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 $7.06/gram calculate the black market profit

To find the black market profit when the ceiling price is $7.06/gram, we first need to determine the quantities demanded and supplied at this price and then compute the potential profit resulting from selling at a higher price than the ceiling price.

### Step 1: Find the quantities demanded and supplied at the ceiling price

The demand and supply functions are given by:

\[
P_d = 16.5 - 0.025Q
\]

\[
P_s = 2.4 + 0.018Q
\]

where $P$ is the price in $/gram, and $Q$ is the quantity in kilograms.

To find the quantities demanded and supplied at the ceiling price of $P = 7.06$:

1. **Calculate Quantity Demanded ($Q_d$)**:

\[
7.06 = 16.5 - 0.025Q_d
\]

Solve for $Q_d$:

\[
0.025Q_d = 16.5 - 7.06 \implies Q_d = \frac{9.44}{0.025}
\]

2. **Calculate Quantity Supplied ($Q_s$)**:

\[
7.06 = 2.4 + 0.018Q_s
\]

Solve for $Q_s$:

\[
0.018Q_s = 7.06 - 2.4 \implies Q_s = \frac{4.66}{0.018}
\]

Let's compute the values of $Q_d$ and $Q_s$.The quantities demanded and supplied at the ceiling price of $7.06 per gram are:

- **Quantity Demanded ($Q_d$)**: 377.6 kg
- **Quantity Supplied ($Q_s$)**: 258.89 kg

### Step 2: Determine the Black Market Quantity

The black market quantity is the excess demand, which is the difference between the quantity demanded and the quantity supplied:

\[
\text{Black Market Quantity} = Q_d - Q_s = 377.6 - 258.89 = 118.71 \, \text{kg}
\]

### Step 3: Calculate the Black Market Price

Assuming sellers sell at the equilibrium price (where demand equals supply) in the black market, we first need to find the equilibrium price by equating the demand and supply functions:

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

Solve for $Q$ to find the equilibrium quantity and then the equilibrium price ($P$).

Let's calculate these values.The equilibrium quantity and price are:

- **Equilibrium Quantity ($Q_{equilibrium}$)**: 327.91 kg
- **Equilibrium Price ($P_{equilibrium}$)**: $8.30 per gram

### Step 4: Calculate the Black Market Profit

The black market price is assumed to be the equilibrium price of $8.30 per gram, while the ceiling price is $7.06 per gram. The difference between these prices represents the profit per gram in the black market.

\[
\text{Profit per gram} = P_{equilibrium} - P_{ceiling} = 8.30 - 7.06 = 1.24 \, \text{USD/gram}
\]

The total black market profit is:

\[
\text{Black Market Profit} = \text{Black Market Quantity} \times \text{Profit per gram} \times 1000
\]

(converting kilograms to grams).

Let's compute the total black market profit.The total black market profit when the ceiling price is $7.06 per gram is **$147,477.85**.

### Summary
- **Ceiling Price:** $7.06 per gram
- **Equilibrium Price:** $8.30 per gram
- **Black Market Quantity:** 118.71 kg
- **Black Market Profit:** $147,477.85

Would you like further details, or do you have any questions?

### Related Questions
1. How would the black market profit change if the ceiling price were different?
2. What is the significance of the equilibrium price in this context?
3. How does a price ceiling create conditions for a black market?
4. What would happen if the government enforced the ceiling price strictly?
5. How does elasticity of demand and supply affect the black market?

### Tip
To understand market dynamics better, explore how supply and demand respond to changes in external factors like taxes, subsidies, or government regulations.

Explore how to calculate black market profit using demand and supply functions. Learn how to find quantities demanded and supplied at a ceiling price of $7.06 per gram, and determine the black market profit. Detailed step-by-step solution with mathematical formulas and computations.

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