Midterm General Questions:
Practice MT Questions:
Homework Questions:
Topical Questions:
Q: I don¡¦t understand why the answer is B for multiple choice #4. I thought it would take 2 units of X for
1 Y to increase the person¡¦s utility since the function is 2x, y
A: Remember
min{A,B} = minimum of A and B.
The optimal bundle always satisfies A = B, because you only get the minimum of the two if they are not equal.
Here
A = 2x, B = y
So the optimal bundle must satisfy
2x = y
Now for any two optimal bundles (x,2x) and (x¡¦,2x¡¦),
(x,2x) - (x¡¦,2x¡¦) = (x-x¡¦, 2(x-x¡¦))
which also satisfy 2x = y.
So the optimal way to increase utility is to take 2 units of y per unit of x.
HW 1 #12 (Govnment control, excess demand)
Q: On the first problem set, I had a question about the answer to 12 d¡K
The answer key says that Qd is 11200 and Qs is 13750, but that the excess
production is 2030. Shouldn¡¦t excess production be 2550?
A: It is a mistype; the correct answer is 2550.
Shape of Indifference Curve
Q: How are we supposed to know the shape of an indifference curve given
any type of situation, whether it is the person liking both goods, hating
both goods, likes good y over good x, likes good x over good y, hates one
good but likes the other, there are many possibilities and I am worried
that we will be given a situation where I will be unable to graph the
indifference curve, so can you please give us all the possibilites of what
the indifference curve will look like or a general idea of a starting
point?
A: Please refer to the Sign of Derivatives (version 2) handout.
Difference between demand curve and indifference curve
Q. What are the differences between a demand curve and an indifference
curve, relating to MRS and marginal benefit and marginal cost?
A: They are very different.
What they represent:
demand curve--quantity
demanded of one good at each given price
indifference curve--all
bundles of goods that give the same given level of utility
Axes:
demand curve--Quantity (Q) on
the horizontal axis and Price (P) on the vertical axis
indifference curve--good
x on the horizontal axis and good y on the vertical axis
Bundle Represented:
demand curve--optimal
quantity at the given price
indifference curve--all
bundles that given the same given level of utility; price and optimality
does not enter at all
MRS applies to indifference curve only; it represents the trade-off of x and y for a given level of utility--if x and y are goods so that more of x gives more utility, we must reduce the amount of y you have in order to make you "as happy as before".
MRS and Px/Py
Q. Given the price of two goods, is it always true that the MRS will be
Px/Py? How will we know which good relates to Px and which good relates to
Py?
A: MRS will always be Px/Py *for the optimal bundle*. Every point on an indifference curve has a certain MRS, which does not equal to Px/Py in general.
Px has to be the price of the good in the horizontal axis and Py that in the vertical axis.
Engel Curve
Q: Can you please explain more about engel curves?
A: Engel Curve represents the relationship between income and quantity demanded of a good. An Engel Curve and quantity demanded of the good on the horizontal axis and income on the vertical axis. Each point on an Engel Curve represents the optimal amount of the good given income.
Practice MT 1 #13, 16, 25 (Elasticity)
Q: Can you explain #13, 16, 21, and 25 from the practice MT more clearly?I don¡¦t quite understand how to solve the problems where they give you the price elasticity of demand and either the price increased by something or the quantity decreased by something, is there a formlia to solve for these types of problems because I know that Ep = change Q/ change P * P/Q, but how am I supposed to solve these questions?
A: The general formula is
% change in Q = elasticity * % change in P
So given % change in P you can find % change in Q and vice versa.
e.g. : % change in P = 0.1 (i.e. P increase by 10%)
elasticity = -1
then% change in Q = -1 * 0.1 = -0.1 (i.e. Q drop by 10%)
e.g. : % change in Q = 0.3 (i.e. Q increase by 30%)
elasticity = -0.5
then % change in P = 1/(-0.5) * 0.3 = -0.6 (i.e. P drop by 60%)
Does the midterm 1 include chapter 4?
