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Supply Demand Equilibrium, Consumer Surplus, and Price Floor Calculation
Published on March 22, 2026
Calculus
This problem requires calculating market equilibrium, deriving consumer and producer surplus using definite integrals, and analyzing the impact of a mandated minimum price on market outcomes.
Question
please answer
Answer
This is an economics problem involving supply and demand analysis, equilibrium calculation, consumer surplus, producer surplus, and the effect of a price floor.
The given demand and supply functions are:
Demand:
Supply:
Part a. Calculate and illustrate the equilibrium price and quantity where
1. Calculate Equilibrium Price (
Equilibrium occurs where quantity demanded equals quantity supplied (
Add
Add
Divide by 6:
The equilibrium price is
Now, substitute
Using Demand:
Using Supply:
The equilibrium quantity is
Equilibrium Point:
2. Determine Intercepts for Graphing
To illustrate this on a graph (Price on the vertical axis, Quantity on the horizontal axis), we need the price intercepts (where
Demand Intercepts:
- Y-intercept (Maximum Willingness to Pay,
): Point: - X-intercept (
): Point:
Supply Intercepts:
- Y-intercept (Minimum Willingness to Accept,
): Point: - X-intercept (
): (This point is not economically meaningful as quantity cannot be negative, but the intercept occurs at for positive quantities).
3. Illustration (Graph Description)
The graph will have Price (
- The Demand Curve slopes downward, passing through
and . - The Supply Curve slopes upward, starting from
and passing through and beyond. - The Equilibrium Point (E) is where the two curves intersect at
.
Part b. Calculate the consumer surplus and producer surplus at the market equilibrium using the definite integral approach.
To use the integral approach, we need the inverse demand function
Inverse Demand (
Inverse Supply (
Equilibrium quantity
1. Consumer Surplus (CS)
Consumer Surplus is the area under the inverse demand curve and above the equilibrium price, integrated from
Consumer Surplus is 900.
(Check using the triangle method: Base = 60, Height =
2. Producer Surplus (PS)
Producer Surplus is the area above the inverse supply curve and below the equilibrium price, integrated from
Producer Surplus is 450.
(Check using the triangle method: Base = 60, Height =
Part c. If the government imposes a minimum price of 25, calculate the new consumer and producer surplus. Who benefits from the minimum price policy?
The minimum price (price floor) is set at
1. Determine New Quantity Traded (
At
Quantity Demanded (
Quantity Supplied (
Since the quantity traded in the market is limited by the quantity demanded, the new quantity traded is
2. Calculate New Consumer Surplus (
Consumers are willing to buy
New Consumer Surplus is 625.
(Comparison:
(Comparison:
3. Calculate New Producer Surplus (
Producers sell
New Producer Surplus is 687.5.
(Comparison:
(Comparison:
4. Who benefits from the minimum price policy?
We compare the surpluses:
| Surplus Type | Equilibrium (P=20) | Minimum Price (P=25) | Change |
|---|---|---|---|
| Consumer Surplus (CS) | 900 | 625 | Decrease (-275) |
| Producer Surplus (PS) | 450 | 687.5 | Increase (+237.5) |
| Total Surplus (Welfare) | 1350 | 1312.5 | Decrease (-37.5) |
Since the quantity traded decreased from 60 to 50, there is a deadweight loss (reduction in total surplus).
Producers benefit from the minimum price policy because their surplus increased from 450 to 687.5. Consumers are worse off as their surplus decreased from 900 to 625.