Ann lives on island where she can produce and consume two goods x and y. She is endowed with 120...

Ann lives on island where she can produce and consume two goods x and y. She is endowed with 120 units of labour, L, which she can use to produce either of the goods according to the following production functions:

x=1/2 LXw

y=25(LY)1/2,

where LX and LY are units of labour devoted to production of x and y, respectively. Her utility function is U= (xy)1/2.

a ) What is her production possibility curve?

b) What is her utility maximizing production and consumption of x and y?

c) Suppose her island is on a trade route and she is able to buy and sell x at a price of 5 units of y. Calculate her new utility maximizing production and consumption bundle.