Brainscape's Knowledge GenomeTM

Browse over 1 million classes created by top students, professors, publishers, and experts.


See full index

Economic Methods > All Notes > Flashcards

All Notes Flashcards

1
Q

Illustrate the effect of applying a tax / subsidy to the equation Qs= α+βP for the production of a good.

A

Supply post Tax: Qst=α+β(p−t)

Supply Post Subsidy: Qsk= α+β(p+k)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
2
Q

Illustrate the effect of applying a tax / subsidy to the equation Qd= θ+μP for the demand of a good.

A

Post Tax: Qdt= θ+μ(P+t)

Post Sub: Qdk= θ+μ(P−k)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
3
Q

How do you calculate the consumers and producers share of a tax?

A

Consumers Share:
Actual: CP= PT - P
%: CP/T * 100

Producers Share:
Actual: M = £T - CP
%: M/T * 100

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
4
Q

What are the income consumption equations?

A

Y = C + S
C = f(Y) = a+bY
C = f(Y^d)
Y^d=Y−T

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
5
Q

What is the consumption and savings function and what is special about their gradient?

A

C =β+θY
θ = MPC
S = (1−θ)Y −β
(1-θ) = MPS

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
6
Q

What is youngs theorem?

A

Both second order cross partials are equal.

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
7
Q

What is the small increment formula?

A

y=f(z,t)

Dy=∆y=(∂y/∂z×dz)+(∂y/∂t×dt)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
8
Q

How do you perform implicit differentiation?

A 
Set the whole equation = z
Apply SIF (∂z/∂x dx)+(∂z/∂y dy)=0  ∂z/∂x dx+∂z/∂y dy=0
Rearrange to give dy/dx=−∂z/∂x÷∂z/∂y
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
9
Q

In a function with two variables, what SOC layout gives a maximum?

A

Zxx<0
Zyy<0
(Zxx×Zyy)−(Zxy)^2>0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
10
Q

In a function with two variables, what SOC layout gives a minimum?

A

Zxx>0
Zyy>0
(Zxx×Zyy)−(Zxy)^2>0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
11
Q

How would you calculate MR if only given PED and price?

A

R=P(1+(PED)^(−1))

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
12
Q

What is the quotient rule?

A

dy/dx= (u’v−v’u)/v^2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
13
Q

How do you prove DRM using differentiation?

A

QL>0 & QLL<0

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
14
Q

How do you prove returns to scale?

A 
Q=AK^αL^β
Then multiplying by t
 Q=A(tK)^α (tL)^β=  At^α (K)^α  t^β (L)^β= t^(α+β)  AK^αL^β=t^(α+β) Q0
Constant Returns to Scale: α+β=1
Decreasing Returns to Scale: α+β<1
Increasing Returns to scale: α+β>1
How well did you know this?
1
Not at all
2
3
4
5
Perfectly
15
Q

What are the two types of constrained optimisation?

A

Primal: Max Utility subject to a budget constraint
Duality: Min Budget constraint given utility

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
16
Q

How might you solve a constrained optimisation problem?

A

Substitution: Sub Constraint into origninal and differentiate
Lagrangian: Create new equation, partial differentiation, (1)/(2) and sub into 3

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
17
Q

How would you create an indirect utility function?

A

Sub the values of x and y back into the orginal

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
18
Q

What is the conformity rule?

A

If A =mxn and B= nxk then C=AB=mxk and n=n

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
19
Q

How do you find the determinant of a 2x2 matrix?
AB
CD

A

AD-BC

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
20
Q

How do you find the determinant of a 3x3 matrix

A

Find the minors, find the co factors and evaluate them

A11|A11|-A12|A12|+A13|A13|

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
21
Q

How do you evaluate a co factor?

A

If m+n is even +

If m+n is odd -

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
22
Q

What is a co-factor matrix?

A

A matrix where every factor is the determinant
+-+
-+-
+-+

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
23
Q

What is an adjoint matrix?

A

A cofactor matrix that has been transposed

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
24
Q

How do you find a co-factor matrix 2x2?

A

The minors are the diagonal oposits

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
25
Q

What is the formula for an inverse matrix?

A

A^-1= 1/|A| x adjA

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
26
Q

How do you find the adjoint of a 2x2 matrix?

A

Switch the principle diagonals and negate the others

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
27
Q

What are the two methods for solving matrix equations?

A

Inverse & Cramers Rule

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
28
Q

How do you solve a matrix equation using the inverse method?

A

x=A^-1*B

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
29
Q

How do you solve a matrix equation using cramers rule?

A

Create a new matrices by subbing b into a on each column

Perform |Ai|/|A|

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
30
Q

What are the three reasons for money to not be in a bank account?

