PROBLEM SET- 2
Solve the following questions.
1. Heidi receives utility from two goods, goat’s milk (m) and strudel (s), according to the utility
function U(m, s) = m.s
a). show that increases in the price of goat’s milk will not affect the quantity of strudel Heidi
buys; that is, show that ∂s/∂pm = 0.
b). Show also that ∂m/∂ps = 0.
c). Use the Slutsky equation and the symmetry of net substitution effects to prove that the
income effects involved with the derivatives in parts (a) and (b) are identical.
d). Prove part (c) explicitly using the Marshallian demand functions for m and s.
2. Hard Times Burt buys only rotgut whiskey and jelly donuts to sustain him. For Burt, rotgut
whiskey is an inferior good that exhibits Giffen’s paradox, although rotgut whiskey and jelly
donuts are Hicksian substitutes in the customary sense. Develop an intuitive explanation to
suggest why a rise in the price of rotgut must cause fewer jelly donuts to be bought. That is,
the goods must also be gross complements.
3. Donald, a frugal graduate student, consumes only coffee (c) and buttered toast (bt ). He buys
these items at the university cafeteria and always uses two pats of butter for each piece of
toast. Donald spends exactly half of his meager stipend on coffee and the other half on
buttered toast.
a). In this problem, buttered toast can be treated as a composite commodity. What is its price
in terms of the prices of butter (pb ) and toast (pt )?
b). Explain why ∂c/∂pbt = 0.
C). Is it also true here that ∂c/∂pb and ∂c/∂pt are equal to 0?
4. Mr. Consumer allows himself to spend $100 per month on cigarettes and ice cream. Mr. C’s
preferences for cigarettes and ice cream are unaffected by the season of the year.
(a). In January, the price of cigarettes was $1 per pack, while ice cream cost $2 per pint. Faced
with these prices, Mr. C bought 30 pints of ice cream and 40 packs of cigarettes. Draw Mr. C’s
January budget line with blue ink and label his January consumption bundle with the letter J.
(b) In February, Mr. C again had $100 to spend and ice cream still cost $2 per pint, but the price
of cigarettes rose to $1.25 per pack. Mr. C consumed 30 pints of ice cream and 32 packs of
cigarettes. Draw Mr. C’s February budget line with red ink and mark his February bundle with
the letter F. The substitution effect of this price change would make him buy (less, more, the
same amount of) cigarettes and (less, more, the same amount of) ice cream. Since this is true
PROBLEM SET- 2
and the total change in his ice cream consumption was zero, it must be that the income effect
of this price change on his consumption of ice cream makes him buy (more, less, the same
amount of) ice cream. The income effect of this price change is like the effect of an (increase,
decrease)(-------------) in his income. Therefore, the information we have suggests that ice
cream is a(n) (normal, or inferior, or neutral) good.
(c) In March, Mr. C again had $100 to spend. Ice cream was on sale for $1 per pint. Cigarette
prices, meanwhile, increased to $1.50 per pack. Draw his March budget line. Is he better off
than in January, worse off, or can you not make such a comparison? How would your answer
to the last question change if the price of cigarettes had increased to $2 per pack?
5. Douglas Cornfield’s demand function for good x is x (px, py, m) = 2m/5px. His income is $1,000,
the price of x is $5, and the price of y is $20. If the price of x falls to $4, then his demand for x
will change from ( ) to ( ).
(a) If his income were to change at the same time so that he could exactly afford his old
commodity bundle at px = 4 and py = 20, what would his new income be? What would be
his demand for x at this new level of income, at prices px = 4 and py = 20?
(b) The substitution effect is a change in demand from ( ) to ( ). The income effect of the
price change is a change in demand from ( ) to ( ).