Budget Line and Optimal Choice for CUET Economics

AnswerB · all the bundles he can buy with his income at the given prices

1. The budget set is every bundle with P₁x₁ + P₂x₂ ≤ M: on or inside the budget line.

2. Bundles costing exactly M form the budget line, a part of the set.

AnswerD · P₁x₁ + P₂x₂ = M

1. Spending on good 1 plus spending on good 2 equals the whole income M.

AnswerC · not affordable with the given income

1. Outside the line, the bundle costs more than M, so it is not in the budget set.

AnswerC · price line

1. Its slope is set by the prices of the two goods, so it is also called the price line.

AnswerA · −P₁ ÷ P₂

1. Rewrite the line: x₂ = M ÷ P₂ − (P₁ ÷ P₂) x₁.

2. The coefficient of x₁, −P₁ ÷ P₂, is the slope: the units of good 2 given up to buy one more unit of good 1.

AnswerC · 20 units

1. Spending everything on good 1: M ÷ P₁ = 100 ÷ 5 = 20 units.

2. This is where the budget line meets the good-1 axis.

AnswerC · A and C

1. A costs 8 × ₹5 + 6 × ₹10 = ₹100: on the budget line, affordable.

2. C costs 6 × ₹5 + 4 × ₹10 = ₹70: inside the line, affordable. B costs 10 × ₹5 + 6 × ₹10 = ₹110: beyond the income.

AnswerC · ₹30

1. C (6, 4) costs 6 × ₹5 + 4 × ₹10 = ₹70.

2. Income left = ₹100 − ₹70 = ₹30.

AnswerD · −0.5

1. Slope = −P₁ ÷ P₂ = −5 ÷ 10 = −0.5.

2. Check from the intercepts: −10 ÷ 20 = −0.5. Half a unit of good 2 is given up for each unit of good 1.

AnswerB · (5, 4)

1. (5, 4): 4 × 5 + 5 × 4 = 20 + 20 = 40. It spends exactly the income.

2. (4, 5) costs 41, (6, 4) costs 44 and (10, 2) costs 50, all more than 40.

AnswerA · P₁ = ₹5 and P₂ = ₹3

1. Horizontal intercept = M ÷ P₁, so P₁ = 60 ÷ 12 = ₹5.

2. Vertical intercept = M ÷ P₂, so P₂ = 60 ÷ 20 = ₹3.

AnswerA · Both A and R are true, and R is the correct explanation of A.

1. Both are true.

2. The trade-off R describes is what gives the line its negative slope, so R explains A.

AnswerA · Only I

1. I is true: each costs exactly M.

2. II is false: equal satisfaction is the property of an indifference curve, not of the budget line.

AnswerB · 6

1. The line is 5x₁ + 10x₂ = 50, or x₁ + 2x₂ = 10.

2. x₂ can be 0, 1, 2, 3, 4 or 5, each with x₁ = 10 − 2x₂ a whole number: 6 bundles.

AnswerB · 5 units

1. 10 units of good 1 cost 2 × 10 = ₹20, leaving ₹20.

2. ₹20 ÷ ₹4 = 5 units of good 2.

AnswerC · (4, 8), costing ₹56

1. (4, 8): 24 + 32 = ₹56 < 60, inside the budget line.

2. (6, 6) costs exactly ₹60 (on the line); the other two cost more than ₹60.

AnswerB · Both A and R are true, but R is not the correct explanation of A.

1. A is true: with fixed prices, the trade-off between the goods is the same everywhere on the line.

2. R is not about the budget line at all: the line depends only on income and prices. So R does not explain A.

AnswerB · P₁ = ₹4 and P₂ = ₹4

1. Moving from (2, 8) to (6, 4): 4 more of good 1 for 4 less of good 2, so P₁ = P₂.

2. 2P₁ + 8P₂ = 40 with P₁ = P₂ gives 10P = 40, so both prices are ₹4.

AnswerD · shifts outward, parallel to itself

1. Both intercepts M ÷ P₁ and M ÷ P₂ rise with M.

2. The slope −P₁ ÷ P₂ is unchanged, so the new line is parallel and further out.

AnswerC · It has risen from ₹100 to ₹150

1. Old income = 20 × ₹5 = ₹100 (or 10 × ₹10). New income = 30 × ₹5 = ₹150 (or 15 × ₹10).

2. A parallel outward shift with prices given means income rose.

AnswerA · The price of good 1 has fallen

1. The good-2 intercept (10) is unchanged, so income and P₂ are unchanged.

2. The good-1 intercept rises from 20 to 25, so more of good 1 can be bought: P₁ has fallen.

AnswerB · does not change

1. Intercepts: 2M ÷ 2P₁ = M ÷ P₁ and 2M ÷ 2P₂ = M ÷ P₂, unchanged.

2. Slope: −2P₁ ÷ 2P₂ = −P₁ ÷ P₂, unchanged. The line stays where it was.

AnswerD · rotates inward around its good-1 intercept

1. M ÷ P₂ falls, so the good-2 intercept moves down.

2. M ÷ P₁ is unchanged, so the line pivots on the good-1 axis and becomes flatter.

AnswerA · Both A and R are true, and R is the correct explanation of A.

