Midterm Review Flashcards
1
Q
What does it mean if a consumer weakly prefers a bundle?
A
She either prefers the bundle or is indifferent to it.
2
Q
What does it mean if a consumer is indifferent between two bundles?
A
The consumer would be just as satisfied, according to her own preferenecs, consuming the bundle (x1, x2) as the bundle (y1, y2)
3
Q
What does it mean that a consumer strictly prefers a bundle?
A
He definitely wants the x-bundle rather than the y-bundle.
4
Q
What is the symbol for strictly preferred bundles?
A
This is the symbol for these bundles.
>
5
Q
What is the symbol for weakly preferred bundles?
A
This is the symbol for these bundles.
≥
6
Q
What does it mean that consumer preference is complete?
A
We assume that any two bundles can be compared. Either one is weakly preferred to the other, or vice versa.
7
Q
What does it mean that consumer preference is reflexive?
A
We assume that any bundle is at least as good as itself; that is, an x-bundle is weakly preferred to itself.
8
Q
What does it mean that consumer preference is transitive?
A
If an x-bundle is preferred to y-bundle, and the y-bundle is preferred to a z-bundle, then the x-bundle is preferred to the z-bundle also.
9
Q
What does monotonicity imply?
A
This assumption implies that more is better. It also implies the slope is negative.
10
Q
What preferences does a convex set imply?
A
This type of set implies that averages are preferred to extremes.
11
Q
What does strict convexity mean?
A
This means that the weighted average of two indifferent bundles is strictly preferred to the two extreme bundles. That is, the indifference curves are rounded: there are no flat spots.
12
Q
What is the slope of the indifference curve?
A
This slope is the marginal rate of substitution (MRS).
13
Q
What two properties do well-behaved preferences have?
A
- monotonic
- convex
14
Q
What can the MRS be interpreted as? The consumer is willing to:
A
It measures how much the consumer is willing to give up of good 2 to acquire more of good 1.
15
Q
What is a monotonic transformation?
A
This is a way of transforming one set of numbers into another set of numbers in a way that preserves the order of the numbers.
16
Q
What are some examples of monotonic transformations?
A
- multiplication by a positive number
- adding any number
- raising u to an odd power
17
Q
What is the utility function for perfect substitutes?
A
u(x1, x2) = ax1 + bx2, where a and b are positive numbers that measure the “value” of goods to the consumer.
18
Q
What is the utility function for perfect complements?
A
u(x1,x2) = min{ax1,bx2} , where a and b are positive numbers that indicate the proportions in which the goods are consumed.
19
Q
What is the utility function for quasilinear preferences? Why called quasilinear?
A
u(x1,x2) = k = v(x1) + x2.
It is quasilinear because it is linear for x2 (good 2), and possibly non-linear for good 1.
20
Q
What is the utility function for Cobb-Douglas?
A
u(x1,x2) = (x1)^c(x2)^d , where c and d are positive numbers that describe the preferences of the consumer.
21
Q
What is a boundary optimum?
A
An optimal bundle that does not have a tangent because it is on an axis.
22
Q
Is tangency a necessary or sufficient condition for optimality?
A
Only necessary. Imagine wavy-line indifference curves: you can have two curves with tangents to the same budget line – and one is clearly less optimal.
23
Q
True or False: The Cobb-Douglas consumer always spends a fixed fraction of his income on each good.
A
True. The size of the fraction is determined by the exponent in the Cobb-Douglas fraction.
24
Q
What is the optimal demand for good 1 for a Cobb-Douglas consumer?
A
x1 = c/(c+d) * (m/p1), or, in the HW terminology, a(m/p1).
25
What is the optimal demand for good 2 for a Cobb-Douglas consumer?
x2 = d/(c+d)\*(m/p2) , or (1-a)(m/p2) in other terminology.
26
What is a **quantity tax**?
This is a tax on the amount consumed of a good; for example, a gasoline tax of 15¢.
27
What is an **income tax?**
Just a tax on income.
28
What is **comparative statics**?
* Comparative = before and after the change in the economic environment
* Statics = not dynamic; we are not concerned with any adjustment process.
29
What is a **normal good**?
The quantity demanded always changes the same way income changes. That is ∆x1/∆m \> 0.
30
What is the **income offer curve**?
