Question

In an isolated village (no trade with the outside world) in which good harvests alternate with bad harvests from year to year, the only crop is wheat. This year the harvest will be 2,000 tons and next year it will be 300 tons. Wheat can be stored, but rats will eat 20% of what is stored in a year. The villagers have the Cobb-Douglas utility function ?(?#, ?$) = ?#?$, where ?# is consumption this year and ?$ is consumption next year.

a. (7 points) What is the budget constraint? Draw the budget constraint on a graph 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. (8 points) How much will the villagers consume in each year? How much wheat will the rats eat? (Hint: You can solve this problem using the Lagrangian function.)

Answer 1