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