Larry consumes only two goods daily, x and y.

Larry consumes only two goods daily, x and y. His preferences can be represented by the utility function 

U(x,y) = x−x2/2 + y

Larry's daily allowance, to be spent on x and y is m, good y is a numeraire with a price of 1, and the price of x is always p, where 0<p≤1.

Hint. For yourselves, write down the demand functions for x and y. Then write utility as a function of x*(p,m) and y*(p,m).

1c. If the price of x rises to $1, how much x would Larry buy? [round to fourth decimal place if necessary]