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3. In an isolated mountain village, the only crop is corn. Good harvests al ternate with bad harvests. This year the harvest will be 1,000 bushels. bushels. There is Corn can be stored from one year to the next, but rats will eat 25% of what is stored in a year. The villagers have Cobb-Douglas utility functions U(c1, C2) c1 c2, where C1 1s consumption this, and сг is consumption next year(a) Draw a budget line, showing consumption possibilities for the vil lage, with this years consumption on the horizontal axis and next years consumption on the vertical axis. Put numbers on your graph to show where the budget line hits the axes. (b) How much corn will the villagers consume this year? How much will the rats eat? How much corn will the villagers consume next year? (c) Suppose that a road is built to the village so that now the village is able to trade with the rest of the world. Now the villagers are able to buy and sell corn at the world price, which is $1 per bushel. They are also able to borrow and lend money at an interest rate of 10%. On your graph, draw the new budget line for the villagers. Solve for the amount they would now consume in the first period and the second period. (d) Suppose that all is as in the last part of the question except that there is a transportation cost of S.10 per bushel for every bushel of grain hauled into or out of the village. On your graph, draw the budget line for the village under these circumstances.

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