Answers to First Wakeup Quiz

Ques 1.   False.  Good 1 and Good 2 are perfect substitutes, but Good 1 is costs $1 per unit and Good 2 costs $2.  Asa will  get the most utility with his $100 if he purchases 150 units of good 1 and no good 2.    See pages 78-79 of your text for further discussion.

Ques 2.  Lil chooses a bundle where her indifference curve is tangent to her budget line.  This is the case where the ratio  of the marginal utilities equals the ratio of the prices.  That is, MU1/MU2=p1/p2 .With utility function U(x1,x2)=x12x2 ,  Lil's marginal utility of good 1 is   found by taking the derivatives with respect to x1, while holding x2 constant.  Thus we have MU1=2x1x2.  Her marginal utility of good 2 is found by taking the derivative with respect to x2, holding x1 constant.  This is MU2=x12.  Thus we have
MU1/MU2 =2x1x2/x12     And making a simple cancellation, we see that  2x1x2/x12 =2x2/x1
Since the prices are p1=3 and p2=4. the answer must be  2x1x2/x12=2x2/x1=3/4.