Micro Flashcards

1
Q

Economic model

A

Provide simplified portraits of the way individuals make decisions, firms behave, and the way these two interact to establish markets.

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2
Q

Two general methods used to verify economic models

A
  1. Direct approach seeks to establish validity of the basic assumptions the model is based on. 2. Indirect approach shows that a simplified model correctly predicts real world events.
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3
Q

3 general features of economic models

A

Ceteris Paribus assumption, economic decision makers seek to optimise something, distinction between positive and normative questions

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4
Q

Exogenous variables

A

Variables that are outside of the decision makers control. E.g households: price of goods, firms: price of inputs

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5
Q

Endogenous variables

A

Variables that are determined within a model as the result of a decision. E.g household: quantities bought, firms: output produced

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6
Q

Agents

A

Rational and optimise. They choose the best given some economic constraints. Assume they have perfect information.

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7
Q

Supply in competitive market

A

Sellers bring these to the market. The goods could be exchanged for other goods or income. If selling goods doesn’t make an improvement, rationality will prevent suppliers from producing.

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8
Q

Demand in competitive market

A

Buyers of goods have a reservation price, maximum willingness to pay.

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9
Q

Perfect competition

A

Buyers and sellers have no influence on price or quantity so R = p*q

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10
Q

Equilibrium in competitive market

A

Prices adjust until demand equals supply. The market clears

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11
Q

Ordinary monopoly

A

Seller can influence price by controlling supply, R = p(q)*q

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12
Q

Positive economics

A

Descriptive. Determines how resources are in fact allocated in an economy.

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13
Q

Normative economics

A

Judgemental. Taking a stance about what should be done.

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14
Q

Pareto improvement

A

Occurs if one persons welfare can be improved without detriments to others. If not possible, we have Pareto efficiency

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15
Q

Although marshallian model is useful …

A

It is a partial equilibrium model, looking at only one market at a time.

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16
Q

Production possibility frontier

A

Various amounts of two goods that an economy can produce using its available resources during some period. Reminds us that resources are scarce. Shows us the opportunity cost of producing more of one good as the decrease in amount of the other.

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17
Q

Preference

A

Is a binary relation over objects of choice

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18
Q

Satiation

A

The effect where the more of a good one possesses, the less one is willing to give up to get more of it. Once you pass satiation point, consuming more means enjoying it less.

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19
Q

Utility

A

A function that represents a preference.

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20
Q

Utility function

A

Translates the behaviour of the consumer into a mathematical function.

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21
Q

Utility rankings

A

Ordinal rankings. It’s not possible to compare utilities of different people.

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22
Q

Preferences must be..

A

Rational: complete and transitive and monotone

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23
Q

A preference is complete if:

A

x>y or y>x or both (x~y)

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24
Q

A preference relation is transitive if:

A

x>y and y>z then x>z

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25
Q

A preference relation is continuous if:

A

The upper contour and low contour sets are closed. The sets have no holes.

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26
Q

Consequence of transitivity

A

Different indifference curves cannot intersect

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27
Q

Ordinal utility

A

Any increasing transformation of a utility function also gives a utility function

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28
Q

Ordinal

A

Tells us that one bundle is better than another. Doesn’t tells by how much.

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29
Q

Indifference curve

A

Represents all alternative combinations of x and y for which an individual is equally well off.

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30
Q

why is the slope of an IC negative

A

to show that if the individual is forced to give up some of y, they must be compensated by an additional amount of x to remain indifferent between two bundles.

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31
Q

convexity definition

A

a set of points is said to be convex if any two points within the set can be joined by a straight line that is contained completely within the set. Implies that ICs are differentiable almost everywhere.

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32
Q

strict convexity

A

assume differentiability everywhere,

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33
Q

marginal rate of substitution

A

is the negative tradeoff between two goods - (dU/dx)/(dU/dy), px/py

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34
Q

perfect substitutes: U(x) = ax1 + bx2

A

MRS is constant (equal to a/b), convexity holds.

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35
Q

perfect complements: U(x) = min{ax1, bx1}

A

smallest numbers decide utility, MRS = 0/infinity/not defined. strict not strong monotonicity. convexity but not strict convexity. L-shaped ICs. consumption occurts at the vertices of the ICs.

