Suppose two individuals (Smith and Jones) each have 10 hours of labour to devote to producing either ice cream (x) or chicken soup (y). Smith's utility function is given by
S U = x y ,
whereas Jones's is given by
J U = x y .
The individuals do not care whether they produce x or y, and the production function for each good is given by 2 x x = l and 3 y y = l , where x l and y l is the total labour devoted to the production of each good x and y, respectively.
(a) What must the price ratio, / x y p p , be?
(b) If the prevailing wage is 1, given this price ratio, how much x and y will Smith and Jones demand?
(c) How should labour be allocated between x and y to satisfy the demands find outd in part (b)?