A kg of traditional herb has a demand function of Q = 945 - 3.4P and supply function of Q = 2P - 120. Due to COVID-19 pandemic, the price of traditional herb keeps increasing. To protect customers, the government sets a price ceiling at P = $ 87/kg. If blackmarkets exists, calculate:
a. the total cost of black marketeers!
b. the total revenue of black marketeers!
c. the profit of black marketeers!

To analyze the situation, we will go step by step to determine the cost, revenue, and profit of the black marketeers based on the given demand and supply functions, and the price ceiling set by the government.

### Given:
- **Demand function**: $ Q_d = 945 - 3.4P $
- **Supply function**: $ Q_s = 2P - 120 $
- **Price ceiling**: $ P = 87 $

First, let's calculate the **equilibrium price and quantity** without government intervention, which occurs when supply equals demand ($ Q_d = Q_s $).

### 1. **Find the equilibrium price** (before the price ceiling):
\[
945 - 3.4P = 2P - 120
\]
Solving for $ P $:
\[
945 + 120 = 2P + 3.4P
\]
\[
1065 = 5.4P
\]
\[
P = \frac{1065}{5.4} = 197.22
\]
So, the **equilibrium price** without the price ceiling is **$197.22**.

### 2. **Find the equilibrium quantity**:
Substitute $ P = 197.22 $ into either the demand or supply function. Let's use the supply function:
\[
Q = 2P - 120 = 2(197.22) - 120 = 394.44 - 120 = 274.44
\]
So, the **equilibrium quantity** is approximately **274.44 kg**.

### 3. **Quantity demanded and supplied at the price ceiling of $ P = 87 $**:
#### Quantity demanded:
\[
Q_d = 945 - 3.4(87) = 945 - 295.8 = 649.2
\]
So, the quantity demanded at $ P = 87 $ is **649.2 kg**.

#### Quantity supplied:
\[
Q_s = 2(87) - 120 = 174 - 120 = 54
\]
So, the quantity supplied at $ P = 87 $ is **54 kg**.

### 4. **Quantity traded in the black market**:
The quantity traded in the black market is the difference between the quantity demanded and the quantity supplied:
\[
Q_{\text{black market}} = Q_d - Q_s = 649.2 - 54 = 595.2 \text{ kg}
\]
This is the amount traded on the black market, as it's the unsatisfied demand due to the price ceiling.

### 5. **Black market price**:
Since the government imposes a price ceiling of $ P = 87 $, the black market price will likely rise to the equilibrium price, which is $ P = 197.22 $. So the price in the black market is $ 197.22 $.

Now, we can calculate the costs, revenues, and profits for the black marketeers.

### a. **Total cost of black marketeers**:
The black marketeers will purchase the herb at the price ceiling $ P = 87 $. The total cost is:
\[
\text{Total cost} = 87 \times 595.2 = 51,782.40 \, \text{(USD)}
\]

### b. **Total revenue of black marketeers**:
The black marketeers will sell the herb at the black market price of $ P = 197.22 $. The total revenue is:
\[
\text{Total revenue} = 197.22 \times 595.2 = 117,489.74 \, \text{(USD)}
\]

### c. **Profit of black marketeers**:
The profit is the difference between total revenue and total cost:
\[
\text{Profit} = 117,489.74 - 51,782.40 = 65,707.34 \, \text{(USD)}
\]

### Final answers:
a. The total cost of black marketeers is **\$51,782.40**.  
b. The total revenue of black marketeers is **\$117,489.74**.  
c. The profit of black marketeers is **\$65,707.34**.

---

Would you like further details on any of these calculations or explanations? Here are five related questions for deeper insight:

1. How would the introduction of a subsidy affect the black market scenario?
2. What would happen to consumer surplus in this case of a price ceiling?
3. How can we determine the deadweight loss from this intervention?
4. If the price ceiling was removed, how would the market correct itself?
5. What role does elasticity of demand and supply play in determining black market profits?

**Tip**: Understanding the effects of price controls like price ceilings helps in predicting unintended consequences like the creation of black markets.

A kg of traditional herb has a demand function of Q = 945 - 3.4P and supply function of Q = 2P - 120. Due to COVID-19 pandemic, the price of traditional herb keeps increasing. To protect customers, the government sets a price ceiling at P = $ 87/kg. If blackmarkets exists, calculate: a. the total cost of black marketeers! b. the total revenue of black marketeers! c. the profit of black marketeers!

Learn how to calculate the total cost, revenue, and profit of black marketeers in an economic scenario involving traditional herbs, using supply and demand functions. This example includes a price ceiling set by the government, and is suitable for students in Grades 11-12 or college-level economics.

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