1. A consumer has the utility function U(X, Y) = (X + 2)(Y + 4).  Her income is $100, the price of X is $4, and the price of Y is $5.

1. In order to maximize utility subject to her budget constraint, how many units of X and Y will our consumer choose to purchase? Sketch a budget line – indifference curve diagram illustrating this optimum.  Label this optimum A.

2. Suppose the price of X increases to $8, while income and the price of Y remain unchanged.  How many units of X and Y will our consumer now choose to purchase? Add this second budget line and optimum to your diagram.  Label this optimum B.

3. The movement from point A to B on your diagram is the Total Effect of the price change.

In words, how would you decompose (in the Slutsky sense) this total change into a Substitution Effect and an Income Effect?

Do that.  Add the compensated budget line to your diagram and label the associated optimum C.  In terms of the points on your diagram, the substitution effect of the increase in the price of X is the movement from point ______ to _______, and the income effect is the movement from point _________ to __________.

4. Is X a normal or inferior good?  How do you know?

Is Y a normal or inferior good?  How do you know?

Might either X or Y be a Giffen good?  How do you know?

Answer rating: 100% (QA)

To maximize utility subject to the budget constraint we need to find the point on the budget line where the consumers indifference curve is tangent This occurs at the intersection of the highest possi... View the full answer