Calculating Consumer Income from Expenditure

Understanding how a consumer's income relates to their spending is a fundamental concept in economics. When a consumer spends their entire income on goods and services, their total income is equal to their total expenditure.

In this problem, the consumer buys specific quantities of two goods, X and Y, at given prices and spends her entire income. To find her income, we need to calculate the total amount she spent on both goods.

The total expenditure is calculated by summing the cost of good X and the cost of good Y.

• Expenditure on Good X = Quantity of Good X $\times$ Price of Good X
• Expenditure on Good Y = Quantity of Good Y $\times$ Price of Good Y
• Total Expenditure (Income) = Expenditure on Good X + Expenditure on Good Y

We are given the following information:

• Quantity of Good X = 8 units
• Price of Good X = ₹7 per unit
• Quantity of Good Y = 10 units
• Price of Good Y = ₹9 per unit

Now, let's calculate the expenditure on each good:

Expenditure on Good X \( = 8 \text{ units} \times ₹7/\text{unit} = ₹56 \)

Expenditure on Good Y \( = 10 \text{ units} \times ₹9/\text{unit} = ₹90 \)

The consumer's total income is the sum of these expenditures:

Total Income \( = ₹56 + ₹90 = ₹146 \)

Based on the quantities and prices provided, the consumer's income is calculated to be ₹146.

Examining the Options for Consumer Income

Let's look at the given options:

• Option 1: ₹142
• Option 2: ₹146
• Option 3: ₹143
• Option 4: ₹145

Our calculation based on the provided numbers yields an income of ₹146. Comparing this with the options, we see that Option 2 matches our calculated value.

However, if we consider the possibility that the income is indeed ₹142 (as presented in Option 1), this would imply that the total expenditure must equal ₹142. With the given prices, this would mean the quantities purchased must satisfy the equation: \( 8 \times ₹7 + 10 \times ₹9 = ₹142 \). As calculated earlier, this gives \( ₹56 + ₹90 = ₹146 \), which is not equal to ₹142.

Therefore, based on the explicit quantities and prices provided in the question, the income is ₹146.

Revision Table: Key Concepts

Additional Information on Consumer Budget

This problem relates to the concept of a budget constraint in consumer theory. A budget constraint shows all the combinations of goods and services that a consumer can purchase given their income and the prices of the goods.

The equation for a budget line with two goods (X and Y) is:

\( P_X \cdot Q_X + P_Y \cdot Q_Y = I \)

Where:

• \( P_X \) is the price of good X
• \( Q_X \) is the quantity of good X
• \( P_Y \) is the price of good Y
• \( Q_Y \) is the quantity of good Y
• \( I \) is the consumer's income

In this question, we were given \( P_X = ₹7 \), \( Q_X = 8 \), \( P_Y = ₹9 \), and \( Q_Y = 10 \). We used these values to find \( I \).

\( I = ₹7 \cdot 8 + ₹9 \cdot 10 \)

\( I = ₹56 + ₹90 \)

\( I = ₹146 \)

The point (8 units of X, 10 units of Y) lies exactly on the budget line, as the consumer spends her entire income. The slope of the budget line is \( -P_X / P_Y \), which represents the rate at which the consumer can trade one good for another in the market.