Economic Equilibrium Calculator
This calculator finds the market equilibrium price (P*) and quantity (Q*) where the quantity demanded equals the quantity supplied, based on linear supply and demand equations.
Enter the coefficients for your linear Demand and Supply equations in the form:
Qd = a + bP
Qs = c + dP
Where Q is Quantity, P is Price, and 'a', 'b', 'c', 'd' are constants.
Enter Supply and Demand Equations Coefficients
Understanding Economic Equilibrium
What is Market Equilibrium?
Market equilibrium is a state where the supply of an item equals its demand at a certain price. At this equilibrium price (P*), the quantity that consumers are willing and able to buy (Quantity Demanded, Qd) is exactly equal to the quantity that producers are willing and able to sell (Quantity Supplied, Qs). This point represents an efficient allocation of resources in a competitive market.
Linear Supply and Demand Equations
In simple economic models, supply and demand can be represented by linear equations:
- Demand Equation:
Qd = a + bPa: The quantity demanded when the price is zero (the Q-intercept). Often positive.b: The slope of the demand curve. Typically negative, representing the law of demand (as price increases, quantity demanded decreases).
- Supply Equation:
Qs = c + dPc: The quantity supplied when the price is zero (the Q-intercept). Can be positive, negative, or zero.d: The slope of the supply curve. Typically positive, representing the law of supply (as price increases, quantity supplied increases).
Finding Equilibrium Mathematically
Equilibrium occurs where Qd = Qs. To find the equilibrium price (P*) and quantity (Q*), we set the two equations equal to each other and solve for P:
a + bP = c + dP
Rearranging to solve for P:
bP - dP = c - a
P(b - d) = c - a
P* = (c - a) / (b - d)
Once P* is found, substitute it back into *either* the Demand or Supply equation to find Q*:
Q* = a + b * P*
or
Q* = c + d * P*
Special Cases: Parallel Curves
What happens if the slopes are equal, i.e., b = d? The denominator (b - d) becomes zero.
- If
b = dANDa = c: The demand and supply equations are identical. The lines are the same, meaning every point is an equilibrium point. There are infinite equilibria. - If
b = dANDa ≠ c: The demand and supply lines are parallel but distinct. They never intersect, meaning there is no price at which quantity demanded equals quantity supplied. There is no equilibrium.
This calculator identifies these special cases.
Economic Equilibrium Examples
Click on an example to see the calculation:
Example 1: Standard Market Equilibrium
Equations:
- Demand:
Qd = 100 - 2P(a=100, b=-2) - Supply:
Qs = 10 + 3P(c=10, d=3)
Calculation:
- Set Qd = Qs:
100 - 2P = 10 + 3P - Solve for P*:
100 - 10 = 3P + 2P->90 = 5P->P* = 90 / 5 = 18 - Substitute P* into Qd:
Q* = 100 - 2 * 18 = 100 - 36 = 64 - (Check with Qs:
Q* = 10 + 3 * 18 = 10 + 54 = 64. Matches!)
Result: P* = 18, Q* = 64
Conclusion: Equilibrium occurs at a price of 18 and quantity of 64.
Example 2: Different Coefficients
Equations:
- Demand:
Qd = 500 - 0.5P(a=500, b=-0.5) - Supply:
Qs = -100 + 1.5P(c=-100, d=1.5)
Calculation:
- Set Qd = Qs:
500 - 0.5P = -100 + 1.5P - Solve for P*:
500 + 100 = 1.5P + 0.5P->600 = 2P->P* = 600 / 2 = 300 - Substitute P* into Qd:
Q* = 500 - 0.5 * 300 = 500 - 150 = 350
Result: P* = 300, Q* = 350
Conclusion: Equilibrium is at a price of 300 and quantity of 350.
Example 3: Negative Intercept (Supply)
Equations:
- Demand:
Qd = 220 - 4P(a=220, b=-4) - Supply:
Qs = -20 + 6P(c=-20, d=6)
Calculation:
- Set Qd = Qs:
220 - 4P = -20 + 6P - Solve for P*:
220 + 20 = 6P + 4P->240 = 10P->P* = 240 / 10 = 24 - Substitute P* into Qs:
Q* = -20 + 6 * 24 = -20 + 144 = 124
Result: P* = 24, Q* = 124
Conclusion: Equilibrium is at P=24, Q=124.
