PE = Qd = QS if QD = -8p+220.000 and QS = 10p+50.000

To find the equilibrium price (PE) where quantity demanded (QD) equals quantity supplied (QS), we need to set the two equations equal to each other and solve for \( p \).

Given:
- \( QD = -8p + 220,000 \)
- \( QS = 10p + 50,000 \)

At equilibrium:  
\[ QD = QS \]

### Step-by-step solution:

1. Set the equations for \( QD \) and \( QS \) equal to each other:
   \[
   -8p + 220,000 = 10p + 50,000
   \]

2. Combine like terms:
   \[
   220,000 - 50,000 = 10p + 8p
   \]
   Simplifying:
   \[
   170,000 = 18p
   \]

3. Solve for \( p \) by dividing both sides by 18:
   \[
   p = \frac{170,000}{18}
   \]
   \[
   p = 9,444.44
   \]

So, the equilibrium price \( p \) is approximately **9,444.44**.

### Step 4: Solve for the equilibrium quantity (Q)
Now that we know the price, substitute \( p = 9,444.44 \) into either the \( QD \) or \( QS \) equation. Let's use the \( QS \) equation:

\[
QS = 10p + 50,000
\]
\[
QS = 10(9,444.44) + 50,000
\]
\[
QS = 94,444.44 + 50,000 = 144,444.44
\]

Thus, the equilibrium quantity (Q) is approximately **144,444.44**.

### Final answer:
- Equilibrium price (PE): **9,444.44**
- Equilibrium quantity (Q): **144,444.44**

Would you like further details or have any questions?

Here are 5 related questions to expand on this concept:
1. How would the equilibrium change if the supply equation became \( QS = 15p + 70,000 \)?
2. What happens to the equilibrium price if there is an increase in demand?
3. How does a price ceiling affect the equilibrium in this market?
4. What role does elasticity play in adjusting equilibrium after a price change?
5. How would the introduction of a subsidy for suppliers shift the equilibrium?

**Tip**: When solving for equilibrium in markets, always ensure that both supply and demand functions are clearly defined, as changes in one can affect the equilibrium significantly.

Learn how to calculate the equilibrium price and quantity using linear supply and demand equations: QD = -8p + 220,000 and QS = 10p + 50,000. This problem provides a step-by-step solution and explores algebraic concepts in supply and demand, suitable for high school students.

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