This curve illustrates the bundles of goods that are demanded at the different levels of income. That is, it goes through the optimal bundle at each budget constraint: the axes are still x1, x2.
31
What is an **Engel curve**?
* It is a graph of the demand for one of the goods as a function of income, with all prices being held constant. That is, it has axes of x1 and m; it shows for each m, what is the optimal x1?
* Its axes are x1, m.
32
What is the Engel offer curve for good 1 for a quasilinear preference?
A straight vertical line.
33
What is the logic behind Giffen goods?
Say there is a reduction in the price of good 1. This has increased your purchasing power – it is like an income change. You may use it to reduce your consumption of good 1.
34
What is the **price offer curve**?
* Increasing/decreasing the price of good 1 to **rotate budget constraint**
* This curve then connects the tangent points to indifference curves
* It represents the different bundles that would be demanded at different prices for good 1.
35
What is a **demand curve**?
It is a plot of the demand function x1(p1,p2,m), holding p2 and m fixed at some predetermined values. The x and y axes are x1 and p1, respectively.
36
What is the **reservation price**?
It is the price at which the consumer is just indifferent to consuming or not consuming the good.
37
What is a **substitute**?
* Demand for good 1 goes up when the price of good 2 goes up.
* In terms of rates of change, good 1 is a substitute for good 2 if ∆x1/∆p2 \> 0.
38
What is a **complement**?
* The demand for good 1 goes down when the price of good 2 increases.
* In terms of rates of change, ∆x1/∆p2 \< 0.
39
What is WARP? (Weak Axiom of Revealed Preference)
This axiom says the following.
* If a consumer chooses commodity bundle A when she can afford bundle B, then she will never choose bundle B from any budget in which she can also afford A.
* The idea behind this axiom is that if you choose A when you could have had B, you must like A better than B.
* But if you like A better than B, then you will never choose B when you can have A.
40
What does it mean for A to be directly revealed preferred to B? What does WARP say about this?
If somebody chooses A when she can afford B. WARP says if A is directly revealed preferred to B, then B is not directly revealed preferred to A.
41
What is the Law of Demand?
If the demand for a good increases when income increases, then the demand for that good must decrease when its price increases.
42
What is the substitution effect with perfect complements?
The substitution effect is zero.
43
What is the substitution effect with perfect substitutes?
The substitution effect is equal to the total effect.
44
What is the income effect for quasilinear preferences? What is the substitution effect?
The substitution effect is the total effect for quasilinear preferences; thus, the income effect is zero.
45
The Hicks substitution effect keeps _____ constant; the Slutsky substitution effect keeps _______ constant.
* Hicks ∆x^s= utility constant
* Slutsky ∆x^s = purchasing power constant
46
What is a consumer's **endowment**?
The bundle of goods he enters the market with.
47
What is a consumer's **gross demand**?
what he actually ends up consuming: that is, how much of each good he takes home from the market
48
What is a consumer's **net demand**?
The difference between what he actually consumes (gross demand) and his endowment.
49
If the price of a good that a consumer is selling goes down, and the consumer remains a seller, what can we conclude about her welfare?
By revealed preference, we can conclude that it has declined.
50
If the price of a good that a consumer is selling goes down, and the consumer becomes a buyer, what can we conclude about her welfare?
Nothing. She may be better or worse off.
51
If the price of a good that a consumer is buying increases, and she decides to remain a buyer, what can we conclude about her welfare?
By revealed preference, she is definitely worse-off.
52
If the price of a good that a consumer is buying increases, and she decides to become a seller, what can we conclude about her welfare?
Nothing. She may be better or worse off.
53
If the price of a good that a consumer is buying decreases, will she decide to remain a buyer?
Definitely yes.
54
If the price of a good that a consumer is selling increases, will she decide to remain a seller?
Definitely yes.
55
What is the **ordinary income effect**?
In the Slutsky model, when a price falls, you can consume the same bundle and have money left over.
56
What is the **endowment income effect**?
In the buyer/seller model, a price decrease lowers the value of your endowment
57
What is the consumer's **nonlabor income**?
Initial money M that she receives whether she works or not (e.g., investment income, inheritance)
58
What is the budget constraint that takes into account the opportunity cost of leisure?
pC + wR = pC' + wR' , where R is leisure, the left hand side is two choice variables and the right-hand side is two endowment variables
59
What term could be called the opportunity cost of leisure?
the wage rate, w
60
What is a consumer's **full income**?
pC' + wR' ; that is, it measure the value of what the consumer owns – her endowment of consumption goods and her endowment of her own time
61
What is a consumer's **measured income**?