A

Mt- Transactions- Keeping money available for transactions
Mp- Precautionary- May need money quickly in future
Mz- Speculative- Tasking a risk, US currency markets are speculating on if the FED will rise IR

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
31
Q

What is the structure of a hessian?

A

xx xy xz
yx yy yz
zx zy zz

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
32
Q

How do you calculate the determinant of a 3x3 hessian matrix?

A

After entering values, calculate:
H1 = |a11|
H2 = |2x2|
H3 = |3x3|

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
33
Q

How do you evaluate the hessian?

A

If H1>0 & H2>0 and…. Hn>0⁆ Then we have a positive definite and this fulfils the SOC for a minimum.

If H1<0 & H2>0 and…. H_n>0
Alternating ( if odd <0 and if even > 0)
Then we have a negative definite and this fufulls the SOC for a maximum

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
34
Q

When would you use the hessian?

A

For unconstrained optimisation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
35
Q

When would you use the bordered hessian?

A

For constrained optimisation

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
36
Q

What is the structure of the bordered hessian?

A

0 g1 g2
g1 xx xy
g2 yx yy

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
37
Q

How do you evaluate the bordered hessian?

A

Postive definitive if |H̅ |<0 this gives a relative minimum

Negative definitive if |H̅ |>0 this gives a relative maximum

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
38
Q

Evaluate y=∫e^ϑx dx

A

1/ϑ e^ϑx+c

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
39
Q

How could the investment over time be shown?

A

I(t) = dK(t)/dt =K’(t)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
40
Q

What is the formula for consumer surplus?

A

The integral of the function - PQ

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
41
Q

What is the formula for producer surplus?

A

PQ- the integral of the function

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
42
Q

What is the formula for the gini coefficent?

A

2∫x−lorenz(x)dx between 0 and 1

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
43
Q

What is the formula for the multiplier?

A

1/(1-MPC)

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
44
Q

What is the difference between a population and a sample?

A

Population is all firms under investigation, sample is the observed set

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
45
Q

What are the conditions for a random sample?

A

Each member of the population is chosen strictly by chance
Each member of the population is equally likely to be chosen
Every possible sample of 𝑛 objects is equally likely to be chosen

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
46
Q

What are the three category’s of data?

A

Categorical
Discrete
Continuous

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
47
Q

Name some methods for displaying Categorical Variables?

A

Frequency Distribution
Bar Chart
Pie Chart

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
48
Q

Name some methods for displaying numerical variables?

A

Frequency distribution
Histogram
Scatter Plot

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
49
Q

How do you calculate a mean?

A

Sum of all divided by number

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
50
Q

How do you calculate the median

A

Order data

N+1/2

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
51
Q

What is the mode?

A

Most common

How well did you know this?
1
Not at all
2
3
4
5
Perfectly
52
Q

What are the skews of data?

A 
Left:
Tail on left
Mean < Median
Right
Tail on Right
Mean > Median
53
Q

How do you calculate quartiles?

A

0.25(n+1)

54
Q

What is a 5 number summary?

A 
Minimum
First quartile
Median
Third quartile
Maximum
55
Q

Name the measures of Central Tendency

A

Mean, Median, Mode, Quartiles

56
Q

Name the measures of variability

A

Range, IQR, Variance, Standard Deviation, Coefficient of Variation, Weighted Mean & Variance

57
Q

How do you calculate the Population Variance?

A

Mean of the squared deviations form the mean

58
Q

How do you calculate the sample Variance?

A

Same as population but divide by n-1

59
Q

How do you calculate the standard deviation>

A

Square-root the variance

60
Q

How do you calculate the coefficient of variation?

A

Standard Deviation / Mean x 100

61
Q

What are the measures of relationship between variables?

A

Co variance and correlation coefficent

62
Q

Define Random Experiment, Basic Outcome, Sample Space and Event

A 
Random Experiment – a process leading to an uncertain outcome
Basic Outcome – a possible outcome of a random experiment 
Sample Space (𝑆) – the collection of all possible outcomes of a random experiment
Event (𝐸) – any subset of basic outcomes from the sample space
63
Q

What is an intersection of events?

A

If A and B are two events, 𝐴∩𝐵 is all outcomes that belong to both

64
Q

Define mutally exclusive.

A

No outcomes in common

𝐴∩𝐵= 0

65
Q

What is a union of events?

A

If A and B are two events, 𝐴∪𝐵, is all outcomes that belong to either

66
Q

Define Collectivley Exhaustive,

A

If A and B are all events in the sample sapce

67
Q

Define Complements.

A

The complement of A is all events that are not A

=1-A

68
Q

What are the three types of probability?

A

Classical

Relative frequency Subjective

69
Q

What is classical probability?

A

Assumes all events are equally likely to occur

70
Q

How would you calculate the total number of orderings?

