In an isolated peasant village, the only crop is corn. Good harvests alternate with bad harvests. This year the harvest will be 2,000 bushels. Next year it will be 250 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 functionU(c₁,c₂) =c²₁c²₂, wherec₁is consumption this year andc₂is consumption next year.

1)

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.[1]

b.How much will the villagers consume this year?[1]

c.How much will the rats eat?[1]

d.How much will the villagers consume next year?[1]

2) Now assume, that the utility function is:U(c₁,c₂) = min{c₁,c₂}

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.[1]

b.How much will the villagers consume this year?[1]

c.How much will the rats eat?[1]

d.How much will the villagers consume next year?[1]