Suppose two individuals (Smith and Jones) each have 10 hours

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?