Example 4: Parallel Lines (No Equilibrium)
Equations:
- Demand:
Qd = 150 - 3P(a=150, b=-3) - Supply:
Qs = 50 - 3P(c=50, d=-3)
Calculation:
- Set Qd = Qs:
150 - 3P = 50 - 3P - Solve for P*:
150 - 50 = -3P + 3P->100 = 0
Result: The equation 100 = 0 is a contradiction.
Conclusion: The lines have the same slope but different intercepts. They are parallel and never intersect. There is no equilibrium.
Example 5: Identical Lines (Infinite Equilibria)
Equations:
- Demand:
Qd = 75 + 5P(a=75, b=5) - Supply:
Qs = 75 + 5P(c=75, d=5)
Calculation:
- Set Qd = Qs:
75 + 5P = 75 + 5P - Solve for P*:
75 - 75 = 5P - 5P->0 = 0
Result: The equation 0 = 0 is always true.
Conclusion: The lines are identical. Any price and quantity combination on the line is an equilibrium. There are infinite equilibria.
Example 6: Supply Dependent on Price Only
Equations:
- Demand:
Qd = 300 - P(a=300, b=-1) - Supply:
Qs = 2P(c=0, d=2)
Calculation:
- Set Qd = Qs:
300 - P = 2P - Solve for P*:
300 = 2P + P->300 = 3P->P* = 300 / 3 = 100 - Substitute P* into Qs:
Q* = 2 * 100 = 200
Result: P* = 100, Q* = 200
Conclusion: Equilibrium is at P=100, Q=200.
Example 7: Resulting in Negative Price (Mathematical only)
Equations:
- Demand:
Qd = 50 + 2P(a=50, b=2) - *Note: Upward sloping demand often non-standard* - Supply:
Qs = 10 + 3P(c=10, d=3)
Calculation:
- Set Qd = Qs:
50 + 2P = 10 + 3P - Solve for P*:
50 - 10 = 3P - 2P->40 = P->P* = 40 - Substitute P* into Qs:
Q* = 10 + 3 * 40 = 10 + 120 = 130 - *Correction*: Let's adjust this example to *actually* result in a negative price to demonstrate that case.
Revised Equations:
- Demand:
Qd = 10 - 2P(a=10, b=-2) - Supply:
Qs = 20 + 3P(c=20, d=3)
Revised Calculation:
- Set Qd = Qs:
10 - 2P = 20 + 3P - Solve for P*:
10 - 20 = 3P + 2P->-10 = 5P->P* = -10 / 5 = -2 - Substitute P* into Qd:
Q* = 10 - 2 * (-2) = 10 + 4 = 14
Result: P* = -2, Q* = 14
Conclusion: Mathematically, the lines intersect at P=-2, Q=14. In standard economics, price cannot be negative, so there is no market equilibrium at a non-negative price. The intersection is only theoretical.
Example 8: Resulting in Negative Quantity (Mathematical only)
Equations:
- Demand:
Qd = 10 - 0.5P(a=10, b=-0.5) - Supply:
Qs = -5 + P(c=-5, d=1)
Calculation:
- Set Qd = Qs:
10 - 0.5P = -5 + P - Solve for P*:
10 + 5 = P + 0.5P->15 = 1.5P->P* = 15 / 1.5 = 10 - Substitute P* into Qd:
Q* = 10 - 0.5 * 10 = 10 - 5 = 5 - *Correction*: Let's adjust this example to *actually* result in a negative quantity (with a positive price).
Revised Equations:
- Demand:
Qd = 5 - 2P(a=5, b=-2) - Supply:
Qs = -10 + 3P(c=-10, d=3)
Revised Calculation:
- Set Qd = Qs:
5 - 2P = -10 + 3P - Solve for P*:
5 + 10 = 3P + 2P->15 = 5P->P* = 15 / 5 = 3 - Substitute P* into Qd:
Q* = 5 - 2 * 3 = 5 - 6 = -1
Result: P* = 3, Q* = -1
Conclusion: Mathematically, the lines intersect at P=3, Q=-1. In standard economics, quantity cannot be negative. The intersection is theoretical and not a valid market equilibrium outcome under typical assumptions.
