To determine the equilibrium price (Pe) and quantity (Qe), we need to find the point where the quantity supplied equals the quantity demanded.

Approach:

1. From the table:

   • Prices: $5, $10, $15, $20, $25.
   • Supply and demand values are listed for each price.

2. Equilibrium condition:

   • At equilibrium, Number of supply = Number of demand.
   • Look for the price where supply equals demand in the table, or interpolate between two prices if necessary.

Observation:

No price directly matches where supply equals demand. Thus, we calculate the equilibrium using linear equations based on the trends:

Supply equation:

Supply increases as price increases. Using two points (5, 30) and (25, 450), the supply equation is: $Q_s = m_s P + b_s$

• Slope $m_s = \frac{450 - 30}{25 - 5} = 21$.
• $b_s = 30 - (21)(5) = -75$.

Thus, the supply equation is: $Q_s = 21P - 75$

Demand equation:

Demand decreases as price increases. Using two points (5, 175) and (25, 75), the demand equation is: $Q_d = m_d P + b_d$

• Slope $m_d = \frac{75 - 175}{25 - 5} = -5$.
• $b_d = 175 - (-5)(5) = 200$.

Thus, the demand equation is: $Q_d = -5P + 200$

Solve for equilibrium:

At equilibrium, $Q_s = Q_d$: $21P - 75 = -5P + 200$ $26P = 275 \implies P_e = \frac{275}{26} \approx 10.58$

Substitute $P_e$ into either equation to find $Q_e$: Using $Q_s = 21P - 75$: $Q_e = 21(10.58) - 75 \approx 147.18$

Thus, equilibrium price $P_e \approx 10.58$, and equilibrium quantity $Q_e \approx 147.18$.

Do you want a detailed breakdown of how interpolation works or further assistance?

Related Questions:

1. How do we derive linear supply and demand equations from points?
2. What happens to equilibrium if supply or demand shifts?
3. How does elasticity affect equilibrium price and quantity?
4. Can equilibrium exist at multiple points under certain conditions?
5. What are the implications of disequilibrium (excess supply or demand)?

Tip: Always use interpolation when exact data isn't available to identify trends between points.