1. For each of following utility functions

a) U(x,y) = xy

b) U(x,y)= x + 2y

c) U(x,y)= min[x,3y]

d) U(x,y) = 2xy - 5

e) U(x,y) = ln(x) + ln(y)

f) U(x,y) = x0.5 + y

g) U(x,y)= max[x,3y]

i. Graph the indifference curve through the bundle (9,2). *

ii. Find one other bundle on the indifference curve through (9,2).

iii. Find the formula for the Marginal Rate of Substitution (if possible)

iv. Find the value of the MRS at (9,2)

*For some of these, you can try using a graphing calculator such as Desmos (online). This will give you an idea of the shape of indifference curves for these particular utility functions. If you do use a graphing calculator, then try indifference curves through other bundles not on the indifference curve to see how the curves change when the bundles change.