We have a price ceiling situation where the government imposes a maximum price, $P = 87$ dollars per kg for traditional herbs. We are tasked with calculating the costs, revenues, and profits of black marketeers under the assumption that they buy herbs at the ceiling price and sell them illegally at the equilibrium price.

Let's break this down step by step.

Given Functions:

• Demand function: $Q_d = 945 - 3.4P$
• Supply function: $Q_s = 2P - 120$
• Price ceiling: $P = 87 \, \text{dollars/kg}$

Step 1: Calculate the Equilibrium Price

The equilibrium price is where the quantity demanded equals the quantity supplied:

$Q_d = Q_s$

Substituting the demand and supply functions into the equation:

$945 - 3.4P = 2P - 120$

Solve for $P$.

$945 + 120 = 2P + 3.4P$ $1065 = 5.4P$ $P = \frac{1065}{5.4} \approx 197.22 \, \text{dollars/kg}$

The equilibrium price is approximately $P = 197.22 \, \text{dollars/kg}$.

Step 2: Calculate the Quantity at the Ceiling Price and Equilibrium Price

Quantity supplied at the ceiling price $P = 87$:

$Q_s(87) = 2(87) - 120 = 174 - 120 = 54 \, \text{kg}$

At the ceiling price, only 54 kg of the herb is supplied.

Quantity demanded at the ceiling price $P = 87$:

$Q_d(87) = 945 - 3.4(87) = 945 - 295.8 = 649.2 \, \text{kg}$

At the ceiling price, 649.2 kg is demanded, creating a shortage.

Equilibrium quantity at $P = 197.22$:

$Q_s(197.22) = 2(197.22) - 120 = 394.44 - 120 = 274.44 \, \text{kg}$

At the equilibrium price, the supply and demand balance out at around 274.44 kg.

Step 3: Black Market Calculations

Black marketeers are assumed to purchase the herbs at the ceiling price and sell them at the equilibrium price. The black market volume is the shortage created by the price ceiling.

The shortage is:

$\text{Shortage} = Q_d(87) - Q_s(87) = 649.2 - 54 = 595.2 \, \text{kg}$

So, black marketeers can sell 595.2 kg of herbs in the black market.

a. Total cost of black marketeers:

The total cost is the amount black marketeers pay when buying the herbs at the ceiling price:

$\text{Total Cost} = 87 \times 595.2 = 51,782.4 \, \text{dollars}$

b. Total revenue of black marketeers:

The total revenue is the amount black marketeers earn by selling the herbs at the equilibrium price:

$\text{Total Revenue} = 197.22 \times 595.2 = 117,472.94 \, \text{dollars}$

c. Profit of black marketeers:

The profit is the total revenue minus the total cost:

$\text{Profit} = 117,472.94 - 51,782.4 = 65,690.54 \, \text{dollars}$

Final Answers:

a. The total cost of black marketeers: $\mathbf{51,782.4} \, \text{dollars}$

b. The total revenue of black marketeers: $\mathbf{117,472.94} \, \text{dollars}$

c. The profit of black marketeers: $\mathbf{65,690.54} \, \text{dollars}$

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Would you like more details or explanations on any step?

Here are 5 related questions to expand on this:

1. How does a price ceiling create black markets in general?
2. What would happen if the price ceiling were lower than $87/kg?
3. How would government enforcement affect the black market size?
4. Can price floors have a similar effect as price ceilings?
5. What policies could the government introduce to reduce black market activity?

Tip: Understanding the interaction between supply, demand, and government intervention helps explain economic issues like inflation and shortages.