Economics 11: Problem Set 6
Maurizio Mazzocco
Due: 11/13/2025 by 9:30 am
Problem 1
Jeff consumes burrito bowls (B) and chicken tenders (C). His Marshallian demand for
burrito bowls is
∗ I 0.4 p0.3
C
B = 0.7
5pB
(a) Find and interpret the income elasticity of demand for burrito bowls (eB,I ) and in-
terpret the value. Are burrito bowls an inferior or normal good?
(b) Find the own price elasticity of demand for burrito bowls (eB,pB ) and interpret the
value. Does the own price elasticity of demand for burrito bowls depend on the
value of pB ?
(c) Find the cross price elasticity of demand for burrito bowls (eB,pC ) and interpret the
value. Are burrito bowls and chicken tenders gross substitutes or gross comple-
ments?
Solution
(a) The income elasticity of demand for burrito bowls is:
∂B ∗ I
eB,I = ·
∂I B ∗
I −0.6 pC
0.3
5p0.7
B
= 0.4 · 0.7
· I · 0.4 0.3
= 0.4
5pB I pC
Alternatively, you could note that ln(B ∗ ) = 0.4 ln(I) + 0.3 ln(pC ) − ln(5) − 0.7 ln(pB ),
∗)
and eB,I = ddln(B
ln(I)
= 0.4. Since eB,I > 0, burrito bowls are a normal good. When
income increases by 1%, consumption of burrito bowls increases by 0.4%.
1
, (b) The own price elasticity of demand for burrito bowls is:
∂B ∗ pB
eB,pB = ·
∂pB B ∗
I 0.4 p0.3
C 5p0.7
B
= −0.7 · 1.7
· p B · 0.3
= −0.7
5pB I 0.4 pC
∗
Alternatively, you could note that dd ln(B )
ln(pB )
= −0.7. At the optimal consumption level,
if price of burrito bowls increases by 1%, demand for burrito bowls will decrease by
0.7%. It does not depend on pB , i.e. the own price elasticity of demand for burrito
bowls is constant in pB .
(c) The cross price elasticity of demand for burrito bowls is:
∂B ∗ pC
eB,pC = ·
∂pC B ∗
−0.7
I 0.4 pC 5pB0.7
= 0.3 · · pC · 0.4 0.3 = 0.3
5p0.7
B I pC
∗
Alternatively, you could note that dd ln(B )
ln(pC )
= 0.3. Since eB,pC > 0, burrito bowls and
chicken tenders are gross substitutes. When the price of chicken tenders increases
by 1%, consumption of burrito bowls increases by 0.3%.
Problem 2
Suppose the preferences of an individual are represented by a quasilinear utility function
√
U (x, y) = 8 x + y
Let px = 2, py = 4, and I = 160.
(a) Calculate the Marshallian demands for x and y.
(b) Find and interpret the income elasticity of demand for x and for y.
(c) Find and interpret the own price elasticity of demand for x and for y.
(d) Find and interpret the cross price elasticity of demand for x and for y.
2
Maurizio Mazzocco
Due: 11/13/2025 by 9:30 am
Problem 1
Jeff consumes burrito bowls (B) and chicken tenders (C). His Marshallian demand for
burrito bowls is
∗ I 0.4 p0.3
C
B = 0.7
5pB
(a) Find and interpret the income elasticity of demand for burrito bowls (eB,I ) and in-
terpret the value. Are burrito bowls an inferior or normal good?
(b) Find the own price elasticity of demand for burrito bowls (eB,pB ) and interpret the
value. Does the own price elasticity of demand for burrito bowls depend on the
value of pB ?
(c) Find the cross price elasticity of demand for burrito bowls (eB,pC ) and interpret the
value. Are burrito bowls and chicken tenders gross substitutes or gross comple-
ments?
Solution
(a) The income elasticity of demand for burrito bowls is:
∂B ∗ I
eB,I = ·
∂I B ∗
I −0.6 pC
0.3
5p0.7
B
= 0.4 · 0.7
· I · 0.4 0.3
= 0.4
5pB I pC
Alternatively, you could note that ln(B ∗ ) = 0.4 ln(I) + 0.3 ln(pC ) − ln(5) − 0.7 ln(pB ),
∗)
and eB,I = ddln(B
ln(I)
= 0.4. Since eB,I > 0, burrito bowls are a normal good. When
income increases by 1%, consumption of burrito bowls increases by 0.4%.
1
, (b) The own price elasticity of demand for burrito bowls is:
∂B ∗ pB
eB,pB = ·
∂pB B ∗
I 0.4 p0.3
C 5p0.7
B
= −0.7 · 1.7
· p B · 0.3
= −0.7
5pB I 0.4 pC
∗
Alternatively, you could note that dd ln(B )
ln(pB )
= −0.7. At the optimal consumption level,
if price of burrito bowls increases by 1%, demand for burrito bowls will decrease by
0.7%. It does not depend on pB , i.e. the own price elasticity of demand for burrito
bowls is constant in pB .
(c) The cross price elasticity of demand for burrito bowls is:
∂B ∗ pC
eB,pC = ·
∂pC B ∗
−0.7
I 0.4 pC 5pB0.7
= 0.3 · · pC · 0.4 0.3 = 0.3
5p0.7
B I pC
∗
Alternatively, you could note that dd ln(B )
ln(pC )
= 0.3. Since eB,pC > 0, burrito bowls and
chicken tenders are gross substitutes. When the price of chicken tenders increases
by 1%, consumption of burrito bowls increases by 0.3%.
Problem 2
Suppose the preferences of an individual are represented by a quasilinear utility function
√
U (x, y) = 8 x + y
Let px = 2, py = 4, and I = 160.
(a) Calculate the Marshallian demands for x and y.
(b) Find and interpret the income elasticity of demand for x and for y.
(c) Find and interpret the own price elasticity of demand for x and for y.
(d) Find and interpret the cross price elasticity of demand for x and for y.
2
