Consumer Theory

(A) Theory of moral sentiments was written by Adam Smith.
(B) Theories of surplus value were proposed by Karl Marx.
(C) General Theory is by J.M. Keynes.
(D) On liberty was written by J.S. Mill.
Thus, the correct match is (d).

*Public goods* are characterized by two main properties: *non-excludability* (it is not possible to prevent someone from using the good) and *non-rivalry* (one person's use of the good does not reduce its availability to others).

Hence, the correct answer is (b).

For , the order of the expressions from largest to smallest is:

• (A)
• (C)
• (B)
• (D)

Thus, the correct order is

To calculate , we use the formula for the expected value of the square of a random variable:

Substitute the given values: \[ E[X^2]

Thus, the correct answer is

Since the variance of Y is given by:


Thus, the correct answer is (a).

To find ​, we apply the chain rule to :

Thus, the correct answer is (c).

The weighted arithmetic mean is calculated as:

For (B) with weights :

Thus, the correct answer is (b).

Satish spends Rs 13 per day:
- Roti costs Rs 1 and dal costs Rs 2. He consumes 3 rotis and 5 cups of dal per day to meet the calorie intake limit.

Thus, the total expenditure is:

Thus, the correct answer is (a).

Step 1: Budget constraint and utility maximization.
The budget constraint is: To maximize utility, the individual will choose values of and that maximize , subject to the budget constraint.

Step 2: Solve for optimal quantities.
Substitute into the utility function: Maximizing gives and .

Step 3: Conclusion.
The utility maximizing choice is 2.5 units of M and 2.5 units of B.

Step 1: Understand the Expenditure Function.
The expenditure function represents the minimum expenditure required to achieve a certain level of utility, given the prices of goods. It has several key properties that are linked to the behavior of consumers and their responses to price changes.

Step 2: Analysis of options.
- (A) It is homogeneous of degree zero in all prices: This is correct. The expenditure function is homogeneous of degree zero in prices, meaning if all prices change proportionally, the expenditure required to achieve a certain level of utility remains unchanged.
- (B) It represents the maximum expenditure to achieve a given level of utility: This is correct. The expenditure function represents the minimum amount of money required to reach a certain utility level, not the maximum.
- (C) It is non-decreasing in prices: This is correct. As prices increase, the required expenditure to maintain the same utility level will either stay the same or increase.
- (D) It is concave in prices: This is correct. The expenditure function is concave in prices because it reflects the diminishing marginal utility of income as more is spent.

Step 3: Conclusion.
All the options are applicable to the individual's expenditure function, so the correct answer is (A), (B), (C) and (D).