Appendix A — Graphing and Algebra Review

A refresher for readers who need to brush up before Chapter 5. This appendix takes about 30–45 minutes.

A.1 Reading graphs

A graph has two axes. The horizontal axis (x-axis) runs left to right. The vertical axis (y-axis) runs bottom to top. Each point on the graph represents a pair of values (x, y).

In economics, price is on the y-axis and quantity is on the x-axis. This is a convention (Marshall chose it in the 1890s) that every economics textbook follows.

A.2 Slopes

The slope of a line = rise / run = Δy / Δx.

  • Positive slope: line goes up from left to right (supply curves)
  • Negative slope: line goes down from left to right (demand curves)
  • Zero slope: horizontal line
  • Undefined slope: vertical line

Example: A demand curve goes through (Q=10, P=$50) and (Q=20, P=$30). Slope = (30−50)/(20−10) = −20/10 = −2. For each additional unit, the price falls by $2.

A.3 Linear equations

A straight line can be written as: y = mx + b (or in economics: P = a − bQ for demand, P = c + dQ for supply).

  • m (or b, d) is the slope
  • b (or a, c) is the y-intercept (where the line crosses the y-axis)

Example: Demand: P = 100 − 2Q. When Q = 0, P = 100 (y-intercept). Slope = −2. When Q = 50, P = 0 (x-intercept).

A.4 Solving for equilibrium

Equilibrium: set demand = supply and solve.

Example: Demand: P = 100 − 2Q. Supply: P = 20 + Q.

Set equal: 100 − 2Q = 20 + Q → 80 = 3Q → Q = 26.67. P = 20 + 26.67 = $46.67.

A.5 Percentages and percent changes

Percent = part / whole × 100. "15 out of 60 = 25%."

Percent change = (new − old) / old × 100. Price goes from $10 to $12: percent change = (12−10)/10 × 100 = 20%.

The midpoint formula (Chapter 6): uses the average of old and new as the denominator. (12−10)/[(10+12)/2] × 100 = 2/11 × 100 = 18.2%.

A.6 Areas of triangles and rectangles

Rectangle area = base × height. Used for: total revenue (P × Q), producer surplus rectangles, tax revenue.

Triangle area = (1/2) × base × height. Used for: consumer surplus, producer surplus, deadweight loss.

A.7 Practice problems

  1. Plot the demand curve P = 80 − 4Q. Find the intercepts.
  2. Plot the supply curve P = 10 + 2Q on the same axes. Find the equilibrium.
  3. If price rises from $25 to $30, compute the percent change using both the simple formula and the midpoint formula.
  4. A triangle has base = 20 units and height = $15. What is the area? (This is a consumer surplus calculation.)

Answers: 1. Y-intercept: P=80 at Q=0. X-intercept: Q=20 at P=0. 2. Set 80−4Q = 10+2Q → Q=11.67, P=$33.33. 3. Simple: 20%. Midpoint: 18.2%. 4. Area = (1/2)(20)(15) = $150.

If you can do all four, you're ready for Chapter 5.