The Budget Set includes all consumption bundles that satisfy p_1x_1+p_2x_2≤Mbecause they are affordable. The Budget Line consists of bundles where the consumer spends the entire income, satisfying p_1x_1+p_2x_2=M. An Affordable Bundle has total expenditure less than or equal to the consumer's income, while an Unaffordable Bundle costs more than the available income. Therefore, the correct matching is: 1 → a 2 → b 3 → c 4 → d

The budget constraint is p₁x₁ + p₂x₂ ≤ M. If both prices and income double, the new constraint becomes 2p₁x₁ + 2p₂x₂ ≤ 2M. Dividing by 2 gives the original constraint p₁x₁ + p₂x₂ ≤ M. Therefore, the budget set remains unchanged.

On the budget line, the consumer spends the entire income. If x₁ increases, expenditure on x₁ rises by p₁∆x₁. To remain on the same budget line, expenditure on x₂ must fall by an equal amount. Therefore, the net change in total expenditure must be zero: p₁∆x₁ + p₂∆x₂ = 0

Starting from p₁x₁ + p₂x₂ = M, subtract p₁x₁ from both sides to get p₂x₂ = M - p₁x₁. Then divide by p₂ to obtain x₂ = M/p₂ - (p₁/p₂)x₁.

The budget set includes all affordable bundles. Therefore, quantities must be non-negative, meaning x₁ ≥ 0 and x₂ ≥ 0. Also, total expenditure must be less than or equal to income: p₁x₁ + p₂x₂ ≤ M. Statement III is incorrect because bundles costing more than income are outside the budget set.

The consumer has an income of Rs 20, and both bananas and mangoes cost Rs 5 per unit. (1,2): Cost = (1×5) + (2×5) = Rs 15 ✓ (4,0): Cost = (4×5) = Rs 20 ✓ (3,2): Cost = (3×5) + (2×5) = Rs 25 ✗ (2,2): Cost = (2×5) + (2×5) = Rs 20 ✓ Since Rs 25 exceeds the available income of Rs 20, bundle (3,2) is not part of the budget set.

If the consumer spends the entire income (M) only on bananas, then the quantity of bananas that can be purchased is obtained by dividing income by the price of bananas. [ x_1=\frac{M}{p_1} ] This represents the horizontal intercept of the budget line.

The horizontal intercept is given by: [ \frac{M}{p_1} ] It represents the maximum quantity of bananas that the consumer can purchase by spending the entire income on bananas. At this point: x₂ = 0 It depends only on income (M) and the price of bananas (p₁). A change in p₂ does not affect the horizontal intercept.

A point on the vertical axis indicates that the consumer purchases only mangoes. Therefore, [ x_1=0 ] The maximum quantity of mangoes that can be purchased at this point is M/p₂.

The vertical intercept represents the maximum quantity of mangoes that can be purchased when all income is spent on mangoes. Vertical Intercept=M/p_2=40/8=5 Hence, the consumer can purchase 5 units of mangoes.

The slope of the budget line is −p₁/p₂. Its absolute value is p₁/p₂, which shows how many units of good 2 must be sacrificed to obtain one more unit of good 1 in the market. Therefore, it represents the price ratio of the two goods.

The negative slope of the budget line means that if the consumer increases consumption of x₁, she must reduce consumption of x₂ to keep total expenditure equal to income M. It reflects the trade-off between two goods under a fixed budget. Statement I is incorrect because prices are positive. Statement III is incorrect because negative slope does not mean income is falling.

At any point on the budget line, the consumer spends her entire income. If she wants one more banana, she must pay p₁ for it. Since income is fixed, she must reduce expenditure on mangoes by the same amount, p₁. This explains the market substitution rate.

To buy one additional banana, the consumer must reduce mango expenditure by p₁. Since each mango costs p₂, the quantity of mangoes sacrificed is: {p_1}/{p_2} Thus, the market substitution rate is determined by the price ratio.

The budget line equation is: x_2 = M p2 - p1 p2 x1 When income changes from M to M', while prices remain constant: The slope term −p₁/p₂ remains unchanged. The intercept term changes from M/p₂ to M'/p₂. Prices p₁ and p₂ remain constant. Therefore, the budget line shifts parallel inward or outward depending on whether income falls or rises.

When the consumer's income decreases while prices remain constant, both the horizontal and vertical intercepts of the budget line decrease proportionally. Since the slope remains unchanged, the budget line shifts parallel inward. Consequently, the budget set (the collection of affordable bundles) shrinks, meaning its area decreases.

When only the price of bananas (p₁) decreases: The absolute value of the slope (p₁/p₂) decreases. The budget line becomes flatter. Since neither income (M) nor the price of mangoes (p₂) changes, the vertical intercept (M/p₂) remains unchanged. Therefore, only Statements I and II are correct.

When the price of bananas increases: The vertical intercept (M/p₂) remains unchanged because income and the price of mangoes do not change. The horizontal intercept (M/p₁) decreases because bananas become more expensive. The budget line pivots inward around the vertical intercept and becomes steeper. Hence, the correct sequence is 1 → 2 → 3.

A point below the budget line leaves some income unspent and cannot be optimal under monotonic preferences. The tangency point represents the consumer's equilibrium bundle. A point above the budget line is unaffordable. The highest attainable indifference curve touching the budget line gives the best affordable consumption bundle. Thus, the correct matching is 1-a, 2-b, 3-c, 4-d.

A point above the budget line represents a bundle whose total expenditure is greater than the consumer's income (p₁x₁ + p₂x₂ > M). Since these bundles lie outside the budget set, they are unaffordable. Therefore, even if they lie on a higher indifference curve, the consumer cannot choose them. Hence, both the Assertion and the Reason are true, and the Reason correctly explains the Assertion.