Let's break down the given problem step-by-step:

Part (a) - Identifying the demand and supply functions:

You are given two lines:

1. Line 1: Begins at point $D(0, 100)$ and passes through $C(300, 250)$.
2. Line 2: Begins at point $A(0, 400)$ and passes through $C(300, 250)$.

• The supply function typically has a positive slope, indicating that as the quantity $q$ increases, the price $p$ also increases. This reflects the fact that suppliers are willing to supply more at higher prices.
• The demand function usually has a negative slope, meaning that as the price $p$ decreases, the quantity $q$ demanded increases. This is because consumers are willing to buy more at lower prices.

Based on this:

• Function 1 (which starts at $D(0, 100)$ and passes through $C(300, 250)$) has a positive slope, so it is the supply function.
• Function 2 (which starts at $A(0, 400)$ and passes through $C(300, 250)$) has a negative slope, so it is the demand function.

So:

• Function 1 is the supply function.
• Function 2 is the demand function.

Part (b) - Identifying the equilibrium point:

The equilibrium point is where the supply and demand curves intersect. This represents the price and quantity where the amount suppliers are willing to supply equals the amount consumers are willing to purchase.

From the given description, the two curves intersect at Point C $(300, 250)$.

• Point C is the equilibrium point.

Part (c) - Determining the price and quantity at equilibrium:

At the equilibrium point $C(300, 250)$:

• The price is the $p$-coordinate, which is $250.
• The quantity is the $q$-coordinate, which is 300 units.

Final Answer:

• (a)
  • Function 1: Supply
  • Function 2: Demand
• (b)
  • The equilibrium point is Point C.
• Price at equilibrium: $250
• Quantity at equilibrium: 300 units

Would you like more details or have any further questions?

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Here are 5 related questions to expand on this concept:

1. How do you derive the equations for the supply and demand curves from the graph?
2. What happens to equilibrium if the supply curve shifts due to external factors?
3. How would you calculate consumer surplus using this graph?
4. What does it mean for the market if the price is set above or below the equilibrium price?
5. How can you use algebra to solve for equilibrium algebraically instead of graphically?

Tip: In economics, equilibrium represents an efficient market where there is no shortage or surplus. Understanding how shifts in supply or demand affect this point is crucial for analyzing market dynamics.