The income she receives from selling off some of her time.
62
What is the slope of the budget constraint pC + wR = pC' + wR'?
The slope is -w/p
63
What is the **real wage**?
w/p , the amount of consumption that the consumer can purchase if she gives up an hour of leisure
64
Why is the labor supply curve backward bending?
The income effect: when the wage rate increases, you have more money that you may spend on leisure.
65
Why does an **overtime wage** lead to an unambiguous increase in labor supply?
It is pure substitution effect. It is the change in the optimal choice by pivoting the budget line around the chosen point.
66
The present value of an endowment can be found where on a budget constraint?
Its x-intercept. This is where you maximize period 1 consumption.
67
The future value of an endowment can be found where on the budget constraint?
Its vertical axis. This is where period 2 consumption is maximized.
68
What is the intertemporal budget constraint accounting for inflation?
c2 = m2 + (1 + rho)(m1 - c1), where rho = real interest rate
69
What does the real interest rate tell you?
How much extra consumption you can get
70
The real interest rate rho is approximately equal to :
r - π ; that is, the nominal rate of interest minus the rate of inflation.
71
A consumption plan is affordable if the present value of consumption equals :
the present value of income
72
If a consumer can freely borrow and lend at a constant interest rate, then the consumer would {always, never} prefer a pattern of income with a higher present value to an income with a lower present value
always
73
What is a **probability distribution**?
It consists of a list of different outcomes––in this case, consumption bundles––and the probability associated with each outcome.
74
What is a contingent consumption plan?
a specification of what will be consumed in each different state of nature––each different outcome of the random process
75
What is the slope of the budget line through the endowment given two possible states of nature?
- gamma / (1 - gamma)
76
When is a function a positive affine transformation?
when it can be written in the form v(u) = au + b, where a \> 0. That is, multiplying by a constant and adding a constant.
77
What happens if you subject an expected utility function to a positive affine transformation?
* it retains preferences
* has the expected utility property
78
What is the independence assumption?
The choices that people plan to make in one state of nature should be independent from the choices that they plan to make in other states of nature.
Utility functions must be additive.
79
The more concave a graph is, the more risk {loving, averse} a consumer is.
He is more risk averse.
80
If a consumer is a risk-averse, expected utility maximizer and if he is offered fair insurance against a loss, then the will optimally choose to :
insure
81
What is risk spreading?
Each consumer spreads his risk over all of the other consumers and thereby reduces the amount of risk he bears.
82
What does the income offer curve look like for quasilinear preferences?
A vertical line
83
For present value of intertemporal budget constraints, what it is the numeraire?
c1 – consumption in the first period
84
85
True or False: Every Giffen good is an inferior good.
True. By the Slutsky equation the total effect of a decrease in price is the
sum of the substitution effect and the income effect. By revealed preference, when the price decreases the SE is positive. Hence the TE can be negative only if the IE is negative. But this negative income effect was a result of an increase in income (from m - (p1 - p1')x1 to m). Hence, the good must be an inferior good.
86
True or False: (g) According to the Law of Demand, the demand for a good is downward sloping.
False. The Law of Demand asserts that if the consumption of a good increases when income increases (holding prices fixed), then demand is downward
sloping. Some inferior goods may fail to have downward sloping demand, and that
does not violate the Law of Demand.
87
True or False: The slope of the budget line has a kink whenever the two goods are perfect complements.
False. Whether the budget set has a kink or not does not depend on the
consumer’s preferences at all. Rather that depends on whether there are nonlinear
taxes or subsidies. One example of kinked budget set is the food stamps subsidy
example from Homework #2.
88
True or False: c) The marginal rate of substitution between two goods equals (minus) the ratio between the marginal utilities
True. The MRS is the slope of the indifference curve at a point. Along an
indifference curve, we have u(x1, x2) = constant for all (x1, x2). Hence,
MU1dx1 + MU2dx2 = 0;
which implies MRS = dx2/dx1 = MU1/MU2.
89
True or False: Every consumer whose preferences are represented by a utility function has transitive preferences.
