The Consumer's Problem: how to optimize one's utility with a constrained budget. The consumer's problem is a typical maximization problem, in that it has both aims and constraints

• aims: acheiving the highest possible level of satisfaction - shown through indifference curves

• contraints: limited budget, limited time, limited available information - shown through the budget line

Budget Line: a line that consists of all of the possible combinations of x & y that the consumer can just afford, given a fixed income or a particular endowment bundle. (note, this model assumes two goods, for simplicity)

• Equation of the Budget Line:

Px = price of x
Py = price of y
M = income

X = units of x consumed
Y = units of y consumed

• Point A: feasable

• Point B: feasable, uses entire budget
• Point C: unattainable, given current constraint
  
  
• Slope of the Budget Line:
  - measures the relative price of good X in terms of good Y
  - how much of Y you have to give up in order to acquire an additional unit of X
  - usually negative, as consuming more of one good involves the sacrifice of another
  
  
• Significance: The budget line represents the constraint side of the consumer problem.
  

Preferences: refers to the ranking of bundles of goods based on the amount of utility their consumption would yield. Preferences determine whether or not the consumer would choose one bundle of goods over another, based on differences in utility. In dealing with preferences, we must consider one pair of goods, (Xa,Ya), and whether or not it is preferred to another bundle (Xb,Yb).

• Assumptions:
  
  
  • Completeness: Consumers always make up their minds. Either they prefer bundle A to bundle B, they prefer bundle B to bundle A, or they are indifferent between the two.
  • Transitivity: If a consumer prefers A to B, and if the consumer prefers B to C, then he or she prefers bundle A to bundle C. Stated differently, if the consumer is indifferent between both A and B, and if he or she is also indifferent between B and C, then the consumer is indifferent between A and C.
  • Monotonicity: More is better. Consumers prefer more of any quantity to less. (note: this assumption will not hold if one or both goods in the bundle cause disutility)

Indifference Curves: a way to graphically and mathematically represente preferences. Given the form u(x,y) = K, indifference curves are drawn for various levels of K such that points A & B lying on one particular curve yield the same utility. Because all points on an indifference curve represent bundles for which the consumer has the same utility, the consumer is indifferent between these bundles.

Indifference Map: consists of various indifferences curves that show different level curves of a utility function

General Equation for Indifference Curves:

• K = ordinal utility value - the actual number that K corresponds to for each indifference curve doesn't matter - all that matters is the ranking, (is A < B, etc)
  
  

• according to above diagram, A < B < C and thus, bundles that make up the indifference curve u(x,y) = C are more desirable than bundles that make up u(x,y) = A or bundles that make up u(x,y) = B
  
  

• Properties of Indifference Curves:
  
  

  1. Indifference curves cannot have thickness
  2. Distinct indifference curves can never intersect
  3. If more is better, indifference curves must slope downwards

• Slope of the Indifference Curve:
  
  - MRSxy = marginal rate of substitution - the maximum amount of Y you are willing to sacrifice to get an extra unit of X, remaining indifferent or keep the same utility
  - MUx = marginal utility gained from the consumption of X
  - MUy = marginal utility gained from the consumption of Y
  
  

• Diminishing Marginal Returns:
  
  - as X gets bigger, MRSxy dimishes
  - this means essentially, the more X and less Y you have, the less willing you become to substitute X for Y
  

Families of Indifference Curves:

• Perfect Substitutes: indifference curves have same slope everywhere, because MRSxy is constant everywhere - at endpoints, 0 units of X and 4 units of Y yields the same amount of utility as 4 units of X and 0 units of Y

• Perfect Compliments: goods should be consumed in fixed ratios - like milk and cereal - use a min function to create an L shaped curve

• One good is a bad: if a good is a bad, or if it yields negative utility from consumption, in order for the consumer to remain indifferent, he or she must consume more of the positive utility yielding good. Thus, indifference curves are uncharacteristically drawn with positive slopes.

• Satiation: there is a point of satiation, where a specified amount of x and y consumed yields the highest utility possible - the indifference curves spread out around that point in a circular or elliptical fashion, and utility increases as the curves get closer and closer to the satiation point.

Subscribe to our newsletter!  Enter your email address here:

Like our intro movie?  Download the Short Run's screen saver.