# Recitation Sheet 8 1. If the quantity of good ( ) is plotted along the ```ECON 202 Microeconomics
Winter 2008
Economics Department
Faculty of Management Technology
Dr. Abdel-Hameed Nawar
German University in Cairo
Recitation Sheet 8
1.
If the quantity of good ܽ (ܳ௔ ) is plotted along the horizontal axis, the quantity of
good b (ܳ௕ ) is plotted along the vertical axis, the price of good ܽ is ܲ௔ , the price of
good ܾ is ܲ௕ and the consumer's income is ‫ܫ‬, then the slope of the consumer's
budget constraint is:
−
−
−
−
−
ܳ௔ /ܳ௕
ܳ௕ /ܳ௔
ܲ௔ /ܲ௕
ܲ௕ /ܲ௔
‫ܫ‬/ܲ௔ or ‫ܫ‬/ܲ௕
2.
Consider the following table which presents Mina's marginal utility for each good
while exhausting his income.
Bundle
A
B
C
D
i.
ii.
iii.
MUX
2.41
1.5
0.84
0.33
MUY Marginal Rate of Substitution (MRS)
0.25
0.31
0.42
0.66
Fill in the remaining column in the table.
If the price of good X is twice the price of Y, at what consumption
bundle in the table is Mina maximizing his level of satisfaction?
Which market basket entails the largest level of good X consumption?
Why?
3.
Consider the following utility function:
ܷሺܺ, ܻሻ = ܺ ଴.ହ ܻ ଴.ହ
..
Holding the value of Y constant at 9,
i. calculate and graph the marginal utility of X. Is it diminishing?
ii. calculate and graph the total utility function. Is it diminishing?
4.
Sophia consumes two goods, X and Y. The marginal utility of X and the marginal
utility of Y satisfy the following equations:
‫ܷܯ‬௑ = ܻ
‫ܷܯ‬௒ = ܺ.
The price of ܺ is EGP 9, and the price of ܻ is EGP 12.
i. Write an expression for Sophia's MRS.
ii. What is Sophia's optimal demand for X and Y?
iii. Sophia is currently consuming 15 units of ܺ and 10 units of ܻ per
time period. Is she consuming an optimal mix of X and Y?
5.
Consider the following consumption expenditure data at three different price sets,
and three consumption choices. For each pair of prices and demand choices:
i.
ii.
iii.
Draw the budget line and the point of choice.
Apply the Weak Axiom of Revealed Preferences (WARP).
Is there violation of consistent consumer behavior?
Observation PX PY
A
1 2
B
2 1
C
1 1
X
1
2
2
Y
2
1
2
```