Hi,

A student asked for more information on a couple problems in the practice packet (1. question c on pg.21, 2. pg.23 regarding the three indifference curves, 3. pg. 27 part b and c). I'm forwarding my answers, below, just so everyone is on the same page.

1 To be just as well off as before, the consumer has to achieve the same utility as before U* = (X*Y*)^.5 = 15. We need to make sure that, when the consumer is given M, her choices Xc and Yc yield her a utility of 15. Using the approach shown on p20 part d, you can find Xc = (.5M)/25 and Yc = (.5M)/4 and plug these formulas into the equation 15 = (Xc)^.5(Yc)^.5 to solve for M:

15 = M/20

M = 3002 These are perfect complements preferences. Each indifference curve — associated with a particular utility level U — will be L shaped, with the corner at the point where the two terms in the min{} are equal to each other and also equal to U. Picking U = 1, we find X = .5, Y = 1 as the corner point.

1 = 2X —> X = .5

1 = Y —> Y = 1

Scaling up from here to U = 2 and U = 3, we can find the other curves. You can pick different utility levels when making this graph; the important things are labeling axes and marking the coordinates of the corner points.3 Similar to your previous question, we can graph this isoquant by finding the corner point associated with a quantity of q = 30. At this corner point, the two terms in the min{} will be equal to each other and to 30.

30 = 3L —> L = 10

30 = 2K —> K = 15

Best,

Frank