1. Both are true.

2. Because the slope depends only on prices, an income change moves the line without tilting it: R explains why the shift is parallel.

AnswerD · A is false, but R is true.

1. A is false: only the good-1 intercept moves, so the line rotates; it does not shift in parallel.

2. R is true: M ÷ P₁ rises.

AnswerA · 40 to 30

1. Good-2 intercept = M ÷ P₂: 200 ÷ 5 = 40 before, 150 ÷ 5 = 30 after.

AnswerC · Both I and II

1. Higher income pushes the line out, adding bundles: I is true.

2. A higher price pulls one intercept in, removing bundles: II is true.

AnswerA · 20 to 10, and the line becomes steeper

1. M ÷ P₁: 100 ÷ 5 = 20 before, 100 ÷ 10 = 10 after.

2. Slope P₁ ÷ P₂ rises from 0.5 to 1: the line pivots inward on the good-2 axis and gets steeper.

AnswerA · Only I

1. I is true: money saved on good 1 buys more of it.

2. II is false: the most of good 2, M ÷ P₂, does not depend on P₁.

AnswerB · ₹4

1. On AC, the most of good 1 is 25 units, so P₁ = M ÷ 25 = 100 ÷ 25 = ₹4.

AnswerA · The good-1 intercept stays at 20; the good-2 intercept rises from 30 to 45

1. Good-1 intercept: before 120 ÷ 6 = 20, after 180 ÷ 9 = 20, unchanged.

2. Good-2 intercept: before 120 ÷ 4 = 30, after 180 ÷ 4 = 45. The line pivots outward on the good-1 axis.

AnswerC · Both I and II

1. The slope's size is P₁ ÷ P₂. A lower P₂ raises it (steeper): I is true.

2. A lower P₁ lowers it (flatter): II is true.

AnswerA · Both A and R are true, and R is the correct explanation of A.

1. Both are true, and R explains A: equal percentage rises leave both ratios, and so both intercepts, unchanged.

AnswerD · bundles of two goods that give the consumer the same satisfaction

1. The consumer is indifferent among all bundles on one curve: each is as good as any other.

2. Bundles costing the same lie on a budget line; what can be produced lies on a PPC.

AnswerD · can never cut each other

1. If they crossed, the crossing bundle would give two different levels of satisfaction at once, which is impossible.

AnswerA · a higher level of satisfaction

1. With monotonic preferences, more of at least one good and no less of the other is better.

2. A higher curve has such bundles, so it means more satisfaction.

AnswerB · the marginal rate of substitution diminishes along it

1. As the consumer has more of good 1 and less of good 2, he gives up fewer units of good 2 for each extra unit of good 1.

2. A falling MRS makes the curve flatter as it moves right: convex to the origin.

AnswerC · 5 units of good 2 per unit of good 1

1. From A (2, 15) to B (3, 10): good 1 rises by 1, good 2 falls by 5.

2. MRS = ΔY ÷ ΔX = 5 ÷ 1 = 5 units of good 2 per unit of good 1.

AnswerC · 2 units of good 2 per unit of good 1

1. From B (3, 10) to C (5, 6): good 1 rises by 2, good 2 falls by 4.

2. MRS = 4 ÷ 2 = 2 units of good 2 per unit of good 1, lower than the 5 from A to B: the MRS diminishes.

AnswerB · the consumer values each extra unit of good 1 less as he has more of it

1. Moving down the curve the consumer has more good 1 and less good 2, so he will part with less good 2 for each further unit of good 1.

2. C to D: good 2 falls by 3 while good 1 rises by 5, so MRS = 3 ÷ 5 = 0.6.

AnswerD · a bundle with more of at least one good and no less of the other is preferred

1. Monotonic preferences mean more is better: a bundle with more of something, and less of nothing, ranks higher.

AnswerA · an indifference map

1. An indifference map shows many indifference curves, each for a different level of satisfaction.

AnswerC · to keep satisfaction the same, more of one good must come with less of the other

1. With monotonic preferences, more of good 1 alone would raise satisfaction.

2. To stay on the same curve, the consumer must give up some of good 2: a downward slope.

AnswerD · A is false, but R is true.

1. A is false: a falling MRS makes the curve convex, not concave.

2. R is true.

AnswerA · Only I

1. I is true.

2. II is false: the MRS is the consumer's own willingness to exchange; the market rate is the price ratio, the slope of the budget line.

