7 Dan is deciding which country to settle in He has utility

7. Dan is deciding which country to settle in. He has utility over two goods u(x:y) = 3x + y. He is considering three countries: UK, United States, and Australia. Prices and his potential income vary depending upon the countries. For Australia, (px; Py; m)11;10). For the USA, (pxi Py; m) (5: 2:30). For the UK, (??.py:m)-(2:5:30). What are Dan\'s preferences? (a) USA > Australia > UK (b) UK > Australia > USA (c) Australia > USA UK (d) USA UKAustralia (e) None of the above

Solution

a)Dan\'s utility over two goods=

U(x,y)=3x+y

MRS=3/1=3

He is considering three countries Australia, USA, UK and prices and income depend on the countries

Australia(p_x,p_y,m)=(1,1,10)

budget line is given by 1x+1y=10

or x+y=10

In this case p1/p2=1/1=1

MRS>p1/p2 so daniel will consume only good 1 in australia

x+y=10

x+0=10

x=10

U(x,y)=3*10=30

USA=(5,2,30)

budget line is given by 5x+3y=30

5x+3(0)=30

5x=30

x=6

Utility= 3*6=18

UK=(2,5,30)

2x+5y=30

2x+5(0)=30

x=15

Utility=3(15)=45

UK>AUSTRALIA>USA so the correct option is b.

b) Utility of Valentina is given by

U(x,y)=min[2x.y]

budget line remains the same.

In australia the budget line is x+y=10

2x=y

substitute this value in budget line

2x+2x=10

4x=10

x=2.5

y=2*2.5=5

Utility=min[2.5,5]=2.5

In USA the budget line is given by

5x+2y=30

2x=y

5x+2(2x)=30

5x+4x=30

9x=30

x=30/9=3.34

y=2x=2*(3.34)=6.67

utility =min(3.34,6.67)=3.34

In UK the budget line is given by

2x+5y=30

2x=y

2x+5(2x)=30

2x+10x=30

12x=30

x=30/12=2.5

y=2x=2*2.5=5

utility= min[2.5,5]=2.5

USA>UK=Australia

e (none of the above)