Topic 5 - Functions of several variables Flashcards
Utility
Refers to the satisfaction pleasure or benefit a consumer derives from consuming goods and services.
Utility function
This is how utility is represented. Mathematically shows consumer satisfaction.
Ordinal utility
Focuses on ranking rather than measurement e.g. if A=10, B=1000. All we care about is that B>A.
Cardinal utility
Assigns specific values and the different in these can be measured in utils (imaginary unit of satisfaction).
Monotonic transformation
A way of transforming one set of numbers into another that preserves the order of numbers. E.g. multiplying by a positive number. Monotonic transformation always has a positive rate of change.
Level set
u(x1,x2) = x1x2
Set of bundles such that the utility of (x1,x2) equals a constant.
x2=k/x1 where k is a constant.
Each value of K yields a different IC.
Perfect substitutes
u(x1,x2) = ax1 + bx2.
These ICs have a constant slope often -1.
Perfect compliments
u(x1,x2) = min{ax1,bx2}.
b and a the proportions in which goods 1 and 2 are consumed respectively.
Quasilinear preferences
u(x1,x2)=v(x1) + x2.
Curves are vertically “shifted” can be used as they are easy to work with.
Cobb-Douglas indifference curves
u(x1,x2) = x1^c x2^d
can transform to
v(x1,x2) = x1^a x2^1-a
c and d are positive numbers that describe preferences of the consumer.
Marginal utility
Additional satisfaction gained from one additional unit of a good or service.
MU1 = change in U/change in x1.
Law of diminishing marginal Utility
As you consume more units of a good the additional utility from each units tends to decrease.
Marginal rate of substitution
MRS = -MU1/MU2
To find MU?
Differentiate U(x1,x2) with respect to whatever good you are finding the MU for.
