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First Year PPE > Economic Methods Part 1 > Flashcards

Economic Methods Part 1 Flashcards

1
Q

What is excess supply and demand?

A

The difference between the amount of units demanded and the amount of units supplied when goods are at a certain price, 0 in equilibrium, created by government interference in market

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2
Q

What is important about tax collection?

A

It must be higher than tax revenue

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3
Q

Where Qs = a + BP, what is the supply function post-tax and post-subsidy?

A

Qs(t) = a + B(P-t) and Qs(k)= a + B(P+k)

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4
Q

Where Pd = a-BQd, what is the reverse demand function post-tax?

A

Pd-t = a-BQd

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5
Q

What is the rule with taxation and subsidisation in demand and supply functions?

A

The transformation always occurs in the price

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6
Q

What is the consumer share of tax imposed?

A

P**-P*, or the post-tax equilibrium price - the pre-tax equilibrium price

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7
Q

What is the percentage consumer share?

A

(P**-P*)/t x 100

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8
Q

What is the producers’ share of tax imposed and percentage share?

A

£t - (P**-P*) = M or share

M/t x 100 = percentage share

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9
Q

What is the secondary method of taxation?

A

Through the total revenue, where firms pay a tax tpq, or a percentage tax multiplied by their total revenue (pq)

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10
Q

What is the calculation for tax revenue?

A

Qt x t

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11
Q

What is Pc and Ps

A

The price consumers will pay and the price suppliers will pay

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12
Q

Capital and Labour: Substitutes?

A

They can be in certain circumstances so straight line on graph, other times not

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13
Q

What is the Cobb-Douglas production function?

A

AK^aL^b with A being technology, a the proportion of whole capital put into the single product being viewed on the graph, b is the same but for labour

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14
Q

What is the relationship between a and b and returns to scale?

A

(a+b) > 1 : increasing returns to scale
(a+b) < 1 : decreasing returns to scale
(a+b) = 1 : constant returns to scale

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15
Q

What does MC equate to in terms of cost and output?

A

Change in total cost/change in output

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16
Q

What is the break even point?

A

MR (Q) = MC (Q), or where TR = TC

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17
Q

What was the belief in macroeconomics before Keynes?

A

Assumption that demand will create itself as supply is increased, but stagflation of Great Depression dispelled this idea

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18
Q

Equation for closed economy

A

Supply : Y = C + I(r) + G = P(L, K) : Demand

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19
Q

What is the relationship between interest rates and investment?

A

Inversely proportional, the lower the interest rate, the higher the level of investment

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20
Q

Which formula’s allow the government to influence consumption C?

A 
C = f(Yd), a function of disposable income
Yd = Y - t
C = a + bYd where a is autonomous consumption coming from private savings or borrowing and b is induced consumption, affected by income, creating bYd =MPC
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21
Q

What is the formula for b or MPC?

A

Change in consumption / change in Y

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22
Q

What is the formula for MPS based off of savings function?

A

(1-b)Y

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23
Q

What is the function for national savings?

A

Sn (national savings) = Sp (private savings) + Sg (government savings)

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24
Q

What are the two methods for measuring national income equilibrium?

A

Keynesian Cross and by use of savings and investment

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25
Q

How does the Keynesian cross work?

A

Where Y = AD and AD = C + I + G cross, there is equilibrium. Above this point AD < Y so a tax break should be brought in, where AD > Y, increase taxes

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26
Q

How do savings and investment measurements of national income equilibrium work?

A

As S = I, and I is set as an exogenous variable against
S = -a + (1-b)Y, where these two lines cross, that is the equilibrium point, so therefore interest rates can be adjusted so savings equal investment

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27
Q

How does government affect savings and investment graphs?

A

S + T = I + G

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28
Q

What is the formula for an open economy?

A

Y = C + I + G + NX(e) where e is the exchange rate, strong net importers have strong exchange

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29
Q

What is Young’s Theorem?

A

d²y/dwdx = d²y/dxdw

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30
Q

Where y = f(z, t), what is change in y?

A

Change in y or dy = (dy/dz) x dz + (dy/dt) x dt, so dy can be found when figures for z, t, dz and dt are given

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31
Q

What is the result of positive and negative FOCs?

