a) Market research on T.K VENTURES has revealed the following information about their market for chocolate bars: their demand function can be represented by the equation QD = 1600 – 300P, where QD is the quantity demanded and P is the price. T. K. VENTURE

To analyze the market for T.K. VENTURES chocolate bars, let's break down the problem step by step.

### a) Calculate Equilibrium Price and Quantity

The equilibrium in the market is reached when the quantity demanded (QD) equals the quantity supplied (QS). We start with the given functions:

**Demand Function:**
\[ QD = 1600 - 300P \]

**Supply Function:**
\[ QS = 1000 + 700P \]

To find the equilibrium price (P), we set \( QD \) equal to \( QS \):
\[
1600 - 300P = 1000 + 700P
\]

Now, we will collect like terms:
\[
1600 - 1000 = 700P + 300P
\]
\[
600 = 1000P
\]

Now, solve for \( P \):
\[
P = \frac{600}{1000} = 0.6
\]

Now that we have the equilibrium price, we can calculate the equilibrium quantity by substituting \( P \) back into either the demand or supply function. We'll use the demand function:
\[
QD = 1600 - 300(0.6)
\]
\[
QD = 1600 - 180 = 1420
\]

Therefore, the equilibrium price and quantity are:
- **Equilibrium Price (P)** = 0.6
- **Equilibrium Quantity (Q)** = 1420

### b) Diagram to Illustrate Equilibrium Condition

To illustrate the equilibrium condition, we can draw a simple diagram with the price on the vertical axis and quantity on the horizontal axis.

1. The demand curve, represented by the equation \( QD = 1600 - 300P \), would slope downwards from left to right.
2. The supply curve, represented by the equation \( QS = 1000 + 700P \), would slope upwards from left to right.
3. The intersection point of the two curves will represent the equilibrium price (0.6) and equilibrium quantity (1420).

Unfortunately, I cannot directly draw diagrams, but I can describe how to create it:
- **X-axis**: Quantity (Q)
- **Y-axis**: Price (P)
- Draw the downward sloping demand curve and upward sloping supply curve. Mark the intersection at point (1420, 0.6).

### c) Market Situation with a Price of 0.5

Now, if the market price is 0.5, we can analyze the market situation. 

1. **Determine the Quantities at Price = 0.5**:
   - **Quantity Demanded (QD)** at \( P = 0.5 \):
   \[
   QD = 1600 - 300(0.5) = 1600 - 150 = 1450
   \]

   - **Quantity Supplied (QS)** at \( P = 0.5 \):
   \[
   QS = 1000 + 700(0.5) = 1000 + 350 = 1350
   \]

2. **Analyze the Results**:
   - At a price of 0.5, the quantity demanded (1450) exceeds the quantity supplied (1350).
   - This indicates a **shortage** in the market of chocolate bars, as consumers are willing to buy more than producers are willing to sell at that price.

### Diagram for a Price Below Equilibrium

For the diagram:
- In the same diagram with demand and supply, represent the horizontal line at P = 0.5.
- Mark the new quantities:
  - QD at 1450 (above the intersection).
  - QS at 1350 (below the intersection).

The area between the QD and QS at the price of 0.5 demonstrates the market's shortage, as the demand is greater than the supply.

### Summary

- **Equilibrium Price and Quantity**: P = 0.6, Q = 1420
- **Market Price of 0.5**: Leads to a shortage with QD = 1450 and QS = 1350. The market is demanding more than it's supplying.