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36
Q

Cobb Douglas: U(x) = x^a + x^b

A

satisfy all requirements in strongest form: convexity and monotonicity. MRS changes along Ic.

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37
Q

constant elasticity of substition: U(x) = (x^§ + x^§)^1/§

A

value of delta is not euqal to 0 but smaller than 1. if delta was larger than 1, IC would be concave. when delta = 1, this is perfect subtitutes. as delta approaches 0, the function approaches Cobb Douglas. as delta approaches negative infinity, the function approaches perfect complements.

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38
Q

Shephards Lemma

A

dE/dpi = h*i

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39
Q

Marshallian demand solves

A

maximisation problem

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40
Q

Hicksean demand solves

A

minimisation problem

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41
Q

Roy’s identity

A

x*i = - Vpi / Vy. Consumers demand given by ratio of marginal indirect utilities.

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42
Q

corner solution

A

an individual’s preferences may be such that they obtain maximum utility by choosing no amount of one of the goods.

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43
Q

marshallian demand for cobb douglas

A

x1=(ay)/p1, x2=(by)/p2

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44
Q

direct utility

A

utility across all possible consumption bundles

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45
Q

indirect utility

A

represents the maximum utility a consumer can attain given the prices of goods and the consumer’s income. Substituting marshallian demand into utility function gives indirect utility. V(p,w) = max U(x) subject to p*x <= w

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46
Q

properties of indirect utility

A

continuous in prices, utility and income, small changes have small effects. assume differentiability. homogenous of degree 0, strictly increasing in income and decreasing in prices.

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47
Q

properties of the expenditure function

A

continuous in prices and target utility. homogenous of degree 1 in prices. expenditure function and indirect utility are inverse functions of one another. expenditure is strictly increasing and unbounded in target utility. non-decreasing and concave in prices

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48
Q

homogenous of degree 0

A

if you change prices and income, the outcome doesnt change

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49
Q

homogenous of degree 1

A

if you double prices, outcome doubles

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50
Q

normal good

A

dx/dm >= 0

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51
Q

inferior good

A

dx/dm < 0

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52
Q

income effect

A

the change in demand for a good caused by a change in consumer’s purchasing power or real income.

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53
Q

substitution effect

A

consumers replace one good with another due to price change

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54
Q

increase in demand

A

outward shift of demand curve

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55
Q

increase in quantity demanded

A

movement along the curve

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56
Q

compensated demand function can be found from

A

differentiating expenditure function with respect to prices

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57
Q

inferior good def

A

when income increases, consumption decreases

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58
Q

income elasiticty def

A

measures the sensitivity of changes in consumption relative to changes in income.

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59
Q

income elasticity formula

A

(dxi/dm)(m/xi)

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60
Q

own price elasiticty

A

changes in demand relative to changes in price: (dxi/dpi)(pi/xi)

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61
Q

cross price elasiticty

A

(dxi/dpj)(pj/xi)

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62
Q

inelastic demand

A

-1 < e < 0

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63
Q

elastic demand

A

e < -1

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64
Q

slutsky equation in elasticity form

A

e = ẽ - se, where s=(px/m) is income share

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65
Q

whether hicksean and marshallian price elasticities differ much depends on…

A

the importance of income effects in the overall demand.

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66
Q

the slutsky elasticity equation shows that hicksean and marshallian own-price elasticities will be similar if….

A

either of the two conditions hold: 1) the share of income devotes to x is small, 2) the income elasticity of demand of x is small. These both reduce the importance of the income effect

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67
Q

engel’s law

A

percentage of income allocated for food purchases decreases as a household’s income rises, while the percentage spent on other things increases.

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68
Q

cournot aggregation

A

budget share s1 of good 1 is small when good 1 has many substitutes (ϵi1>0), and big when it has many complements (ϵi1<0)

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69
Q

euler theorem

A

the net sum of all price elasticities together with the income elasticity for a good must sum to zero

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70
Q

consumer surplus

A

monetary measure of the utility gains and losses that individuals experience when price changes. Area below the compensated demand curve and above market price.

