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?

1.  x2=9/2, x1=11/4

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

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

answer; experimentation;