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Econ 100A Midterm #1
Review Session
Hemaxi Desai, Chen Meng, Michael Nguyen-Mason, Amy Qin
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Student Learning Center Econ Program
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Courses offered: Econ 1, 2, 100A, 100B, 136, 140
●
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●
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100A pod: Friday 3-4 pm |
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Agenda
Main Topics:
1.
2.
3.
4.
5.
6.
7.
Indifference Curve
Inferior vs. normal, complements vs. substitutes
Utility Maximization
Income and Substitution Effect
Marshallian and Hicksian Demand
Elasticity
Engel curve
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T/ F Questions
1.
Hicksian demand curve is more elastic than Marshallian demand curve when
a good is normal.
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Effect of Falling Prices on Different Goods
●
Normal Good
As your income goes up, you consume more of it.
Substitution and Income effect go into the same
direction.
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Inferior Good
As your income goes up, you consume less of it.
Substitution and income effect go into opposite
direction
●
Giffen Good
A special type of inferior good
As price of a good rises, you consume more of it.
Substitution and income effect go into opposite
direction and the magnitude of income effect is
larger.
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FALSE!
BC0
●
Marshallian demand is the normal
demand curve that accounts for both
substitution and income effect, while
Hicksian is just substitution effect.
●
For a normal good, substitution and
income effect go in the same
direction so quantity change for
Marshallian demand is larger
compared to the Hicksian demand
(given a price change).
●
Therefore, Marshallian demand
curve is flatter.
BC1
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T/ F Questions
2. If pizza and soda are perfect complements, the utility maximization point
would be a corner solution.
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Perfect complements | Perfect Substitutes
●
Perfect complements: one’s well-being depends on having both goods in set quantities
●
Perfect substitutes: one is indifferent between consuming one good or another (you consume the
cheaper good)
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FALSE!
Corner vs Interior Solution:
★
Perfect Complements:
Utility Maximization is where the budget line is tangent to the highest indifference curve
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T/ F Questions
3. Alice likes sushi (the x-axis good) and the more money she has, the more sushi
she will eat. If the price of sushi increases, the Engel curve for sushi shifts to the
right.
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FALSE!
●
Engel curves relate the QUANTITY (X) of a
good consumed to INCOME (Y) holding price
constant.
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NORMAL: the Engel curve is upward sloping
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INFERIOR: the Engel curve is downward
sloping
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Higher income, larger quantity -> normal good
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At any given income level, as the price of the
good increases, Alice will consume less of it
(both income and substitution effect)
●
Shift to the left
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T/ F Questions
4. Along a single linear demand curve, elasticity is increasing as quantity
consumed is increasing.
Price elasticity of Demand (PED) refers to the degree of responsiveness of quantity
demanded of a good given a change in the price of the good itself, ceteris paribus.
Elasticity Value
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FALSE!
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T/ F Questions
5. The optimal bundle obtained by minimizing expenditure is different than the
optimal bundle obtained by maximizing utility.
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FALSE!
The bundle for expenditure minimization and profit maximization are the same →
the tangent point of the highest indifference curve and given budget constraint.
We solve both problems by the Lagrangian method.
For expenditure minimization, utility is held constant as the constraint; for profit
maximization, income is held constant.
Profit maximization: L = U(X,Y) + λ(I - Px X - Py Y)
Cost / Expenditure minimization: L = I(X, Y) + λ(U - U(x))
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T/ F Questions
6. If Hicksian demand is downward sloping, then Marshallian demand must be
downward sloping as well.
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FALSE!
Hicksian demand (compensated demand curve): substitution effect
-
Utility held constant
Always downward sloping
Marshallian demand: substitution effect + income effect
-
Income held constant
Downward sloping for normal good & inferior good
Upward sloping for Giffen good
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T/ F Questions
7. If price elasticity of demand is negative then the good must be normal.
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FALSE!
Elasticity =( Q / P) * P/Q
P, Q > 0
Price elasticity of demand is negative:
Q/ P<0
Price increases → Quantity decreases
=> the good can be either a normal good, or an inferior good (Income up, quantity
decreases)
=> However, the good cannot be a Giffen good
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T/F Questions
8. A good cannot be both normal and inferior.
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False!
Backward bending engel curve.
For a certain level of income, Corolla would be a normal good. However, once
your income gets high enough, you might want something more fancy and Corolla
became inferior.
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T/F Questions
9. An inferior good cannot be represented with a Cobb-Douglas utility function.
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True!
Recall the optimal bundle for Cobb-Douglas:
X* = αI/Px
Y* = (1- α)I/Py
When we take the partial derivative of Qx or Qy with respect to I, we always get a
positive number, so they are normal goods.
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Cobb Douglas Utility Function
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T/F Questions
10. If cereal and milk are perfect complements and the price of milk
decreases, the substitution effect is smaller than the income effect.
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True!
For perfect complements, substitution effect is always 0.
