Microeconomic Theory 11th Edition by Walter Nicholson,Christopher Snyder

Exercise 2

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 utility function is given by

where as Jones' is given by

The individuals do not care whether they produce x or y, and the production function for each good is given by
x = 2l and y = 3l,
where l is the total labor devoted to production of each good.
a. What must the price ratio, p x /p y , be?
b. Given this price ratio, how much x and y will Smith and Jones demand? Hint: Set the wage equal to 1 here.
c. How should labor be allocated between x and y to satisfy the demand calculated in part (b)?