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71
Q

compensating variation

A

compensation required to reach same utility level after a price change: CV = E(p1x, py, U) - E(p0x, py, U)

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72
Q

1st proof that the slope of compensated demand curve is negative

A

based on quasi-concavity of utility functions, any IC must exhibit diminishing MRS, any change in price will induce a quantity change in opposite direction when moving along IC

73
Q

2nd proof slope of compensated demand curve is negative

A

derives from shephards lemma. because the expenditure function is concave in prices, the compensated demand function (the derivative of expenditure) must have a negative slope

74
Q

theory of revealed preferences

A

two bundles, A and B. At some price and income level, the individual can afford both bundles but chooses A, A has been revealed preferred to B. Principle of rationality says under any different price-income arrangement, B can never be revealed preferred to A. If B is chosen at another price-income arrangement, the individual could not afford A.

75
Q

primal relationship among demand concepts

A

maximise U(x,y) s.t. I = (p_x)x + (p_y)y –> indirect utility function U*=V(p_x, p_y, I) –> Roys identity –> marshallian demand x(p_x, p_y, I) = (dV/dp_x)/(dV/dI)

76
Q

marshallian demand in relation to indirect utility function

A

x(p_x, p_y, I) = (dV/dp_x) / (dV/dI)

77
Q

dual relationship among demand concepts

A

minimise E(x,y) s.t. Ū=U(x,y) –> expenditure function E*=E(p_x, p_y, Ū) –> shephards lemma –> compensated demand x(p_x, p_y, U) = dE/dp_x

78
Q

two goods are said to be gross substitutes is

A

dxi/dpj > 0

79
Q

two goods are said to be gross complements if

A

dxi/dpj < 0

80
Q

consumption smoothing

A

saving some income so you can rely on savings if you lose job. income is smooth over time

81
Q

weak axiom of revealed preferences

A

if both x and y are available in 2 different price situations and x is chosen in the first, consistent behaviour is revealed if y is not chosen in the next instant

82
Q

if x is directly revealed preferred to y, and y is directly revealed preferred to z, then…

A

x is indirectly revealed preferred to z

83
Q

Strong axiom of revealed preferences SARP

A

if x is indirectly or directly revealed preferred to y then y cannot be indirectly or directly revealed preferred to x.

84
Q

preference sign with a star

A

preference is based on choice which is based on the revealed preference

85
Q

will a rational and continuous preference always generate a choice function that satisfied WARP?

A

yes.

86
Q

index numbers are

A

averages

87
Q

quantity index with weights w1, w1; baseline x1B, x2B; choice at time x1T, x2T

A

= (w1x1T + w2x2T) / (w1x1B + w2x2B)

88
Q

endowments

A

time, assets

88
Q

Paasche index with weights p1T, p2T

A

= (p1x1T + p2x2T) / (p1x1B + p2x2B)

89
Q

if net demand > 0

A

net buyer

90
Q

if net demand < 0

A

net seller

91
Q

changes in endowment affect

A

only the budget constraint, equivalent to income changes

92
Q

changes in prices affect

A

jointly affect income and price

93
Q

price offer curve

A

The curve containing all the utility- maximising bundles

94
Q

slutsky equation with endowment income effect

A

dxi(p,m)/dpj = (dxi(p,U)/dpj) + (wj - xj(p,m))*(dxi(p,m)/dm)

95
Q

what does strict convexity ensure

A

there is only one tangent line at IC

96
Q

how to get whole market demand

A

add up all the demands at every price

97
Q

competitive market with endowments

A

consumers are endowed with goods and choose optimally. consumers have no influence on how trade happens

98
Q

pure exchange

A

feasible (re)allocations

99
Q

pareto efficient allocation

A

a feasible allocation such that there is no way to improve any of the consumers without harming someone

100
Q

contract curve

A

the set of all pareto efficient allocations

101
Q

tangency condition to get the contract curve

A

in a two goods case, two MRS are equal at one particular allocation in feasible set.