A

Positive - increasing function

Negative - decreasing function

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32
Q

What is the result of positive and negative SOCs?

A

Positive - increasing rate of change - convex, often consumers desiring more of an item in U-shaped graph
Negative - decreasing rate of change - concave, item not desired by consumers

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33
Q

When z = f(x, y), how can a maximum and minimum b found?

A

d²z/dx² < 0 and d²z/dy² < 0 for maximum, reverse for minimum, in both cases d²zd²z/dx²dy² - (d²z/dxdy)² > 0 according to Young’s Theorem, where less than zero, no maximum or minimum, saddle point therefore

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34
Q

Formula for PED

A

Percentage change in Qd/percentage change in P or

dQd/dP x P/Qd so that by having a demand function and price P, PED can be solved

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35
Q

What do different sizes of the absolute value of n mean for price sensitivity?

A

|n| > 1 : elastic, price sensitive
|n| < 1 : inelastic, less price sensitive
|n| = 1 : unitary demand elasticity, change in Q = change in P
|n| = infinity perfectly elastic demand
|n| = 0 perfectly inelastic demand

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36
Q

How does elasticity affect TR when price is increased?

A

Inelastic: increase in price leads to increase in TR
Elastic: increase in price leads to decrease in TR

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37
Q

MR in terms of elasticity

A 
MR = P + Q(dP/dQ) and PED = dQ/dP x P/Q rearranged and substituted so
MR = P( 1 + 1/e)
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38
Q

What are the formulas for income demand of elasticity?

A

Percentage change in Qd/Percentage change in Y = YED

YED = dQd/dY x Y/Qd

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39
Q

How does the size of YED affect the value of goods?

A

YED > 1 : luxury good
YED < 1 : normal good
YED < 0 : inferior good

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40
Q

Formula for cross-price elasticity of demand

A 
CPED = Percentage change in Qa/Percentage change in Pb
CPED = dQa/dPb x Pb/Qa
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41
Q

How is substitutability affected by CPED?

A

CPED > 0 : substitutes
CPED < 0 : complements
CPED = 0 : no relationship

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42
Q

What is the formula for MU where TU = f(x, y)?

A 
MU = dTU(x, y)/dx
MU = dTU(x, y)/dy
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43
Q

What is the important thing about utility on the indifference curve?

A

It stays the same, so du = 0

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44
Q

Where U = f(x, y), what is the marginal rate of substitution?

A

|dy/dx| = -f ‘(x)/f ‘(y) = (dU/dx)/(dU/dy) = MRS

45
Q

Formula for MPL and MPK in short and long run

A 
MPL = dTP(Q)/dL in short run
MPL = dTP(L, K)/dL in long run
MPK = dTP(L, K)/dK in long run
46
Q

How can indifference curves be described?

A

Isoquants

47
Q

What is the marginal rate of technical substitution?

A

MRTS = dK/dL = MPL/MPK, rate at which labour can be substituted for capital to create the same amount of production

48
Q

How does production change in the short run as inputs increase?

A

Returns to variable inputs or law of diminishing returns, MRTS falls to 0 as extra workers do not increase output

49
Q

How does production change in the long run as inputs increase?

A

Returns to scale (powers of Cobb-Douglas function summed, a+b), or law of diminishing marginal returns
Q = AK^aL^b
d²Q/dL² > 0 - new labour is increasing production
d²Q/dL < 0 - new labour is not increasing production
Can be used for capital as well

50
Q

What can the SOC show in a production function in terms of returns?

A

d²Q/dL² > 0 - increasing marginal returns

d²Q/dL² < 0 - decreasing marginal returns

51
Q

What is a homogenous function?

A

A factor which can be built into another function without changing it

52
Q

What is the production elasticity function for labour and capital?

A

Relative change in output relative to the percentage change in input, superscript a and b in a Cobb-Douglas Production Function
E(L): dQ/dL x L/Q where capital is held constant
E(K): dQ/dK x K/Q where labour is held constant

53
Q

How can you explain MPS = 1 - MPC

A 
Y = C + S
dY/dY = dC/dY + dS/dY
1  = MPC + MPS
54
Q

Basic formula for multiplier effect

A

1/(1-MPC) = 1/MPS or Change in real GDP (Y)/Change in injections (J)

55
Q

When is output maximized in the short run?

