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
0.3 0.7
S U = x y ,
whereas Jones's is given by
0.5 0.5
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 calculated in part (b)?