Demand and supply functions of a product are Pd=16.5-0.025Q and Ps=2.4+0.018Q. Where P in $/gram and Q in kg.
When the ceiling price is $7.91/gram calculate the profit by the black market in 000$ (if exist).
(Notes: Use 2 digits after decimal point)
The answer is                  (000$)

To calculate the profit by the black market under a price ceiling, we need to follow these steps:

1. **Identify the quantity demanded (Qd) and quantity supplied (Qs) at the ceiling price** using the demand and supply functions.
2. **Determine if a black market exists** by comparing Qd and Qs.
3. **Calculate the equilibrium price and quantity** in the absence of the ceiling to find the market price.
4. **Determine the black market price** and profit.

Let's go through these steps.

### 1. Calculate Qd and Qs at the Ceiling Price
Given:
- Demand function: $ P_d = 16.5 - 0.025Q $
- Supply function: $ P_s = 2.4 + 0.018Q $
- Ceiling price: $ P = 7.91 $ $/gram

**For Quantity Demanded (Qd):**

\[
7.91 = 16.5 - 0.025Q_d
\]

Solving for $ Q_d $:

\[
0.025Q_d = 16.5 - 7.91 = 8.59
\]

\[
Q_d = \frac{8.59}{0.025} = 343.60 \text{ kg}
\]

**For Quantity Supplied (Qs):**

\[
7.91 = 2.4 + 0.018Q_s
\]

Solving for $ Q_s $:

\[
0.018Q_s = 7.91 - 2.4 = 5.51
\]

\[
Q_s = \frac{5.51}{0.018} = 306.11 \text{ kg}
\]

### 2. Existence of Black Market
Since $ Q_d = 343.60 $ kg and $ Q_s = 306.11 $ kg, the quantity demanded exceeds the quantity supplied at the ceiling price, indicating that a black market may exist.

### 3. Calculate the Equilibrium Price and Quantity
Set $ P_d = P_s $:

\[
16.5 - 0.025Q = 2.4 + 0.018Q
\]

Solving for $ Q $:

\[
16.5 - 2.4 = 0.025Q + 0.018Q
\]

\[
14.1 = 0.043Q
\]

\[
Q = \frac{14.1}{0.043} = 327.91 \text{ kg}
\]

Substitute $ Q = 327.91 $ into either the demand or supply equation to find the equilibrium price:

Using the demand function:

\[
P = 16.5 - 0.025 \times 327.91 = 8.30 \text{ $/gram}
\]

### 4. Calculate Black Market Profit
In the black market, sellers can sell the excess demand (Qd - Qs) at the equilibrium price:

\[
\text{Excess Demand} = Q_d - Q_s = 343.60 - 306.11 = 37.49 \text{ kg}
\]

Profit per kg in the black market:

\[
\text{Black Market Profit per kg} = 8.30 - 7.91 = 0.39 \text{ $/gram}
\]

Total profit in the black market:

\[
\text{Profit} = 37.49 \times 0.39 \times 1000 = 14622.66 \text{ $}
\]

Converting this to thousands of dollars:

\[
\text{Profit} = \frac{14622.66}{1000} = 14.62 \text{ (000$)}
\]

### Final Answer:
The black market profit is **14.62 (000$)**.

Would you like further details or have any questions? Here are five related questions you might consider:
1. How does the black market price affect the overall market equilibrium?
2. What would be the effect of increasing the ceiling price on the black market?
3. How can government intervention reduce black market activities?
4. What would be the black market profit if the ceiling price were set at $8.00/gram?
5. How do demand and supply elasticities influence black market profits?

**Tip:** Understanding how price ceilings create shortages can help in predicting black market activities and their impacts on the economy.

Learn how to calculate black market profit under a price ceiling using supply and demand functions. Understand equilibrium price, excess demand, and the economic impact of black market activities. Solve practical examples with step-by-step explanations.

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