for mapping , see the Indirect Utility Function

def. Utility Function. a utility function maps goods to utility (happiness) that satisfies the assumption of Rational Taste including convexity.

⇒ such that if then

Types of Utility Functions

Let be the allocation bundle to agent . contains items (””) where defines what percentage of that item is allocated to . Then ’s utility can take various forms.

  • def. Additive Utility.
  • def. Cobb-Douglas Utility. where (See the case for two goods)
  • def. Leontief Utility.

Homothetic, Quasilinear, Perfect Substitutes

In addition to the constrains of Rational Taste we can also have these particular tastes that characterize a utility function.

def. Quasilinear Tastes. If a utility function has quasilinear tastes against good , then the function (or a Monotonic Transformation of the function) is linear against , e.g.:


def. Perfect Substitutes. If a utility function means goods and are perfect substitutes, then every indifference curve of the utility function is a linear function, e.g.

Perfect Compliments.

  • e.g. ![[Untitled 6 2.png|Right shoe and left shoe|380]]
  • Formula looks something like:

Indifference Curves

def. Indifference Curve. A set of bundles that an agent with rational taste is indifferent about

  • Indifference curves are horizontal slices of a utility function.
    • i.e. a level field of a scalar field defined by the utility function of two goods—.
    • Indifference curves from the same utility function cannot cross (obviously)
  • North-east side is always better.
    • ∵ monotonic taste—if this is not the case, change the direction of the curve.
  • The convexity assumption causes ICs to bend to the origin
  • Multiple indifference curves form one indifference map =[Utility Function]. Indifference maps are considered the same when 1. the order of the indifference curves is the same 2. MRS at every point for every curve is the same
  • Budget Lines are drawn on the same graph as ICs
  • When tastes are strictly convex (a taste for variety) then:
    • in the Graph

Analyzing Indifference Curve Shapes