And as we can see on the graph, the
income effect is always positive, which
means perfect complements are always
normal goods.
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T/F Questions
11. An increase in income will shift both the uncompensated and
compensated demand curves.
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True!
When income increases, the original budget constraint
shifts out and the original bundle contains more of both X
and Y. Therefore, if we look at the demand graph, at a
certain price of Px, we will buy more X, so it can be
considered as an parallel shift to the right of both demand
curves.
Easier way to think is to follow the ideas in Econ 1. When a
variable that’s not on the axis changes, the curve will shift.
Here, since income increases and on the axis, we only
have Qx and Px, both of the demand curves shifts upward.
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Short Answer #1
What is the ECONOMIC meaning of the equality MUx/PX = MUy/PY? Explain when it might not be
valid.
The marginal utility per dollar spent on good X is equal to the marginal utility per dollar spent on good Y.
(The last dollar spent on either good, gives the same level of marginal utility)
This means that the slopes of MRS and MRT are equal --- profit maximization bundle.
This is violated whenever we have corner solution. (Ex. Perfect Substitute.)
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Short Answer #2
Trace the demand curve for a Giffen good by using the 2-panel graph. On the top
panel, find two optimal bundles for different prices. On the bottom panel, plot the
corresponding demand curve. Make sure your axes are labeled.
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Effect on Giffen Goods
C
A
●
When the price of X decreases, the budget
constraint rotates to the right, and substitution
effect is the horizontal distance between
bundle A and B.
●
Because the question is asking for a Giffen
good, we know the income effect is to the
opposite direction and is larger than
substitution effect, so we end up with final
bundle C to the left of A.
●
On the lower graph, we have two bundles A
and C for before and after the price change of
X. Therefore, we can trace the demand curve
by connecting those two bundles.
B
A
C
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Short Answer #3
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Solution
α
α
α
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Short Answer #4
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Short Answer #4 a Solution
Pr increases
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Short Answer #4
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Short Answer #4 b solution
Income increase
B
A
BC0
BC1
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Short Answer #5
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Short Answer #5 solution
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Long Answers #1
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Long Answers #1
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Long Answers #1
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Long Answers #1
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Long Answers #1
→
→
→
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Long Answers #1
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Long Answers #1
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Long Answers #1
d. How much more money is needed to maintain the same utility?
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Long Answers #1
In order to find the substitution bundle, we need to find bundle at NEW price,
OLD utility
We already calculated the substitution bundle in part c, which is (X, Y) = (4.2,
7.5). Therefore, the total expenditure = (2 x 4.2) + (1 x 7.5) = $15.9
Thus, 15.9 - 11 = 4.9, which is the extra amount that is needed to keep the
same utility.
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Long Answers #1
e. How much more money is needed to afford the original bundle?
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Long Answers #1
The original bundle is (6,5) and so the total expenditure after the price change
would be 6 x 2 + 5 x 1 = 17
Thus, 17 - 11 = 6, which is the extra amount needed.
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Long Answers #1
f. Set up and solve the expenditure minimization problem.
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Long Answers #1
Plug the relationship in the budget constraint E = Px * X + Py * Y to find the optimal bundle.
Y* = (E - Py) / 2Py X* = (Py + E) / 2Px
Plug the optimal bundle into utility function U = X(1+Y) = [(Py + E)/2px] [1 + (E-Py)/2Py]
= (Py + E)^2 / 4PxPy
Then solve for E:
E = sqrt(4UPxPy)-py
Note:
When we take the partial derivative of E with respect to Px and Py, we get the compensated demand
function.
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Long Answer Question #2
Jason is in charge of the government agency that supplies electricity to the city. Electricity is sold in units
of kilowatt-hours (kwh). The price per kwh is PE = $1.00. Assume that the average resident of the city has
a monthly budget of $200 to spend on either kilowatts of electricity, E, or dollars-worth of all other goods,
Y. To make sure that very poor residents get their basic electricity needs met, the city council has recently
passed a law whereby each resident can use up to 25 kwh of electricity for free each month. Jason has to
decide how to set the exact pricing policy for this law. He has two plans, plan A and plan B.
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Long Answer Question #2
Jason is in charge of the government agency that supplies electricity to the city. Electricity is sold in units
of kilowatt-hours (kwh). The price per kwh is PE = $1.00. Assume that the average resident of the city has
a monthly budget of $200 to spend on either kilowatts of electricity, E, or dollars-worth of all other
goods, Y. To make sure that very poor residents get their basic electricity needs met, the city council has
recently passed a law whereby each resident can use up to 25 kwh of electricity for free each month.
Jason has to decide how to set the exact pricing policy for this law. He has two plans, plan A and plan B.
So from this question, we can deduce the following:
I = 200, PE = $1.00 , Py = $1.00
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Long Answer - Part A
Plan A) For the first 25kwh each month, electricity is free. For any additional units after 25, the price is
$1.00.
i) Compute the monthly budget constraint for the average resident under Plan A.
ii) Graph this budget constraint, with electricity on the horizontal axis.
