Problem 1 (Cobb Douglas Utility function) Tony likes nuts 61 and berries (112, and his preferences are described by the following utility function U ($1,332) = $31333. Find the following variables: 1) the optimal fraction (percentage) of income spent on berries; 2) the optimal amount of total cash (dollars) spent on berries; 3) the optimal quantity of nuts consumed; 4) the slope of the indifference curve at the optimal bundle for the following values of parameters: a) a =4,b=8,p1 = 5,192 = 10,m= 60 b) a = (1/30,!) = (1/3),p1 = 4,132 = 1m = 12 C) a = (1/2)1b : (3/2)3p1 = 5:192 = 1,77} = 20 Hint: Instead of calculating optimal choices using "two secrets of happiness", take advantage of the demand formulas for Cobb Douglas utility that we derived in the class