U=min{X, 2Y}and the price of X is 1, the price of Y is 1 and income is $15.

1. (7 points) Find the utility maximizing combination of X and Y.
2. (7 points) If the price of X increases to 2, find the new utility maximizing combination of X and Y after the price change.
3. (6 points) Calculate the income effect and the substitution effect of the increase in price of X from $1 to $2 in terms of units of X bought.
4. (5 points) Derive the demand function for Y at original prices and income.