Consider a $2-$consumer, $2-$good economy with utility functions

u

$(1)$

$($

x

$)=$

x

$1$

$+100$

$$

$(1$

$$

e

$$

x

$2$

$/$

$10$

$)$

$,$ u

$(2)$

$($

x

$)=110$

$$

$(1$

$$

e

$$

x

$1$

$/$

$10$

$)+$

x

$2$

and endowments

e

$(1)$

$=(40$

$,$

$0)$

$,$e

$(2)$

$=(0$

$,$

$50)$

$.$

Normalize prices so that

p

$=($

P$,$

$1)$

$.$

$1.$ Find each consumer$$s Marshallian demand for each good as a function of

P$.$

$($Check

carefully for corner solutions for

both

goods.$)$