Suppose there exists a consumer with a Cobb-Douglas utility function. U = x1 to the power a x2 to the power (1a) Recall that in this case, the demand equations are given by the following: x1 = a m/p1 x2 = (1 a) m/p2 Suppose the value of a is a = 4 5 . Suppose that this consumer has an income of $1,000. Suppose that the price of good 1 is p1 = $5 and the price of good 2 is p2 = $10. a) Calculate the amount demanded of good 1 at this initial equilibrium. b) Suppose the price of good 1 decreased to p1 = $4. What will be the new amount demanded of good 1 at this new equilibrium? c) This change in consumption of good 1 can be broken down into a substitution effect and an income effect. Calculate these two effects. d) Is good 1 a normal good, inferior good, or Giffen good? How do you know?