Mr. Leontief always drinks each cup of coffee (good x,) with two spoons of sugar (good x,), and everytime he drinks a cup of coffee, he gets 2 units of happiness. Therefore, his preferences for the two goods can be represented by the utility function u(x,, x,) = min {2x,,x}. Suppose that Mr. Leontief s income (m)is 100 dollars, the price per cup of coffeeis 10 dollars and the price per spoon of sugar is 7.5 dollars. (a) (5 points) What is his optimal consumption plan? (b) (5 points) Suppose that, due to new import taxes, the prices go up to 15 dollars and 17.5 dollar, respectively. Find his new optimal choice. How much will he be paying in taxes? (c) (5 points) Suppose prices go back to the initial levels (10 dollars and 7.5 dollar, respectively), but that Mr. Leontief's income is 150 dollars (d) (5 points) Derive his demand functions for cups of coffee and spoons of sugar. Use m for income, pi and p, for prices of coffee and sugar, respectively. Are the goods normal or inferior, ordinary or Giffen, substitutes or complements?