What doesn't kill me makes me stronger

Transivity

If bundle B > A and C > B, then C > A

Bad’s

Goods you don’t want (ex, garbage. waste), tends to create an IDC with a positive MRS (slope)

Budget Constraint equation

p₁x₁ + p₂x₂ = m

Normal Good

A good that is bought more when income (m) increases

Inferior good

A good that is bought less when income (m) increases

Giffen Good

A good that is brought more when price (p) increases

Ordinary good

A good that is bought less when price (p) increases

Marginal Rate of substitution

Slope of any given point on the indifference curve, how much of good 2 would be given for good 1. Tangent

Steps to to find optimal bundle of a perfect substitute?

1- Find MRS.

2- If MRS > PR, only consume good 1. If MRS < PR, only consume good 2

How to find optimal bundle of a perfect complement?

1. Set ax₁ = bx₂.

2. Plug into budget constraint

How to find optimal bundle of Cobbs Douglas preference?

USE THE SHORTCUT:

x₁* = a/a+b X m/p₁

x₂*= b/b+a X m/p₂

How to find optimal bundle of Quasilinear preference?

1. Find MRS.

2. See if MRS decreases when x₁ increases and x₂ decreases.

3. If MRS diminishes, treat like cobb douglas, set MRS = PR. 4. If MRS increases, find corner solutions, find which good gives max utility when you only buy that one.

General form of perfect substitutes utility function

ax₁ + bx₂

General form of Perfect Complement utility function

min{x₁, x₂}

General Form of CB utility function

x₁ᵃx₂ᵇ

General form of quasilinear function

V(x₁) + x₂

Interior optimum

Optimal bundle just touches the budget line

Monotonicity

More is better

Convex preferences

Averages are preferred to extremes

Concave preferences

Extremes are preferred to the average

Discrete Goods

Goods only available in integer amounts (not fractional)

Perfect Substitutes

Goods who can substitute perfectly for one another, straight curve with a constant MRS. Usually has a corner solution

Perfect Compliments

Consumer values goods only when consumed together in fixed proportions, L shaped graph, always an interior solution

Cobbs Douglas

Monotonic and strictly convex IDC’s, well behaved preferences, usually has diminishing MRS , always has an interior solution

Well behaved preferences

Monotonic and convex

Marginal utility

Also known as Mu₁ or ₂, the amount of utility a given good adds when increased by 1.

Diminishing marginal utility

With a well-behaved IDC, you’re less willing to give up amounts of good 2 for good 1 as you get more of it and vice versa.

Demand function

Finds the consumer’s most preferred affordable bundle

Scale Invariance

Changing the inputs by the same scaling factor does not change the output

MRS

= Mu₁ / Mu₂

When does price ratio equal MRS?

Cobb Douglas

How to check if an equation is concave

if MRS increases as x₁ increases and x₂ decreases

What to do with coupons?

Add the value of the coupon(s) to your income