A: Yes it does.
Do I need to know Langrangian Multiplier?
Q: I just have one more quick question regarding the MT, I was just
re-reading over the Chapter 4 appendix, and I was just wondering how much
of that we will need to know for the first MT? I have looked at the list
of topics that the Professor put online and there seems to be nothing
about Lagrange Multipliers or Duality. If we do need to know this for the
first MT, can you please send us an example and maybe a brief explaination
because the book does not give a very concrete example and I do not
understand their explaination. Thanks.
A: There is no need to know Langrangian; equal-marginal
principle or equaling the slopes of IC and BC give you the same
answer.
Finding Corner Solution
Q: How, mathematically, can we solve for a corner solution? What do you
mean when you say find U(x, I/Py) and U(I/Px, y) and take the higher of
the two?
A: I made two typos here; what I meant was U(0, I/Py) and U(I/Px, 0).
Let
x,y be two goods
U(x,y) the utility function
Px, Py prices of x and y
I be income
Corner solution corresponds to two bundles (0, I/Px) and (I/Px, 0), where all income is spent on either one of the goods. The optimal solution is the one that gives higher utility.
Thank you for pointing out the mistake.
Convexity, Concavity and MRS
Q: How, mathematically, can we tell whether an IC is concave or convex?
Specifically, can you relate it to dMRS/dx?
A: Convexity is equivalent to d(slope)/dx > 0 ¡Vtake this as a definition in this class.
Since d(MRS)/dx = - d(slope of IC)/dx,
Convex IC <=> d(MRS)/dx < 0
Similarly, concavity is equivalent to d(slope)/dx < 0; so
Cocave IC <=> d(MRS)/dx > 0
Practice MT 1 #21 (Indifference Curve of Grades)
Q: Why is answer not (a)?
A: I think the correct answer is (a) too. First try to see that the two goods in concern are grades
of the two midterms. In Prof. Goodheart's the two goods satisfy U = max{x,y},
while in Prof. Stern's class they are perfect complements--U = min{x,y}. Now
at (x,y) = (20,70) we have x < y. If you have copied the IC graphs of max{.}
and min{.} in section or office hour you should know that for max{.} slope
of IC = 0 when x < y; for min{.} slope of IC = 0 when x > y.
Practice MT 1 #5 (MU and Total Utility)
Q: no answer in solutions, explanation please
A: The answer should be (d). Dminishing MU just means that MU is
decreasing, it could still be positive so that total utility is increasing.
e.g. total utility=ln(x) increasing but MU = 1/x decreasing.
A negative MU, on the other hand, means the same thing as total utility decreasing since MU
is the change in total utility.
Practice MT 1 #7 (MRS and Price Ratio)
Q: For #7, doesn't the answer depend on whether you put food on the horizontal or vertical axis? Seems to me that food on vertical -> MRS price ratio; food on horizontal -> MRS > price ratio.
A: You're right. (c) and (d) are both possible.
Practice MT 1 #13 (Sign of Elasticity of Demand)
Q: For #13, shouldn't the answer be d, since price elasticity is positive? For reference, #16 uses negative price elasticity, and price and quantity demanded have opposite signs, as in #13
A: You're right. My guess is the professor gathered these questions from different sources; one takes the absolute value of the elasticity while the other does not. My advise at this point is to answer the question as if absolute value has *not* been taken. I'll check and make sure that this confusion does not arise in the midterm.
Are Price Indexes, Consumer Surplus and Externalities on the midterm?
Q: Will price indexes (Paasche, Chain-weight, lspeyres...) be covered? Because we didn't have any of that on the Hw. What about 4.6 empirical estimation of demand? Are the topics of consumer surplus and network externalities possible for inclusion?
A:
Price indexes--no. What you need to know is the basic formula for finding
real price.
4.6--no
CS and externality might be on the exam.
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