AnswerD · Q is preferred to P, so Q lies on a higher indifference curve

1. Q has more of good 1 and the same of good 2.

2. Monotonic preferences rank it higher, so it is on a higher indifference curve.

AnswerD · (3, 7) and (5, 4)

1. Bundles on one curve must trade more of one good for less of the other.

2. (5, 4) has more of good 1 and less of good 2 than (3, 7). Each of the others has more of one and no less of the other (or less of both), so it is strictly better or worse.

AnswerA · Only I

1. I is true: the map has one curve per level of satisfaction.

2. II is false: equal cost describes a budget line; bundles on one indifference curve can cost very different amounts.

AnswerA · Both A and R are true, and R is the correct explanation of A.

1. Both are true.

2. If two curves crossed, the shared bundle would have to be on a higher and a lower level at once. Since higher curves mean more satisfaction (R), that is impossible: R explains A.

AnswerB · 1.5 bananas per apple

1. He gives up 10 − 7 = 3 bananas for 6 − 4 = 2 more apples.

2. MRS = 3 ÷ 2 = 1.5 bananas per apple.

AnswerC · straight lines with a constant MRS of 2

1. A constant MRS means a constant slope: the indifference curve is a straight line.

2. This happens when the two goods are perfect substitutes for him.

AnswerB · the budget line just touches the highest indifference curve it can reach

1. The consumer wants the highest satisfaction he can afford: the highest indifference curve that still has a point on the budget line.

2. That curve just touches the line: at the point of tangency, MRS = P₁ ÷ P₂.

AnswerB · MRS = P₁ ÷ P₂

1. At the tangency, the slope of the indifference curve (MRS) equals the slope of the budget line (P₁ ÷ P₂).

2. The rate at which the consumer is willing to swap equals the rate at which the market lets him swap.

AnswerA · At E, on IC₂, with 10 units of good 1 and 5 of good 2

1. IC₃ lies wholly beyond the budget line, so it cannot be reached.

2. IC₁ can be reached but is lower. IC₂ is the highest curve the line touches, at E (10, 5).

AnswerD · Moving along the budget line towards E puts him on a higher indifference curve at the same cost

1. Where IC₁ cuts the line, the bundles are affordable, but the line continues inside better curves.

2. Spending the same income, he can reach IC₂ at E, so those points are not optimal.

AnswerA · Both A and R are true, and R is the correct explanation of A.

1. Both are true.

2. Every point on the budget line costs exactly M, so lying on it (R) is why the whole income is spent (A).

AnswerC · Both I and II

1. I is the tangency condition, MRS = P₁ ÷ P₂: true.

2. II is true too: convexity is what makes the tangency point the best one, not just any touching point.

AnswerC · A-II, B-IV, C-I, D-III

1. The budget line's slope is the market rate, P₁ ÷ P₂; the indifference curve's slope is the MRS.

2. The good-1 intercept is M ÷ P₁, and the tangency marks the optimum.

AnswerA · only ranks bundles, without measuring utility in numbers

1. Indifference-curve analysis needs only to know which bundle is preferred, not by how many utils.

AnswerA · IC₃

1. IC₃ lies wholly beyond the budget line: none of its bundles is affordable.

AnswerA · Both A and R are true, and R is the correct explanation of A.

1. Both are true, and R explains A.

AnswerC · 0.5 unit of good 2 per unit of good 1

1. At the optimum, MRS = P₁ ÷ P₂ = 5 ÷ 10 = 0.5.

2. This also equals the size of the budget line's slope: 10 ÷ 20.

AnswerD · Buy more of good 1 and less of good 2

1. He would give up 3 units of good 2 for one more unit of good 1, but the market asks only P₁ ÷ P₂ = 2.

2. So swapping good 2 for good 1 raises his satisfaction; as he does, his MRS falls towards 2.

AnswerB · buy less of good 1 and more of good 2

1. The market rate is P₁ ÷ P₂ = 2: one unit of good 1 costs 2 units of good 2.

2. He values a unit of good 1 at only 1 unit of good 2, less than it costs, so he should give up good 1 for good 2.

AnswerD · A is false, but R is true.

1. A is false: inside the line some income is unspent, and spending it on more goods raises satisfaction.

2. R is true, and is exactly why a point inside cannot be the optimum.

AnswerB · on a higher indifference curve, where a new, parallel budget line touches one

1. Higher income shifts the budget line out in parallel.

2. The consumer can now reach a higher indifference curve; the new optimum is where the new line touches the highest one it reaches.

AnswerD · A-III, B-I, C-IV, D-II

1. MRS above 2: good 1 is worth more to him than it costs, so buy more. MRS = 2: tangency, the optimum.

2. MRS below 2: good 1 is worth less than it costs, so buy less; the further below, the larger the move.