If the demand and supply curve for computers are:
QD = 100 - 6P
QS = 28 + 3P
where P is the price of computers (in hundreds of dollars).
a) If the price in the market is $600, what is the quantity demanded by consumers and
what is the quantity supplied? Is this market in equilibrium? Why or why not?
b) Find the market equilibrium price and quantity.
c) Find the consumer surplus at market equilibrium.

Let's break this problem down step-by-step and solve each part accordingly.

### a) **If the price in the market is $600:**

Given:
- **Demand function**: $ Q_D = 100 - 6P $
- **Supply function**: $ Q_S = 28 + 3P $
- The price $ P $ is $600, which is $ P = 6 $ (since price is in hundreds of dollars).

#### 1. **Quantity demanded** ($ Q_D $) at $ P = 6 $:
\[
Q_D = 100 - 6(6) = 100 - 36 = 64
\]
The quantity demanded at a price of $600 is 64 units.

#### 2. **Quantity supplied** ($ Q_S $) at $ P = 6 $:
\[
Q_S = 28 + 3(6) = 28 + 18 = 46
\]
The quantity supplied at a price of $600 is 46 units.

#### 3. **Is the market in equilibrium?**

For a market to be in equilibrium, the quantity demanded must equal the quantity supplied. Here:
\[
Q_D = 64 \quad \text{and} \quad Q_S = 46
\]
Since $ Q_D \neq Q_S $, this market is **not in equilibrium**. There is **excess demand** because the quantity demanded (64) is greater than the quantity supplied (46), leading to a shortage of computers in the market.

---

### b) **Find the market equilibrium price and quantity:**

To find the market equilibrium, set $ Q_D = Q_S $.

\[
100 - 6P = 28 + 3P
\]
Solving for $ P $:

\[
100 - 28 = 6P + 3P
\]
\[
72 = 9P
\]
\[
P = \frac{72}{9} = 8
\]

So, the equilibrium price is $ P = 8 $, which corresponds to $800 (since P is in hundreds of dollars).

#### Find the equilibrium quantity by substituting $ P = 8 $ into either the demand or supply equation:

Using the demand function:
\[
Q_D = 100 - 6(8) = 100 - 48 = 52
\]

Therefore, the **equilibrium quantity** is $ Q = 52 $ units.

---

### c) **Find the consumer surplus at market equilibrium:**

The **consumer surplus** is the difference between what consumers are willing to pay (based on the demand curve) and what they actually pay (the equilibrium price), for all units sold.

1. **Maximum price consumers are willing to pay** is when $ Q_D = 0 $, i.e., set $ Q_D = 0 $ in the demand function:
\[
0 = 100 - 6P
\]
\[
6P = 100
\]
\[
P = \frac{100}{6} \approx 16.67
\]
This means the maximum price consumers are willing to pay is $1,667 (since 16.67 × 100 = 1,667).

2. **Consumer surplus formula**: Consumer surplus is the area of the triangle formed by the demand curve, the price line, and the quantity axis. The formula for the consumer surplus is:
\[
\text{Consumer Surplus} = \frac{1}{2} \times (\text{Base}) \times (\text{Height})
\]
Here:
- **Base** = Equilibrium quantity = 52
- **Height** = Difference between the maximum price consumers are willing to pay and the equilibrium price:
\[
\text{Height} = 16.67 - 8 = 8.67
\]

So, the consumer surplus is:
\[
\text{Consumer Surplus} = \frac{1}{2} \times 52 \times 8.67 = 225.42 \, \text{hundreds of dollars}
\]
\[
\text{Consumer Surplus} = 22,542 \, \text{dollars}
\]

---

### Summary:
- **a)** At $ P = 600 $, $ Q_D = 64 $, $ Q_S = 46 $, the market is **not in equilibrium** (there is excess demand).
- **b)** The equilibrium price is $ P = 8 $ ($800), and the equilibrium quantity is $ Q = 52 $.
- **c)** The consumer surplus at equilibrium is $22,542.

Would you like more details on any part of the solution?

---

### 5 Related Questions:
1. How would producer surplus be calculated in this scenario?
2. What happens to equilibrium if the supply curve shifts?
3. How does a price ceiling affect consumer surplus?
4. How would a tax on suppliers affect the equilibrium?
5. What is the elasticity of demand at the equilibrium price?

**Tip**: Always use graphical representation of supply and demand curves to better visualize market equilibrium and surpluses.

If the demand and supply curve for computers are: QD = 100 - 6P QS = 28 + 3P where P is the price of computers (in hundreds of dollars). a) If the price in the market is $600, what is the quantity demanded by consumers and what is the quantity supplied? Is this market in equilibrium? Why or why not? b) Find the market equilibrium price and quantity. c) Find the consumer surplus at market equilibrium.

Solve a supply and demand problem involving computers, calculating the equilibrium price and quantity, and determining consumer surplus. The analysis covers demand and supply equations, equilibrium conditions, and consumer surplus using algebraic methods. Suitable for students in Grades 10-12.

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