Suppose a farmer has a utility function U(Y ) = ln Y . He has a 50% chance of having a normal season and a 50% chance of having an exceptionally wet season. If the season is normal, the wheat crop yields $28,000 and the corn crop yields $19,000. If the season is exceptionally wet, the wheat crop yields $10,000 and corn $15,000.

a) If the farmer has to choose one of these two crops, which would he choose? b) If he can plant wheat on half of his field and corn on the other half, would he prefer this option? would he prefer this option? c) What is the optimal proportion of wheat that the farmer should plant if he can choose how much to diversify his crop between wheat and corn?