Question
what is the exact surplus of a price floor for $15 when the equilibrium price is $10? show all work
Answers
GPT-4o mini
To find the exact surplus created by a price floor of $15 when the equilibrium price is $10, we need to understand how price floors work and the concepts of supply and demand.
1. **Definitions**:
- **Price Floor**: A minimum price set by the government that is above the equilibrium price. Producers cannot sell the product for a price lower than the price floor.
- **Equilibrium Price**: The price at which the quantity demanded equals the quantity supplied.
2. **Given**:
- Price Floor \( P_f = 15 \)
- Equilibrium Price \( P_e = 10 \)
3. **Consequences of the Price Floor**:
- Because the price floor is set above the equilibrium price, it leads to a situation where the quantity supplied (QS) exceeds the quantity demanded (QD).
- At a price of $15, producers are willing to supply more than consumers are willing to buy.
4. **Determining Quantity Supplied and Quantity Demanded**:
To calculate the surplus, we generally need the quantities supplied and demanded at both the equilibrium price and the price floor. However, since we don't have numerical values for these quantities, we will denote them as follows:
- At \( P_e = 10 \):
- Quantity Demanded \( QD_e \)
- Quantity Supplied \( QS_e \)
- At \( P_f = 15 \):
- Quantity Demanded \( QD_f \)
- Quantity Supplied \( QS_f \)
5. **Surplus Calculation**:
The surplus created by the price floor can be expressed as:
\[
\text{Surplus} = QS_f - QD_f
\]
6. **Example Assumption**:
Let's assume hypothetical quantities for illustration:
- At price \( P_e = 10 \):
- \( QD_e = 100 \) (Consumers demand 100 units)
- \( QS_e = 100 \) (Producers supply 100 units)
- At price \( P_f = 15 \):
- Assume \( QD_f = 60 \) (Consumers only demand 60 units)
- Assume \( QS_f = 120 \) (Producers are willing to supply 120 units)
7. **Plug values into the surplus formula**:
\[
\text{Surplus} = QS_f - QD_f = 120 - 60 = 60
\]
Thus, in this example, the exact surplus created by a price floor of $15 when the equilibrium price is $10 is 60 units.
**Final Notes**: The actual numbers for \( QS_f \) and \( QD_f \) would need to be derived from the specific supply and demand functions for the market you are analyzing. This example simply illustrates the mechanism by which we find surplus under a price floor.
1. **Definitions**:
- **Price Floor**: A minimum price set by the government that is above the equilibrium price. Producers cannot sell the product for a price lower than the price floor.
- **Equilibrium Price**: The price at which the quantity demanded equals the quantity supplied.
2. **Given**:
- Price Floor \( P_f = 15 \)
- Equilibrium Price \( P_e = 10 \)
3. **Consequences of the Price Floor**:
- Because the price floor is set above the equilibrium price, it leads to a situation where the quantity supplied (QS) exceeds the quantity demanded (QD).
- At a price of $15, producers are willing to supply more than consumers are willing to buy.
4. **Determining Quantity Supplied and Quantity Demanded**:
To calculate the surplus, we generally need the quantities supplied and demanded at both the equilibrium price and the price floor. However, since we don't have numerical values for these quantities, we will denote them as follows:
- At \( P_e = 10 \):
- Quantity Demanded \( QD_e \)
- Quantity Supplied \( QS_e \)
- At \( P_f = 15 \):
- Quantity Demanded \( QD_f \)
- Quantity Supplied \( QS_f \)
5. **Surplus Calculation**:
The surplus created by the price floor can be expressed as:
\[
\text{Surplus} = QS_f - QD_f
\]
6. **Example Assumption**:
Let's assume hypothetical quantities for illustration:
- At price \( P_e = 10 \):
- \( QD_e = 100 \) (Consumers demand 100 units)
- \( QS_e = 100 \) (Producers supply 100 units)
- At price \( P_f = 15 \):
- Assume \( QD_f = 60 \) (Consumers only demand 60 units)
- Assume \( QS_f = 120 \) (Producers are willing to supply 120 units)
7. **Plug values into the surplus formula**:
\[
\text{Surplus} = QS_f - QD_f = 120 - 60 = 60
\]
Thus, in this example, the exact surplus created by a price floor of $15 when the equilibrium price is $10 is 60 units.
**Final Notes**: The actual numbers for \( QS_f \) and \( QD_f \) would need to be derived from the specific supply and demand functions for the market you are analyzing. This example simply illustrates the mechanism by which we find surplus under a price floor.