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Solutions for Quiz I

Econ5001, Semester 2, 2015

Q1. Colette consumes goods x and y. Her indifference curves are described by the formula y =k/(x + 7). Higher values of k correspond to better indifference curves.

A. Colette likes good y and hates good x.

B. Colette prefers bundle (12, 16) to bundle (16, 12).

C. Colette prefers bundle (8, 5) to bundle (5, 8).

D. Colette likes good x and hates good y.

E. More than one of the above statements are true.

ANS B. Given any consumption bundle (x, y), solve for the value of k , which gives you “level”of the indifference curve. So, for the bundle A = (12, 16) the corresponding vlaue is ka = 16×19while for the bundle B = (16, 12) the corresponding value is kb = 23 × 12. Since ka > kb, Bis true. Moreover for any A = (x, y) and B = (x, y) are such that x > x and y ≥ y, thenka = (x + 7)y > (x

+ 7)y = kb, so A cannot be true and so on.

Q2. Nicks indifference curves are circles, all of which are centered at (12, 12). Of any two indiffer-ence circles, he would rather be on the inner one than the outer one.

Hint: Formula for the square of distance of a point (x, y) from (12, 12) is (x−12)2 + (y−12)2.

A. Nicks preferences are not complete.

B. Nick prefers (16, 17) to (10, 10).C. Nick prefers (10, 17) to (10, 10).

D. Nick prefers (8, 8) to (17, 21).

E. More than one of the above statements are true.

ANS D. Just use the above formula in each case. For instance, the square of the distance of (8, 8) from (12, 12) is (8 − 12)2 + (8 − 12)2 = 32 whereas the same for (17, 21) is (17 − 12)2 +(21 − 12)2 = 106. So the (8, 8) is closer to (12, 12) and is hence preferred.

Q3. If there are only two goods, if more of good 1 is always preferred to less, and if less of good 2

is always preferred to more, then indifference curves

A. slope downward.

B. slope upward.

C. may cross.

D. could take the form of ellipses.

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E. None of the above.

ANS B.

Q4. If two goods are perfect complements,

A. there is a bliss point and the indifference curves surround this point.

B. consumers will only buy the cheaper of the two goods.

C. indifference curves have a positive slope.

D. None of the above.

ANS D. The consumer will choose equal quantities of the two goods, independent of the prices.So not B.

Q5. Preferences are said to be monotonic if

A. all goods must be consumed in fixed proportions.

B. all goods are perfect substitutes.

C. more is always preferred to less.

D. there is a diminishing marginal rate of substitution.


ANS C

Q6. In year 1, the price of good x was $3, the price of good y was $2, and income was $90. In year2, the price of x was $9, the price of good y was $6, and income was $90. On a graph with x

on the horizontal axis and y on the vertical, the new budget line is

A. flatter than the old one and lies below it.

B. flatter than the old one and lies above it.

C. steeper than the old one and lies below it.

D. steeper than the old one and lies above it.


ANS E. The intial slopoe of the budget line is -3/2 and the new slope is -9/6=-3/2, the sameas the old one. The new budget line will have the same slope as the old one.

Q7. Suppose the government imposes a quantity tax uniformly on goods X and Y at the rate t > 0per unit.

A. The budget line shifts outward.

B. If preferences are monotonic, the consumer is worse off.

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C. It has the same effect as reducing the income, keeping the prices fixed.

D. Both B and C.


ANS B This is clear, since the new budget line lies below the old budget line with the X

intercept being M/( px + t) and the Y intercept being M/( py + t). Note D is not the answer,since new slope of the budget line is −( px + t)/( py + t) – if it were teh same as changing theincome, then the slope would have remained at − px/py.

Q8. Suppose A B but the indifference curve through A intersects the one that goes through B .

A. Preferences violate transitivity.

B. Preferences violate completeness.

C. Both A and B.

D. Not enough information to conclude either way.

ANS A.

Q9. Suppose we double the prices and income.

A. The consumer’s demand must remain unchanged.

B. If initially more of X is consumed relative to Y , then even more X will be consumed.

C. If initially more of X is consumed relative to Y , now less of X will be consumed.

D. Any of the three cases is possible, it depends on the initial income.

E. Depends on which good’s price was initially higher, more of that good will now be con-

sumed.

ANS A. We talked about it in class (when I referred to “lack of money illusion”) – with sucha change in income and prices the new budget constraint is the same as the old one.

Q10. The price of Y is fixed at $2. The price of X is $2 for until first 5 units but drops to $1 forevery additional unit. If the income is $20,

A. The budget set is a triangle.

B. The budget set cannot be determined.

C. The budget set is such that there exist consumption bundles A and B both of which arefeasible but their average is not feasible.

D. Need to know the preferences to compute the budget set.


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ANS C. The cost of a consumption bundle (x, y) will be 2x + 2y provided x ≤ 5. If theconsumer chooses more than 5 units, for the first 5 units of X she pays $10 and the remainingx−5 units cost him x−5, since the price has now dropped to $1 for each unit of X . Thereforethe budget constraint is

2x + 2y = 20 if x ≤ 5 (1)

10 + (x− 5) + y = 20 if x > 5

Or x + 2y = 15. if x > 5 (2)

Draw the two lines described by Eq. (1) and Eq. (2) They will look as shown first part of Figure 1. Taking the relevant portions, the budget set is the region described by the thicklines in the other picture. The inward kink shows that we must be able to find two points onthe boundary whose average lies outside the shaded region.

Y

X5

5

Line from Eq. 1

Line from Eq. 2

15

10

Y

X5

5

Line from Eq. 1

Line from Eq. 2

15

10

Figure 1: Budget lines for Q. 10

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