Example 9: Zero Intercepts
Equations:
- Demand:
Qd = -P(a=0, b=-1) - *Downward sloping from origin* - Supply:
Qs = 4P(c=0, d=4) - *Upward sloping from origin*
Calculation:
- Set Qd = Qs:
-P = 4P - Solve for P*:
0 = 4P + P->0 = 5P->P* = 0 / 5 = 0 - Substitute P* into Qs:
Q* = 4 * 0 = 0
Result: P* = 0, Q* = 0
Conclusion: Equilibrium is at Price 0, Quantity 0. This might represent a good with no value or demand/supply only existing at positive prices/quantities.
Example 10: Different Slope Signs
Equations:
- Demand:
Qd = 80 - 5P(a=80, b=-5) - Supply:
Qs = 20 + 2P(c=20, d=2)
Calculation:
- Set Qd = Qs:
80 - 5P = 20 + 2P - Solve for P*:
80 - 20 = 2P + 5P->60 = 7P->P* = 60 / 7 ≈ 8.57 - Substitute P* into Qd:
Q* = 80 - 5 * (60 / 7) = 80 - 300 / 7 = (560 - 300) / 7 = 260 / 7 ≈ 37.14
Result: P* ≈ 8.57, Q* ≈ 37.14
Conclusion: Equilibrium is approximately at P=8.57, Q=37.14.
Frequently Asked Questions about Economic Equilibrium
1. What is Economic Equilibrium?
Economic equilibrium is the state in a market where the quantity of a good or service supplied by producers equals the quantity demanded by consumers at a particular price. This price is known as the equilibrium price, and the corresponding quantity is the equilibrium quantity.
2. How is equilibrium found using equations?
Equilibrium is found by setting the quantity demanded (Qd) equation equal to the quantity supplied (Qs) equation (Qd = Qs). This creates a single equation with Price (P) as the variable, which can then be solved to find the equilibrium price (P*). The equilibrium quantity (Q*) is found by substituting P* back into either the Qd or Qs equation.
3. What do 'a', 'b', 'c', and 'd' represent in the equations Qd = a + bP and Qs = c + dP?
'a' and 'c' are the Q-intercepts, representing the quantity demanded/supplied when the price is zero. 'b' and 'd' are the slopes. 'b' is typically negative (law of demand), and 'd' is typically positive (law of supply).
4. What does it mean if the calculator says "No Equilibrium"?
This occurs when the demand and supply curves are parallel and distinct (they have the same slope 'b' and 'd', but different Q-intercepts 'a' and 'c'). They never intersect, meaning there's no price where quantity demanded equals quantity supplied based on those linear models.
5. What does it mean if the calculator says "Infinite Equilibria"?
This happens when the demand and supply curves are identical (they have both the same slope 'b' and 'd', AND the same Q-intercepts 'a' and 'c'). The lines lie directly on top of each other, so every point on the line is an equilibrium point.
6. Can the equilibrium price or quantity be negative?
Mathematically, the intersection point can occur at a negative price or quantity. However, in most real-world economic contexts, negative prices or quantities are not meaningful market outcomes. The calculator provides the mathematical intersection, and you should interpret it within the context of your specific economic problem (often assuming Q ≥ 0 and P ≥ 0).
7. What are the limitations of this calculator?
This calculator works only for linear supply and demand equations in the specified format (Quantity as a function of Price: Q = constant + slope * P). It does not support non-linear equations or other equation formats (like P as a function of Q).
8. Why is the demand slope ('b') usually negative?
The negative slope reflects the Law of Demand, which states that, all else being equal, as the price of a good or service increases, the quantity demanded decreases, and vice versa.
9. Why is the supply slope ('d') usually positive?
The positive slope reflects the Law of Supply, which states that, all else being equal, as the price of a good or service increases, the quantity supplied increases, and vice versa. Higher prices are typically more profitable, encouraging producers to supply more.
10. Does this calculator consider taxes, subsidies, or other market interventions?
No, this calculator finds the basic equilibrium based *only* on the provided supply and demand equations. It does not incorporate the effects of external factors like taxes, subsidies, price ceilings, or price floors, which would shift the curves or create a disequilibrium.
