Intermediate Macroeconomics Questions, due on April 29, 3:00pm (UTC+8)

Roots:

Example:

This implies that and .

c) Variable substitution

Let .

The transformed equation is quadratic, and we already have the tools to solve it.

d) Simultaneous linear equations

Example:

Step 1: Express in terms of from one of the equations, e.g., .

Step 2: Insert into

2. Exponents.

· Zero exponent rule

· Power rule

· Negative exponent rule

· Product rule

· Quotient rule

Example: Simplify

3. Logarithms

· Relationship between the natural logarithm and the natural number .

A logarithm with a base is the natural logarithm

· Rules of logarithms

· Product rule

· Quotient rule

· Power rule

· Zero rule

· Identity rule

· Log of exponent rule

· Identity rule

Example: Expand the logarithmic expression:

4. Geometry.

a) Calculating areas

· Triangle

· Rectangle

· Trapezoid

b) Gini coefficient (GC)

Suppose that the richest 50 % of the population earn 80 % of all income.