Question: Suppose there exists a consumer with a Cobb-Douglas utility function. U = x a 1x (1a) 2 Recall that in this case, the demand equations

Suppose there exists a consumer with a Cobb-Douglas utility function. U = x a 1x (1−a) 2 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? .

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