A

Marginal product of labour = average product of labour, and also value of L when dAP(L)/dL = 0

56
Q

How can revenue be maximised in perfect competition?

A

Price is constant, P = MR = AR, so it cannot really be maximised

57
Q

How do you minimize costs in the short run?

A

Where ATC = MC or where dATC/dQ = 0

58
Q

What area shows profits maximized in the short run on a graph?

A

Profits bound by the y-axis, Q, the minimum of the ATC and horizontal line MR = MC

59
Q

What formula shows profits maximized?

A

Profit = TR - TC, then differentiate, equate to 0, test SOC

60
Q

How to maximize profits in a multi-product firm with price discrimination?

A

Create separate profit functions using TR and TC, then find FOCs of these equal to 0, then SOCs

61
Q

What does MR equate to in terms of elasticity and why is this useful in multi-product firms?

A

P(1 + 1/n) which can help show how where there is higher elasticity one market than another, there are lower prices

62
Q

What are the two cases in constrained utility maximisation?

A

Primal case - maximising the utility curve given a certain budget constraint
Duality case - given a certain utility, the minimisation of expenditure to reach the curve

63
Q

What is the point which is aimed for in a constrained utility maximisation case?

A

MUx/MUy = Px/Py

64
Q

What is the objective function in a constrained optimisation case?

A

That which we set out to maximise or minimise

65
Q

What is the producer duality case trying to achieve?

A

Cheapest (using budget line) way for firms to reach a certain output (constraint)

66
Q

How does the substitution method work?

A

Substitute the objective function into the constraint so that one of the variables is isolated, then differentiate once for FOC, and again for SOC

67
Q

Where the constraint is given by g(x, y) = m, what does the value of λ* show as m is increased or decreased (to be found in a langrangian equation)?

A

λ* > 0 and +1 unit change in M = increase approximately by λ*
λ* > 0 and -1 unit change in M = decrease approximately by λ*
λ* < 0 and +1 unit change in M = decrease approximately by λ*
λ* < 0 and -1 unit change in M = increase approximately by λ*

68
Q

What is the budget constraint in a production case?

A

wL + rK = c = P(L)L + P(k)K

69
Q

What is the primary point of optimisation in a production case?

A

|dL/dK| = r/w

70
Q

What is the alternative point of optimisation in a production case?

A

P(L)/P(k) = MPL/MPK

71
Q

In cases of integrating marginal revenue and costs to find totals, when is there a constant?

A

No constant in revenue to add on as when TR = 0, Q = 0. In marginal costs, the fixed cost is the constant which should be added to the integral of marginal costs

72
Q

In cases of integrating marginal utility and marginal production, when is there a constant?

A

There is no constant in either case - for marginal utility, some utility is required for there to be a total, and for production, where there is no labour (or no capital), even with the other present, there is no output

73
Q

How is integration used in macroeconomics in terms of savings and consumption and what are the constants?

A

Integral of MPS and MPC are savings and consumption functions, with T (non-income savings) added to savings function and K (autonomous consumption) added to consumption function

74
Q

What are examples of flow (or rate, the derivative) in economics?

A

Deposits with interest and withdrawals, buying and selling shares, and housing stock

75
Q

What are examples of stock (or capital, the integral) in economics?

A

Bank balance, housing investments and depreciation, equity shareholdings

76
Q

What is the equation for net investment in terms of capital stock formation?

A

I(t) = dK(t)/dt

77
Q

When net investment is integrated to find capital, what is the constant?

A

c = Ko = initial capital stock

78
Q

What is the use of integration in economics?

A

Derive marginal functions, find the investment time path, create welfare measurements

79
Q

Where exactly is the consumer surplus and producer surplus?

A

CS - area below demand curve but above equilibrium price

PS - area above supply curve but below equilibrium price

80
Q

What is the use of total surplus?

A

To compare with other markets or the same market across time

81
Q

How is the producer surplus found from the marginal cost function?

