ECON 10000: Principles of Microeconomics
Practice Set 2 – No Submission Required
EMPIRICAL METHODS
1. Author A of a policy research paper finds that average household income in County 1 increased from
$60,000 to $90,000 from year 2014 to 2018, which coincided the effective period of a stimulus
program. Author A concludes that the policy leads to an increase in income by $30,000." You - a peer
reviewer – find that in nearby County 2, which received no stimulus program, the average household
income increased from $50,000 to $70,000 in the same time period. – Provide comments, be specific
on the results and assumptions needed.
The author A fails to control for other factors – such as time, economic growth that would have
happened without the program, in which similar population, or similar characteristics to compare to
County 2. One needs to find the difference-in-difference effect (90,000 – 60,000) – (70,000 – 50,000)
= 10,000 as the net effect.
CONSUMER THEORY: BUDGET CONSTRAINT, PREFERENCE, OPTIMALITY
Question 1 (Budget Line Basics)
1. Write down the equation for the budget line of two goods, when one has an income of $200, the price
of good X is $5 and the price of good Y is $10. What is the slope of this budget line?
2. What happens to the budget line if the price of good X decreases from $5 to $2.5?
3. What happens to the budget line if the price of good Y increases from $10 to $20?
4. What happens to the budget line if the income decreases to $100?
5. What happens to the budget line if one has an income of $100, the price of good X is $2.5 and the
price of good Y is $5?
Question 2
Suppose Andrew’s income is fixed at $100 and he only consumes apples (good X) and oranges (good Y).
Each apple costs $5 and each orange costs $10.
a. Find the equation for Andrew’s budget constraint and graph it.
b. Is the bundle (7, 6) affordable for Andrew? What about the bundle (8, 8)?
c. At the prices given above, Andrew’s utility maximizing bundle is 12 apples and 4 oranges. Graph
Andrew’s indifference curve.
d. Now suppose that price of an apple increases from $5 to $10. Graph Andrew’s new budget
constraint and new indifference curve given that his new utility maximizing bundle is 7 apples
and 3 oranges.
e. Assuming Andrew maximizes his utility, derive his demand curve for apples.
Question 3 – continued from Question 2
Now suppose apples and oranges are perfect substitutes for Andrew. That is, buying 1 apple brings him
the same satisfaction as buying 1 orange and he is indifferent to which one he buys. Initially assume
prices are $10 for apples and $5 for oranges.
a. If Andrew’s income is $100, what bundle will he consume?
b. If the price of apples drops to $2, what bundle will he consume?
c. Is it possible for Andrew to consume 10 apples and 10 oranges at any price?
Indifference curve is a line with slope 1 since an apple (X) or an orange (Y) is equally substitutable oneto-one. Thus, taking away each unit of Y will need a constant one unit of X to make one equally well-off.
Optimal consumption choice: one would go for the cheaper good to get the most amount. Else, if the price
becomes equal, then any combination of X and Y is fine.
Question 4 – continued from Question 2
Now suppose apples and oranges are perfect complements for Andrew. That is, he always buys exactly 1
orange with each apple (maybe for a fruit salad). If he can’t buy 1 orange with an apple, he will not
purchase an apple at all (and vice versa). Assume prices are $10 for apples and $15 for oranges.
a. If Andrew’s income is $100, what bundle will he consume?
b. If Andrew’s income increases to $200, what bundle will he consume?
c. Is it possible for him to consume 10 apples and 12 oranges at any income level?
Indifference curve is an L-shaped since, having for every one unit of X must be accompanied by exactly
one unit of Y – having 2 Y’s when having only 1 X will be indifferent to having 1 Y and 1 X. One
chooses the optimal consumption bundle where the composition of X and Y equal.
Question 5 (Consumer Theory – Tabulated Question Format)
Suppose good X and good Y are indivisible, that is, must be consumed in exact units.
Quantity (Units)
Good X
Good Y
Total Utility
Marginal Utility
Total Utility
Marginal Utility
0
0
0
1
50
40
2
80
60
3
100
70
4
110
75
a. Fill in the marginal utilities in the table above.
Suppose the price of good X is $5, the price of good Y is $10
b. If the income is $40, what is the optimal consumption bundle of good X and Y?
c. If the income is $25, what is the optimal consumption bundle of good X and Y?
d. If the income is $30, what is the optimal consumption bundle of good X and Y?
Question 6 (Consumer Theory – Conceptual Question)
If price of good X is $10, and price of good Y is $20
1. What is the marginal rate of substitution of the optimal consumption bundle?
2. If currently the marginal rate of substitution (MUX/MUY) is 4, then one is consuming [ too many / too
few ] of good X and [ too many / too few ] of good Y.
3. If currently the marginal rate of substitution (MUX/MUY) is 0.5, then one is consuming [ too many /
too few ] of good X and [ too many / too few ] of good Y.
Question 7 (Consumer Theory – Equation Question Format)
1. There are two goods to be consumed, X and Y, at price PX and PY, respectively. Write down the
condition which yields the maximum happiness. Explain the happiness formula.
2. The marginal rate of substitution is given by MRS = MUX/MUY = 3Y/X. If prices of good X and
good Y are $10 and $5, respectively, and you have the income of $120, what is your optimal
consumption bundle? Also draw the solution in the budget line and indifference curve.
3. If prices of good X and good Y are $20 and $10, respectively, and you have the income of $240,
what is your optimal consumption bundle? (Hint: If it takes you more than 5 seconds for this part,
you must have been zoning out in class!)
Question 8
Andrew consumes chocolate and milk. He has $20 per week to spend on chocolate (good X) and milk
(good Y). A bar of chocolate costs $2 and a bottle of milk costs $2. Initially Andrew’s utility maximizing
bundle is 5 bars of chocolate and 5 bottles of milk.
a. Find the equation for Andrew’s budget constraint and graph it. Graph Andrew’s initial
indifference curve.
b. Suppose the price of a bar of chocolate doubles. Write the new equation of Andrew’s budget
constraint and graph it. With this new budget constraint, Andrew decides to consume 3 bars of
chocolate and 4 bottles of milk.
c. If we want him to be able to afford his initial utility maximizing bundle, how much money does
he need?
d. For Andrew to reach the initial utility level, however he would only need an income of $29. What
is his budget constraint at this income level?
e. If at this imaginary budget constraint he chooses to consume 4 bars of chocolate and 6.5 bottles of
milk, how much of Andrew’s change in consumption of chocolate is due to income effect and
how much of it is due to substitution effect?