Questions 1-4 follow a common storyline.
In the 1800s, two isolated farmers on the south side of the Brazos raise steers and corn on their land. Every year, Farmer A produces 144 thousand bushels of corn and 16 steers, i.e., $(\omega_c^A, \omega_s^A) = (144, 16)$, while Farmer B produces 64 thousand bushels of corn and 36 steers, i.e., $(\omega_c^B, \omega_s^B) = (64, 36)$. Being isolated, the farmers would like to better their situations by trading among themselves.
For Questions 1-3, we are in 1870, where both farmers have the Cobb-Douglas preferences, $u(c, s) = cs$, where $c$ is thousands of bushels of corn and $s$ is number of steers.
1. Which of the following must be true of a Pareto-efficient split of the aggregate endowment, $\omega_{AGG} = (208, 52)$?
a. Both farmers end up with identical bundles of steers and corn, i.e., $(s^A, c^A) = (s^B, c^B)$.
b. For every steer Farmer A ends up with, he also ends up with 1 thousand bushels of corn, i.e., $c^A/s^A = 1$.
c. For every steer Farmer B ends up with, he also ends up with 4 thousand bushels of corn, i.e., $c^B/s^B = 4$.
d. Farmer B ends up with more corn than Farmer A, i.e., $c^B > c^A$.
e. None of the other options are correct.
