Suppose two individuals (Smith and Jones) each have 10 hours of labor to devote to producing either ice cream (X) or chicken soup (Y). Smith’s demand for X and Y is given by

XS = 0:3/S /PX

YS = 0:7/S /PY

Whereas Jones’s demands are given by

XJ = 0:5/J /PX

YJ = 0:5/J /PY

Where IS and IJ represent Smith’s and Jones’s incomes, respectively (which come only from working). The individuals do not care whether they produce X or Y and the production function for each good is given by

X = 2L

Y = 3L

Where L is the total labor devoted to production of each good. Using this information, answer the following:

a. What must the price ratio, PX/PY be?

b. Given this price ratio, how much X and Y will Smith and Jones demand?

c. How should labor be allocated between X and Y to satisfy the demand calculated in part b?