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Long Answer - Part A
a)
For the first twenty-five units of E there is no expenditure on E so the consumer can spend their
entire budget on all other goods. Thus, the budget constraint is simply Y = I/Py = 200/1 = 200. For
units of E above twenty-five the budget constraint must take expenditure on E into account, but the
first twenty-five units don’t add to expenditure.
Thus, the budget constraint is (E − 25) + Y = 200.
Solving for Y we get Y = 225 − E, so the full budget constraint in terms of Y is:
Y = 200
if E ≤ 25
Y = 225 – E
if E > 25
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Long Answer - Part B
Plan B) If a resident uses 25 kwh or less in a given month, it is free. But if a resident uses more than 25
kwh in a given month, they have to pay the regular price, $1.00, for every kwh they use, including the first
25.
i) Compute the monthly budget constraint for the average resident under Plan B.
ii) Graph this budget constraint on a new graph, with electricity on the horizontal axis.
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Long Answer - Part B
≤
−
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Long Answer - Part C (1 of 4)
Question: Jason wants to minimize the increase in electricity consumption caused by the new law. Without
knowing anything about consumer’s preferences, which plan would you advise him to choose? Explain.
Nature of Good: Electricity should be considered a normal good because with an increase in income, people
should consume more electricity. Some may argue that electricity is a quasilinear good since an increase in
income may not affect the level of consumption, but we will see that this would not change our response
significantly.
Nature of Consumers: The different possible consumption bundles are
●
●
●
Consumers who are currently using less than 25kwh per month
Consumers who are using around 25kwh per month
Consumers who are using above 25kwh per month
Let us now assess what happens for each type of consumers under Plan A and Plan B. After which, we will
compare the two outcomes.
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Long Answer - Part C (2 of 4)
Question: Jason wants to minimize the increase in electricity consumption caused by the new law. Without
knowing anything about consumer’s preferences, which plan would you advise him to choose? Explain.
PLAN A:
Consumers who are currently using less than 25kwh per month
●
Consumption should go up under Plan A because budget constraint has been pushed out.
Intuitively, if the first 25kwh is free for me and I only start paying the regular rate after I hit the 25kwh
benchmark, I would most certainly increase my electricity consumption (or at the least not change
the level of electricity consumption).
●
Using this same intuition, we realize consumers who are using around 25kwh per month or above
25kwh per month would behave similarly since their budget constraint has been pushed out.
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Long Answer - Part C (3 of 4)
Question: Jason wants to minimize the increase in electricity consumption caused by the new law. Without
knowing anything about consumer’s preferences, which plan would you advise him to choose? Explain.
PLAN B:
Consumers who are currently using less than 25kwh per month & using around 25kwh per month
●
May not change or increase until at most 25kwh per month, if not they have to start paying. In fact,
those using slightly more than 25kwh per month may choose to reduce their consumption to 25kwh
so that they don’t pay anything (possibly gain a higher overall utility).
Consumers who are currently using more than 25kwh per month:
●
No change to their original budget constraint since they are paying for every unit of electricity as
before.
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Long Answer - Part C (4 of 4)
Summary Table of Economic Outcomes for Plan A & Plan B
Consumers Usage /
Electricity Plans
< 25kwh
~ 25kwh
> 25kwh
Overall Effect
Plan A
No change or
increase
consumption
No change or
increase
consumption
No change or
increase consumption
At best no change in
electricity
consumption but
likely to increase
overall
Plan B
No change or
increase
consumption but
limited to 25kwh
Those slightly above
25kwh likely to
reduce consumption
No change
More likely to reduce
electricity
consumption overall
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Long Answers #3
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Long Answers #3
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Long Answers #3
1.
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Long Answers #3
2. Let I = 1000, k = 100, a = 0.5 and Py = 2
a.
b.
C.
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Long Answers #3
3. Now let I = 100 and the rest of the parameters are the same
a.
b.
I = 100 < Py * k = 200 so in this situation, this is a corner solution.
c.
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Long Answers #4
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Long Answers #4
⅔
⅓
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Long Answers #4
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Long Answers #4
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Long Answers #4
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Long Answers #4
For Marshallian demand: e = Elasticity = ( Q / P) * P/Q
= (-200/2)*(2/400)
= -0.5
For Hicksian demand: e = Elasticity =( Q / P) * P/Q
= (-100/2)*(2/400)
= -0.25
The absolute value of the Marshallian price elasticity of demand is bigger, which
means it is more elastic.
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Long Answers #4
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Long Answers #4
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Any Questions?
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Student Learning Center Econ Program
●
Courses offered: Econ 1, 2, 100A, 100B, 136, 140
●
Work closely with Professors from each course to tailor materials accordingly
●
Weekly Drop-in hours: Mon - Thurs, 10am-2pm
●
Pod Tutoring and Review Sessions for Midterms and Finals
●
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