Equilibrium Price and Quantity Calculator

Market Equilibrium:

\[ \text{Equilibrium occurs where } Q_d = Q_s \] \[ \text{Demand: } P = a - bQ_d \] \[ \text{Supply: } P = c + dQ_s \]

Demand Intercept (a):

Demand Slope (b):

$ per unit

Supply Intercept (c):

Supply Slope (d):

$ per unit

Equilibrium Price:

Equilibrium Quantity:

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1. What is Market Equilibrium?

Market equilibrium occurs when the quantity demanded equals the quantity supplied, resulting in an equilibrium price where the market clears. This is the point where supply and demand curves intersect.

2. How the Calculator Works

The calculator solves the system of equations:

\[ \text{Demand: } P = a - bQ_d \] \[ \text{Supply: } P = c + dQ_s \] \[ \text{At equilibrium: } Q_d = Q_s = Q \]

Where:

$ P $ — Price in dollars
$ Q $ — Quantity in units
$ a $ — Demand curve intercept (price axis)
$ b $ — Demand curve slope
$ c $ — Supply curve intercept (price axis)
$ d $ — Supply curve slope

Solution: The equilibrium quantity $ Q $ is calculated as $ (a - c)/(b + d) $, then substituted back to find equilibrium price.

3. Importance of Equilibrium Calculation

Details: Understanding market equilibrium helps predict price and quantity in competitive markets, analyze market efficiency, and evaluate the impact of policies like price controls or taxes.

4. Using the Calculator

Tips: Enter the intercepts and slopes for both supply and demand curves. The demand slope should be negative, while the supply slope should be positive for normal cases.

5. Frequently Asked Questions (FAQ)

Q1: What if my supply curve has a negative slope?
A: This calculator assumes normal upward-sloping supply. For special cases, you may need to solve manually.

Q2: What units should I use?
A: Use consistent units - typically dollars for price and quantity units (could be thousands, millions, etc. depending on context).

Q3: What if the curves don't intersect?
A: The calculator will show no solution if the curves are parallel (same slope) or if demand is always below supply.

Q4: Can I use this for non-linear curves?
A: This calculator is for linear curves only. Non-linear curves require more advanced methods.

Q5: How accurate are these results?
A: Results are mathematically precise for the given linear equations, but real-world markets may have additional complexities.