True. Suppose X ≤ Y and Y ≤ Z, where X, Y and Z are bundles. Let
u be a utility fcn. that represents the consumer’s preference relation . Since u
represents ≤ , we have u(X) ≤ u(Y) and u(Y) ≤ u(Z), which implies u(X) ≤
u(Z). In turn, since u represents ≤, we can conclude that X ≤ Z. Hence, ≤ is
transitive.
90
True or False? The optimal solution of the consumer’s problem depends not only on the consumer’s preferences but also on the particular utility function that the consumer
has. That is, two consumers with different utility functions but same preferences,
may choose different bundles optimally. This is because the marginal rate of substitution is not fully determined by the preference relation, but depends on the utility
function.
False. The optimal solution depends only on the preference relation, not on the particular utility function chosen to represent it. This is because two utility functions represent the same preference if and only if one is a monotone transformation of the other. Another way of seeing this is by noticing that two utility fcns. that represent the same preferences give rise to the same MRS and the optimal is
determined by MRS = - p1/p2.
91
State the Weak and Strong Axioms of Revealed Preference.
A bundle X is said to be directly revealed preferred to a bundle Y if X is chosen
at some prices (p1, p2) at which Y is also affordable. The WARP requires that whenever a bundle X is directly revealed preferred to a bundle Y and Y is chosen when prices are q1 and q2, then X cannot be affordable at prices q1 and q2 (that is, Y is not directly revealed preferred to X).
Now, if a bundle X is directly revealed preferred to a bundle Y and Y is directly revealedpreferred to Z, then we say that X is indirectly revealed preferred to Z. The SARP says that if a bundle X is directly or indirectly revealed preferred to a bundle Y , then Y cannot be directly or indirectly preferred to X.
92
Illustrate (via an example or
picture) why the Strong Axiom is more powerful than the Weak Axiom.
Figure 1 shows that SARP is stronger than WARP. In the picture, X is indirectly revealed
preferred to Z, but not directly. Hence, WARP does not rule out the consumer picking
Z when both X and Z are affordable, but SARP does!
93
Explain the logic
behind the WARP and SARP axioms and why they are automatically satisfied when the consumer’s choices
come from the maximization of a utility function subject to a budget constraint.
The logic behind the axioms is very simple. They can be easily understood when choice comes from the maximization of a utility function subject to a budget constraint: WARP captures the idea that if a bundle X was chosen when bundle Y was also affordable, this can be the case only if X is preferred to Y . Hence, whenever Y is chosen, it must be the case that X is not affordable! The idea of SARP is similar, but it takes a step further than WARP by considering chains of revealed preference and imposing transitivity.
94
Can
you think about reasons why Revealed Preference theory is important to understanding
consumer behavior?
The importance of revealed preference is that it provides consistency conditions on the behavior of consumers in terms of observable data (prices and quantities), without reference to unobservable information such as preferences and incomes. Since consumption behavior that satisfies SARP is equivalent to utility maximizing behavior, revealed preference provides a foundation for the consumer theory that we use in economics (which
is based on utility maximization).
95
What is the final form of the Slutsky equation in terms of rates of change?
96
What is the form of the Slutsky equation accounting for the endowment effect?
97
What is the form of the standard expected utility function? That is, what is the von Neuman - Morgenstern form?
98
What expression indicates the expected return for a risky asset?
The expression inside the following brackets:
99
What do the arrows beneath the graph represent?
From X to Y = substitution effect; from Y to Z = income effect.
100
Draw a graph that shows an income tax that raises the same revenue is better than a quantity tax.
101
Draw a violation of WARP.
102
Draw a violation of SARP.
103
What is the equation for the necessary change in money income for the Slutsky substitution effect?
∆m = x1∆p1
104
True or False: The Law of Demand says that normal goods must have downard-sloping demand curves.
True.
105
Expand ∆x1^s.
∆x1^s = x1(p1',m') - x1(p1, m). That is, is the amt. of good 1 demanded at the new price and the new income (that makes the original bundle affordable) MINUS the original amount demanded at the original price.
106
Expand ∆x1^n. What does it mean?
∆x1^n = x1(p1', m) - x1(p1', m'). That is, it is the amt of good 1 demanded at the new price and original income MINUS the amt. demanded at the new price and new income (i.e., at compensated demand curve).
107
True or Flase: Taxing a consumer and rebating the tax revenues makes the consumer worse-off. Show with a graph.
True.