A

x!

71
Q

What is a permutation and how is it calculated?

A

The number of possible arrangements when x objects are selected from n (Order matters)
n!/(n-x!)

72
Q

What is a combination and how is calculated?

A

The number of possible arrangements when x objects are selected from n (Order does not matter)
n!/(x!(n-x)!

73
Q

What is relative frequency probability?

A

The proportion of times the event occurs from a large number of trials

74
Q

What is subjective probability?

A

Opinons

75
Q

What are the probability postulates?

A

If 𝐴 is any event in the sample space 𝑆, then 0≤P(A)≤1

𝑃(𝑆)=1

76
Q

What is the addition “or” rule?

A

P(AUB)=P(A) +P(B) -P(AnB)

77
Q

What is the complement rule?

A

P(A)+P(A)=1

78
Q

How would you calcuate conditional probability?

A

The probablility of A given B is

P(A|B)=P(AnB)/P(B)

79
Q

What is the multiplication “and” rule?

A

P(AnB)=P(A|B)P(B)

80
Q

What is statistical independence?

A

Probability of one is not effected by another
P(AnB)=P(A)P(B)
P(A|B)=P(A)

81
Q

In Bi-variate Probabilities, what is joint and marginal probabilities?

A

Intersection is joint
P(AnB)
Marginal is probability of one event
P(A)=P(AnB)+P(Anc)

82
Q

What is Bayes Theorem?

A

P(B|A)=P(A|B)P(B)/P(A)

P(A) can be summed using marginal proabability

83
Q

How would you calculate a cumulative probability function for a discrete random variable?

A

Frequency tables

84
Q

How do you calculate the mean of a discrete random variable?

A

Sum( xPx)

85
Q

How do you calculate the variance and standard deviation of a discrete random variable?

A

Variance: Sum(x-meanx)^2 X Px

Standard Deviation: Root variance

86
Q

Discuss linear functions of random varibles

A

Y=a+bX
Meany=a+bMeanx
VarianceY=b^2VarianceX
StandardDeviationY=|b|StandardDeviationX

87
Q

Discuss linear functions of two random variables

A

W=aX+bY
MeanW=aMeanX+bMeanY
VarianceW=a^2VarianceX+b^2VarianceY+2abCov(X,Y)

If W=X-Y
VarianceW=VarianceX+VarianceY -2Cov(X,Y)

Cov(X,Y)=SumX,Y((X-MeanX)(Y-MeanY)P(X,Y)
p=Corr(X,Y)=Cov(X,Y)/SDX x SDY

88
Q

Discuss a continuous random variable

A

Variance=E(X-MeanX)^2

89
Q

Discuss the co-variance and correlation of two continuous random variables

A

Cov(X,Y)=E[(X-MeanX)(Y-MeanY)]
p=Corr(X,Y) = Cov(X,Y)/SDX x SDY
If the variables are independent, co-variance is zero

90
Q

Discuss discrete probability distributions that are binominal

A

Use Bernoulli
Mean = Sum (XPx)
Variance = Sum(X-MeanX)^2P(x)

91
Q

How would you calculate the number of sequences with x successes in n number of independent trials?

A

Cnx=n!/x!(n-x)!

92
Q

How would you calculate the probability of x sucesses in n number of trials?

A

P(x) = n!/x!(n-x)! x P^x x (1-P)^n-x

= Cnx * P^x * (1-P)^n-x

93
Q

Discuss binomial distribution

A 
Meanx=nP
Variance = nP(1-P)
For P(X
94
Q

Discuss uniform distribution.

A 
Where a is minimum and b is maximum
f(x)=1/(b-a)
Mean = a+b/2
Variance = (b-a)^2/12
P(a
95
Q

What are the attributes of a normal distribution

A

Bell shaped, mean = median = mode

96
Q

How do you calculate Z value for normal distribution?

A

Z=(X-Mean)/SD

97
Q

How do you deal with a negative Z value

A

P(Z

98
Q

How would you execute P(a

A

P(Z <b></b>

99
Q

How would you calculate a Z value for a given probability?

A

Use formula Z=Mean + ZSD

Z can be found from table (Round Down)

100
Q

How would you deal with a Z value for two variables?

A

If X and Y are normally distributed then W is normally distributed

101
Q

What is the check to see if a binomial distribution is also normal?

A

nP(1-P)>5

102
Q

How would you calculate a Z value for a binomial?

A

Z=X-nP/(root(nP(1-P))

103
Q

Discuss sampling distributions

A 
Mean = Sum X / N
Variance(SMEAN) = SE = SUM(1/n)^2 x Variance(X)
104
Q

What is sampling with replacement?

A

The same person can be chosen twice

105
Q

How do you correct for sampling without replacement with a large sample size?