A

Where p = Po = output price for producing q = qo = maximising output, Po = MC (qo), therefore:
PS = Poqo - integral (qo to 0) of MC(q)

82
Q

What are causes within countries of income and wealth inequality?

A

Ownership of resources, qualification, motivation, skill, ability, family size

83
Q

What are causes across countries of income and wealth inequality?

A

Factor endowments, size and quality of labour force, good policy, luck, economic power, intuition
Main determinants are education and parental influence

84
Q

How does inequality change as wealth and income increases?

A

First inequality increases, then decreases in U-shaped curve

85
Q

What are the 3 popular measures of inequality?

A

Range ratios, Gini coefficient and Lorenz curve

86
Q

How does the Lorenz curve work?

A

Income = population line drawn on graph with same axis, then a countries wealth distribution that falls below that line is drawn on - the area between the two lines is income inequality

87
Q

Over which figures does the Gini coefficient result in?

A

0 < x < 1 with 0 being no income equality

88
Q

What is the formula for the Gini coefficient?

A

2 (integral max: 1 min: 0 (x - f(x)) dx) where x is the equitable line and f(x) = L(x) or the inequality line a nation

89
Q

What is the transpose of a matrix?

A

Amxn = A1 = AT = Anxm, swapping of the matrix order

90
Q

What is an identity matrix?

A

Principle diagonal is 1 whilst all other values are 0

91
Q

Which types of matrices can be summed?

A

Those with the same matrix dimension/order

92
Q

What is scalar multiplication of a matrix?

A

Where a value multiplies the entire matrix such as 0.5A which causes all values of the matrix to be halved

93
Q

What is the conformability rule for non-scalar multiplication?

A

Amxn x Bnxk = Cmxk, and as a result the order in which variables are multiplied is important

94
Q

What does the determinant of a matrix show in terms of its relation to 0?

A

If |A| = 0 then the inverse of A does not exist, otherwise it does

95
Q

What are the three steps in finding a 3x3 matrix determinant?

A

Find the minors, find the cofactors, and then evaluate the cofactors

96
Q

What is the minor?

A

a11 x |a11| + a12 x |a12| + a13 x |a13|

97
Q

What is a cofactor matrix?

A

One where every element (amxn) is replaced with its cofactor with an appropriate sign

98
Q

What is an adjoint matrix?

A

A transposed cofactor matrix

99
Q

What is the inversion of a matrix?

A

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

100
Q

What happens to a 2x2 matrix when an inversion occurs?

A

The value of all elements are swapped diagonally

101
Q

How is the Inversion Approach used?

A

AX = B rearranged to X = A^-1 x B where the inversion of the matrix is found and multiplied by B

102
Q

How is the Cramer’s Rule Approach used?

A

Create alternative matrices (where differing columns of A is replaced by B), the determinants of these matrices are found and then these are divided by the original determinants
Xi = |Ai| / |A|

103
Q

How does investment change from a Keynesian to Freidman’s model?

A

As money is important in impacting interest rates, creating I(r), investment is no longer exogenous

104
Q

What are the three demands for money?

A

Transaction motive - Mt
Precautionary motive - Mg
Speculative motive - Mz
Equalling Ms when totalled

105
Q

How does Y and r affect demand for money?

A

f(Y+) for Lt and Lp - more money required in a better economy
f(r-) for Lz - increase in interest rates lowers demand for speculative money

106
Q

How is the SOC found in unconstrained optimization using the Hessian in terms of results?

A

Maximum or d²z < 0 when |H1| < 0, |H2| > 0 and |H3|<0, therefore negative definite
Minimum or d²z > 0 when |H1| > 0, |H2| > 0 and |H3| >0, therefore positive definite

107
Q

How is Young’s Theorem applicable in the case of Hessians?

A

(Txx x Tyy) - (Txy)² > 0 should always been the case in 2x2 cases

108
Q

What is the border made up of on the bordered Hessian?

A

The derivative of the constraint, such as gx and gy where gx is placed nearest Lxx

109
Q

How are the results of a bordered Hessian SOC test found?

A

Where the result is positive, the result is a negative definite and is a maximum
Where the result is negative, the result is a positive definite and is a minimum
Use of the whole matrix |H| is required for evaluations to be made

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