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I see the image contains an economics-related problem, likely concerning budget constraints, equilibrium, and changes in consumer behavior based on price changes. Let's break down the questions:

1. **Derive the budget constraint**:
   The budget constraint for two goods, X and Y, given the prices and income, can be expressed as:

   \[
   P_x \cdot X + P_y \cdot Y = I
   \]

   where:
   - \( P_x \) is the price of good X
   - \( P_y \) is the price of good Y
   - \( X \) is the quantity of good X
   - \( Y \) is the quantity of good Y
   - \( I \) is the income

   From the question:
   - \( P_x = 80 \)
   - \( P_y = 60 \)
   - \( I = 800 \)

   Substituting the values:

   \[
   80 \cdot X + 60 \cdot Y = 800
   \]

   This is the budget constraint equation.

2. **Identify the equilibrium point when the consumer allocates the budget equally between the two goods**:
   If the consumer spends the budget equally between the two goods, we can assume that half of the income is spent on X and half on Y. Therefore:

   \[
   \frac{I}{2} = 80 \cdot X \quad \text{and} \quad \frac{I}{2} = 60 \cdot Y
   \]

   Solving each:
   \[
   80 \cdot X = 400 \quad \Rightarrow \quad X = \frac{400}{80} = 5
   \]
   \[
   60 \cdot Y = 400 \quad \Rightarrow \quad Y = \frac{400}{60} \approx 6.67
   \]

   Thus, the equilibrium point when the budget is equally allocated is \( X = 5 \) and \( Y = 6.67 \).

3. **Derive the new budget constraint when the price of X increases to 100**:
   If the price of X rises to Rs. 100, the new budget constraint becomes:

   \[
   100 \cdot X + 60 \cdot Y = 800
   \]

4. **Determine the new equilibrium when the consumer spends Rs. 250 on X and Rs. 480 on Y after the price of X changes**:
   After the price change, the consumer spends Rs. 250 on X and Rs. 480 on Y. We can calculate the quantities of X and Y:

   \[
   X = \frac{250}{100} = 2.5 \quad \text{and} \quad Y = \frac{480}{60} = 8
   \]

   So, the new equilibrium point is \( X = 2.5 \) and \( Y = 8 \).

5. **Explain the consumer's response to the price change**:
   Typically, when the price of a good increases (in this case, X), the consumer reduces the quantity of that good (as observed with X decreasing from 5 to 2.5). Simultaneously, the consumer may increase the consumption of the relatively cheaper good (Y increased from 6.67 to 8).

Would you like more details or have any questions on this?

### Related questions:
1. How is the slope of the budget constraint related to the prices of the goods?
2. What happens to the budget line when income increases but prices remain constant?
3. How can you graphically represent the changes in the equilibrium caused by the price increase of X?
4. What does it mean when a consumer allocates their budget equally between two goods?
5. Can the consumer's equilibrium be affected by a change in preferences as well as prices?

### Tip:
When analyzing consumer behavior, always check how changes in prices and income affect both the slope and position of the budget line to understand their spending adjustments.

A consumer selects two goods, i.e., X and Y for consumption having prices with Rs. 80 and 60 respectively and fixed income with Rs. 800.
1. Derive budget constraint.
2. Identify his equilibrium point when he allocates entire budget equally on two goods.
3. Let price of X good falls to Rs. 60. Sketch the new budget constraint.
4. When he spends Rs. 250 on X good and Rs. 480 on Y good after fall in price of X good. Show the new equilibrium to the consumer.
5. Derive consumer's response. Also derive nature of X and Y.

Analyze a consumer's budget constraint and equilibrium with price changes. Includes solving budget allocation between goods, deriving new budget constraints, and consumer behavior response. Suitable for undergraduate economics students.

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