In an Isolated Peasant Village, the Only Crop Is Corn

Essay

In an isolated peasant village, the only crop is corn. Good harvests alternate with bad harvests. This year the harvest will be 1,000 bushels. Next year it will be 150 bushels. There is no trade with the outside world. Corn can be stored, but rats will eat 25% of what is stored in a year. The villagers have the Cobb-Douglas utility function U(c₁, c₂) = c₁c₂, where c₁ is consumption this year and c₂ is consumption next year.
a. Draw a budget line for the village with this year's consumption on the horizontal axis and next year's consumption on the vertical axis. On your graph show the quantities at which the budget line intercepts the vertical and horizontal axes.
b. How much will the villagers consume this year?
c. How much will the rats eat?
d. How much will the villagers consume next year?