Chapter 4- Utility

Question 1

Utility function

Answer 1

A way of assigning a number to every possible consumption bundle such that more preferred bundles get assigned larger numbers than Less preferred bundles

(X1,X2)>(Y1, Y2) iff u(X1, X2) > u(Y1, Y2)

Question 2

Ordinal utility

Answer 2

The only property of utility that is important is how it orders the bundles of goods (not he absolute number assigned to a bundle)

Question 3

Monotonic transformation

Answer 3

Is a way of transforming one set of numbers in a way that preserves the order of the numbers

Question 4

Utility

Answer 4

A way to describe preferences

Question 5

Marginal Utility

Answer 5

How much utility you get from one more unit of x

MUx(x,y)= the partial derivative of U(x,y) with respect to x.

Question 6

Diminishing Marginal Utility

Answer 6

The marginal utility of each unit of x consumed decreases as the amount of x increases
The utility function exhibits diminishing marginal utility for good x iff x⬆️➡️MUx(x,y)⬇️

Question 7

Marginal rate of substitution (MRS)

Answer 7

Formal definition: the slope of the IDC curve tangent at x,y

Informal Definition: if you gave up one unit of good x how many units of good y would you need to stay just as happy as you were before.

MRS= -MUx/MUy

Question 8

Diminishing MRS

Answer 8

The more of x you have (and the less of y) the less you need to be compensated for giving up one unit of x. (IDCs get flatter as you go down them)

Test X⬆️Y⬇️. ➡️ I MRS I ⬇️

Question 9

Linear utility function

Answer 9

Perfect supplements

U(X1,Y1) =ax1 + by1

Will generally demand to consume either all of good 1 or all of good 2

Test MRS> P1/P2 choose good 1
MRS

Question 10

Cobb-Douglas Utility Function

Answer 10

α β
ax1 (x2)

Cobb- Douglass IDCS represent well behaved preferences (strongly monotonic)

Question 11

Leontief utility function

Answer 11

Amin{X1/a, X2/b}

Perfect complements (L Shaped IDCs) optimal point generally at the kink in IDC.