

 

IV. Assume that every citizen of country

 

X

 

has the utility function of problem

 

(III) above. Say that

 

x

 

denotes cigarettes and

 

y

 

denotes alcohol. The government

 

of country

 

X

 

receives revenue from alcohol and cigarrete purchases but wants to

 

curb alcohol consumption without decreasing its total revenue. Assuming that the

 

government can levy a per unit tax on alcohol consumption, and taking initial prices

 

and income to be

 

p

 

x

 

= 1

 

,p

 

y

 

= 1

 

/

 

2

 

,I

 

= 100, what is the minimal tax rate that will

 

reduce alcohol consumption by at least 10 percent (without decreasing total rev-

 

enue)? Make the convention that whenever prices are such that the consumer is

 

indi?erent between alcohol and cigarettes, he chooses to consume cigarettes.

 

1

 

1

 

To make sense of this, think of the government as playing the role of “tiebreaker” in the case the

 

consumer is himself indi?erent between the two choices. Since the government wants to decrease

 

alcohol consumption, ties will always be broken in the direction of greater cigarette consumption.

 

1

 


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