46.5k views
3 votes
Max has utility function u(x1, x2) = x1(x2 + 1). The price of x1 is $2 and the price of x2 is $1. Income is $10. How much x1 does Max demand? How much x2? If his income doubles and prices stay unchanged, will Max’s demand for both goods double?

User Bing Lu
by
8.0k points

1 Answer

1 vote

Answer:

1. x2=9/2, x1=11/4

2. If his income doubles and prices stay unchanged, his demand for both goods does not double

Step-by-step explanation:

Max has utility function u(x1, x2) = x1(x2 + 1). The price of x1 is $2 and the price of x2 is $1. Income is $10. How much x1 does Max demand? How much x2? If his income doubles and prices stay unchanged, will Max’s demand for both goods double

for ease lets designate x1 as x and x2 as y

max sets (y+1)/x=2

and His budget constraint is 2x + y = 10

solving the the two equations simultaneously

y+1=2x....

2x+y=10

rearrange y-2x=-1

y+2x=10

2y = 9

y=9/2

from equation 2, substitute the value of y into equation 2

y+2x=10

9/2+2x=10

2x=10-9/2

x=11/4

If his income doubles and prices stay unchanged, his demand for both goods does not double

User SupaMario
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.