Calculator
Select a method, enter values, and calculate the equilibrium point. The form stays in one main section, while inputs adapt to screen size.
Example Data Table
| Mode | Example Inputs | Expected Output | Meaning |
|---|---|---|---|
| Two lines | y = 2x + 1 and y = -x + 7 | (x, y) = (2, 5) | The two lines intersect at one point. |
| Two equations | 2x + y = 11 and x - y = 1 | (x, y) = (4, 3) | The simultaneous solution satisfies both equations. |
| Demand and supply | P = 20 - 2Q and P = 4 + Q | Q* = 5.3333, P* = 9.3333 | Quantity and price balance demand with supply. |
Formula Used
1) Two lines in slope-intercept form
For y = m₁x + b₁ and y = m₂x + b₂:
x* = (b₂ - b₁) / (m₁ - m₂)
y* = m₁x* + b₁
2) Two equations in standard form
For a₁x + b₁y = c₁ and a₂x + b₂y = c₂:
Determinant = a₁b₂ - a₂b₁
x* = (c₁b₂ - c₂b₁) / Determinant
y* = (a₁c₂ - a₂c₁) / Determinant
3) Demand and supply equilibrium
For demand P = a - bQ and supply P = c + dQ:
Q* = (a - c) / (b + d)
P* = a - bQ* = c + dQ*
A unique equilibrium exists when the relevant denominator or determinant is not zero. Otherwise, the model may return no unique point or infinitely many points.
How to Use This Calculator
- Select the equilibrium method that matches your problem.
- Enter the coefficients, slopes, intercepts, or market parameters.
- Choose decimal precision and a graph span for visualization.
- Click Calculate Equilibrium to generate the point, checks, and graph.
- Review the result table, interpretation, and plotted equilibrium marker.
- Use the CSV or PDF buttons to export the computed summary.
FAQs
1. What is an equilibrium point?
An equilibrium point is a value pair where two mathematical relationships balance each other. In graphs, it is usually the intersection where both equations are true at the same time.
2. When does the calculator show no unique equilibrium?
That happens when lines are parallel, equations are inconsistent, or the demand-supply denominator becomes zero. In those cases, the system does not produce one exact crossing point.
3. What does the determinant tell me?
The determinant measures whether a two-equation system has one exact solution. A nonzero determinant means a unique equilibrium exists. A zero determinant signals dependence or inconsistency.
4. Can I use decimals and negative values?
Yes. The calculator accepts decimals, fractions entered as decimals, and negative numbers. That makes it useful for algebra, analytic geometry, and theoretical market modeling.
5. Which mode should I choose?
Use the line mode when equations are written as y = mx + b. Use standard form for ax + by = c. Use market mode for quantity-price demand and supply problems.
6. Why are surplus and elasticity shown only in market mode?
Those measures belong to economic equilibrium analysis. They describe how buyers, sellers, and responsiveness behave around the quantity-price intersection, not general line or equation intersections.
7. How is the graph range chosen?
The graph centers around the solution when available and uses the span value you enter. This helps you zoom in or out without changing the mathematical result.
8. What do the CSV and PDF downloads include?
Both downloads contain the result summary table. They are useful for reports, assignments, audit trails, and quick sharing of computed equilibrium outputs.