A

Use the finite population correction factor
Multiply Variance by N-n/N-1
It is unlikely we will need this

106
Q

What is the formulae for for a Z value for sample distribution?

A

Z=SampleMean-PopulationMean / (SD / RootN)

Z=SampleMean-PopulationMean / SE(X)

107
Q

What is the Central Limit Theorem?

A

Even if the population is not normally distributed, if the sample is large enough it is aprox normal (N>25)

108
Q

Discuss sampling distributions of the sample proportion

A

phat = X/N
Normal Distribution if nP(1-P)>5
Variance = P(1-P)/N

109
Q

How would you calculate a Z value for sampling distributions of the sample proportion?

A

Z=Phat-E(phat)/SDP

Z=Phat-P / Root(P(1-P)/N)

110
Q

How would you calculate the confidence interval for the mean with a known Variance?

A

Mean +_ Za/2 SD/Root(N)

Za/2 SD/Root(N) is the Margin of error

111
Q

How would you reduce the ME?

A

Reduce population SD
Increase the n
Decrease the Confidence level

112
Q

How would you calculate a confidence interval for a population mean if population variance is unknown?

A

t=SMean-Pmean/SSD/Rootn

T has n-1 DoF

113
Q

How would you calculate a confidence interval for a population proportion?

A

phat +- Za/2 Root[(P(1-P))/n]

114
Q

How would you perform a confidence interval for a difference in means: dependant samples?

A

Population mean difference: Meanx- Meany
Point estimate difference: dbar = Sum(x-y)/n
SVariance = Sum( d-Dmean)^2 / n-1
Confidence Interval : dbar = Tn-1, a/2 Sd/Rootn

115
Q

How would you calculate a confidence interval for an independent sample with a known population variance?

A

Population mean difference: Meanx- Meany
Point estimate difference: dbar = xsmean - ysmean
SVariance = XVariance/nx + Yvariance/N
Confidence Interval : dbar = Tn-1, a/2 Sd/Rootn

116
Q

How would you calculate a pooled variance?

A

Sp2=(nx-1)sx^2 + (ny-1)sy^2 / nx+ny-2

117
Q

How would you calculate a confidence interval for two unknown variances that are assumed equal?

A

(sxmean - symean) +- tnx+ny-2,a/2 Root[sp2/nx + sp2/ny]

118
Q

How would you calculate a confidence interval for the difference in proportions?

A

(phatx - phaty) +- Za/2 Root [ Phatx(1-phatx)/nx + phaty(1-phaty)/ny

119
Q

Discuss the basics of hypothesis testing

A

H0=Null , H1=Alternative
Always about population parameter
Always true until disproved, cannot accept a hypothesis
Type 1 Error occurs where a true null is rejected: P=a
Type 2 Error occurs where a false null is not rejected P=B
(1-B) is power of test

120
Q

How would you perform a hypothesis test for normal distribution where pop variance is known?

A

Z=S-Mean-TestValue / SD/ROOT(N)

121
Q

Discuss the three types of tests

A

Upper Tail: H0 < U, H1 > U Reject null if Z > Za
Lower Tail: HO > U, H1 < U Reject null Z < -ZA
Two Tail: H0 = 0, H1 not 0 , Reject null if Z > Za/2 or Z < -Za/2
Remember concluding statement

122
Q

How would you perform a hypothesis value for a normal distribution with an unknown pop variance?

A

t=Smean - Target / s / RootN
Tn-1,a
Same rejection criterion as above

123
Q

How would you perform a hypothesis test for a population proportion?

A

z=phat-ptarget/Root(PT(1-PT)/n)

124
Q

How would you perform a hypothesis test for a two sample difference test?

A

dbar=sum(x-y)/n

t=dbar/(sd/RootN)

125
Q

How would you perform a hypothesis test for a independant two sample with known pop variances?

A

Z=(xbar-ybar)/ROOT[ Varx/nx + Vary/ny]

126
Q

How would you perform a hypothesis test for a independant two sample with unknown pop variances but are assumed equal?

A

t=xbar-ybar/ROOT[s2p/nx + S2p/ny]

Tnx+ny-2

127
Q

How would you calculate a pooled sample variance for hypothesis testing?

A

s2p=(nx-1)s2x+(ny-1)s2y / nx+ny-2

128
Q

How would you perform a hypothesis test for two population proportions?

A

z=(phatx-phaty)/ROOT[PCP(1-PCP)/nx + PCP(1-PCP)/ny)

129
Q

How do you calculate PCP?

A

PCP=nxphatx+nyphaty / nx+ny

Economic Methods (1 decks)

Brainscape helps you reach your goals faster, through stronger study habits.
© 2024 Bold Learning Solutions. Terms and Conditions