The demand and supply for bicycles is given by: Qd = 1000 - 10P Qs = 2P - 20 The government imposes a per unit tax of Tax = $12. What is new CS and PS? What is the change in consumer and producer surplus compared to equilibrium? What is the Deadweight Loss? What is government revenue? Graph your results.
The demand and supply for bicycles is given by: Qd = 1000 - 10P Qs = 2P - 20 The government imposes a per unit tax of Tax = $12. What is new CS and PS? What is the change in consumer and producer surplus compared to equilibrium? What is the Deadweight Loss? What is government revenue? Graph your results.
Chapter1: Making Economics Decisions
Section: Chapter Questions
Problem 1QTC
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![### Bicycle Market Analysis with Taxation
#### Demand and Supply Functions
The demand and supply for bicycles are defined by the following equations:
\[ Q_d = 1000 - 10P \]
\[ Q_s = 2P - 20 \]
Where:
- \( Q_d \) is the quantity demanded
- \( Q_s \) is the quantity supplied
- \( P \) is the price of bicycles
#### Government Imposed Tax
The government imposes a per-unit tax \( T_{ax} \) of $12.
##### Key Questions:
1. **New Consumer Surplus (CS) and Producer Surplus (PS):**
- Apply the tax to determine the new equilibrium price and quantity.
- Calculate the new consumer and producer surplus values.
2. **Change in Consumer and Producer Surplus Compared to Equilibrium:**
- Determine the changes in CS and PS before and after the tax.
3. **Deadweight Loss:**
- Compute the deadweight loss resulting from taxation.
4. **Government Revenue:**
- Estimate the total revenue generated from the taxation.
5. **Graph Your Results:**
- Illustrate the demand and supply curves.
- Indicate the shifts and intersections caused by taxation.
##### Analytical Steps:
**Determine Equilibrium Without Tax:**
1. Set \( Q_d = Q_s \):
\[ 1000 - 10P = 2P - 20 \]
2. Solve for \( P \) (equilibrium price):
\[ 1000 + 20 = 12P \]
\[ P = \frac{1020}{12} \]
\[ P = 85 \]
3. Determine \( Q \) (equilibrium quantity):
\[ Q = 2P - 20 \]
\[ Q = 2(85) - 20 \]
\[ Q = 170 - 20 \]
\[ Q = 150 \]
**Determine New Equilibrium with Tax:**
1. Adjust equilibrium conditions to account for tax:
\[ 1000 - 10(P_c) = 2(P_s) - 20 \]
\[ P_c = P_s + 12 \]
2. Bantering with equations:
\[ 1000 - 10(P_s + 12) = 2P_s - 20 \]
\[ 1000 - 10P_s - 120 = 2P_s - 20 \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F300cbca4-f6ea-4709-a050-de562527f506%2F9dc1c53a-ad3c-4960-8bda-4ef855dd04c6%2F16hlari_processed.png&w=3840&q=75)
Transcribed Image Text:### Bicycle Market Analysis with Taxation
#### Demand and Supply Functions
The demand and supply for bicycles are defined by the following equations:
\[ Q_d = 1000 - 10P \]
\[ Q_s = 2P - 20 \]
Where:
- \( Q_d \) is the quantity demanded
- \( Q_s \) is the quantity supplied
- \( P \) is the price of bicycles
#### Government Imposed Tax
The government imposes a per-unit tax \( T_{ax} \) of $12.
##### Key Questions:
1. **New Consumer Surplus (CS) and Producer Surplus (PS):**
- Apply the tax to determine the new equilibrium price and quantity.
- Calculate the new consumer and producer surplus values.
2. **Change in Consumer and Producer Surplus Compared to Equilibrium:**
- Determine the changes in CS and PS before and after the tax.
3. **Deadweight Loss:**
- Compute the deadweight loss resulting from taxation.
4. **Government Revenue:**
- Estimate the total revenue generated from the taxation.
5. **Graph Your Results:**
- Illustrate the demand and supply curves.
- Indicate the shifts and intersections caused by taxation.
##### Analytical Steps:
**Determine Equilibrium Without Tax:**
1. Set \( Q_d = Q_s \):
\[ 1000 - 10P = 2P - 20 \]
2. Solve for \( P \) (equilibrium price):
\[ 1000 + 20 = 12P \]
\[ P = \frac{1020}{12} \]
\[ P = 85 \]
3. Determine \( Q \) (equilibrium quantity):
\[ Q = 2P - 20 \]
\[ Q = 2(85) - 20 \]
\[ Q = 170 - 20 \]
\[ Q = 150 \]
**Determine New Equilibrium with Tax:**
1. Adjust equilibrium conditions to account for tax:
\[ 1000 - 10(P_c) = 2(P_s) - 20 \]
\[ P_c = P_s + 12 \]
2. Bantering with equations:
\[ 1000 - 10(P_s + 12) = 2P_s - 20 \]
\[ 1000 - 10P_s - 120 = 2P_s - 20 \]
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