Chapter 6: Concise

Chapter 6: Consumer Choice Theory

Focuses on the relationship between utility and consumption.
Total Utility (TU) = Happiness = Satisfaction.
Marginal Utility (MU) = ( \Delta TU / \Delta Q ).
TU increases at a decreasing rate; MU diminishes with additional units consumed.
- Example: 1st slice of pizza > 2nd slice > 3rd slice (Diminishing MU).

Example with Calculus:
- TU Function: ( U(x) = x^{1/2} )
- MU: ( U'(x) = \frac{1}{2} x^{-1/2} > 0 ) (TU increasing and concave)
- ( U''(x) = -\frac{1}{4} x^{-3/2} < 0 ) (confirming diminishing MU).
- ( U'''(x) = \frac{3}{8} x^{-5/2} > 0 ) (demonstrating MU is decreasing and convex).

Involves two goods (x, y) with a budget constraint:
- Budget Constraint: ( Px x + Py y \leq M )
- Budget Line: ( Px x + Py y = M )
Marginal Utilities: ( MUx = \frac{\partial U(x, y)}{\partial x}, MUy = \frac{\partial U(x,y)}{\partial y} )
Consumer should maximize utility based on marginal utility to price ratio.
Condition for equilibrium:
- If ( \frac{MUx}{Px} > \frac{MUy}{Py} ) ➔ Consume more of X.
- If ( \frac{MUx}{Px} < \frac{MUy}{Py} ) ➔ Consume more of Y.
- Equilibrium when ( \frac{MUx}{Px} = \frac{MUy}{Py} ).

Utility Function: ( U(x, y) = xy )
Budget Line: ( x + 3y = 12 )
Marginal Utilities: ( MUx = y ), ( MUy = x )
Equilibrium Condition: ( \frac{MUx}{Px} = \frac{MUy}{Py} ) implies ( y = \frac{x}{3} )
Solving yields:
- Developed from budget line: ( x + 3y = 12 ) gives ( y = 2, x = 6 ).

General form: ( Px x + Py y = M ) leads to demand functions:
- ( x = \frac{M}{2Px} ), ( y = \frac{M}{2Py} )
Consumer equilibrium lies at budget line midpoint.
Discussing Income Effect and Substitution Effect postponed to later sections.