102
Q

market clearing

A

when supply = demand

103
Q

blocking coalition

A

a group of consumers that object to a proposed feasible allocation because they lose out. they could leave the economy and do better

104
Q

barter equilibrium

A

a feasible allocation that cannot be blocked by a coalition and is pareto efficeint.

105
Q

equation for the minimum utility required before blocking allocations

A

Ux(wx)

106
Q

core of the exchange economy

A

the set of all barter equilibria - all feasible and unblocked allocations

107
Q

allocation in the core

A

there is no excess demand or supply

108
Q

if excess equation is positive

A

excess demand

109
Q

if excess equation is negative

A

excess supply

110
Q

walras’ law

A

at all prices the value of excess demand is 0.

111
Q

theorem of walrasian equilibrium

A

in a market where consumer behaviour accords with their preferences, then excess demand is continuous in prices, homogenous of degree 0, and Walras’ law holds

112
Q

walrasian equilibrium price vector

A

z(p*)=0

113
Q

1st Welfare Theorem

A

the WEA x(p*) is an allocation in the core, it is pareto efficient - under certain assumptions, any competitive equilibrium in an exchange economy is Pareto efficient. This means that at equilibrium, no other allocation can improve the welfare of one consumer without making another worse off

114
Q

2nd welfare theorem

A

there exists prices p** such that for an appropriate redistribution of intial endowments, allocation is WEA at prices p**.

115
Q

production function

A

indicates the maximum amount of output that can be generated by the efficient combination of inputs

116
Q

production function assumptions

A

strictly increasing, continuous and differentiable, strictly quasi concave

117
Q

isoquants

A

combinations of inputs that lead to the same output level

118
Q

isoquants - perfect substitutes

A

straight diagonal lines

119
Q

isoquants - perfect complements

A

L shaped

120
Q

isoquants - cobb douglas

A

curves

121
Q

isoquants - CES

A

curves that go more into 0,0

122
Q

marginal product

A

measures the additional effect on production of one factor input by keeping others constant - is positive as f is increasing. df/dy

123
Q

change in marginal product will be

A

negative due to diminishing returns

124
Q

factor productivity

A

average product of a factor input, f(y)/y. can be seen as a measure of efficiency when other factors fixed

125
Q

Marginal rate of technical substitution

A

measures the substitutability of two factors, MPy,i / MPy,j

126
Q

elasticity of substitution

A

unit free measure of the degree of substitutability between factors

127
Q

short run

A

at least one factor input is fixed

128
Q

long run

A

firm can change all factor inputs

129
Q

f(sy) = sf(y) = 1

A

constant returns to scale

130
Q

f(sy) = sf(y) > 1

A

increasing returns to scale

131
Q

f(sy) = sf(y) < 1

A

decreasing returns to scale

132
Q

when q(t) = f(t,y) = A(t)f(y) what is changes over time

A

dq/dt = (dA/dt)f(y) + A(df(y)/dt)

133
Q

cost function

A

C(w,q) = min w*y such that f(y) >= q

134
Q

cost function for two inputs

A

C(w1, w2, q) = min w1k + w2l

135
Q

isoquants

A

combinations of input 1 and input 2 that deliver the same level of output, MRTS = w1/w2

136
Q

properties of the cost function

A

C is zero for lowest production level; continuous in input prices and target output; homogenous of degree 1 in prices; cost is strictly increasing; non-decreasing in prices; concave in prices

137
Q

average cost

A

TC(q) / q = C(w,q) / q

138
Q

marginal cost

A

MC(q) = dC(w,q)/dq

139
Q

SR average cost

A

C(q) / q + F/q = AVC + AFC

140
Q

SR marginal cost

A

dC(q)/dq + dF/dq

141
Q

LR decision of firm

A

whether to enter the market or not

142
Q

if AVC is decreasing

A

MC < AVC

143
Q

if AVC is increasing

A

MC > AVC

144
Q

if AC is decreasing

A

MC < AC

145
Q

if AC is increasing

A

MC > AC

146
Q

SR costs vs. LR costs

A

SR costs are at least as high as LR costs

147
Q

SR decision of firm

A

whether to supply to the market or not

148
Q

LR equilibrium

A

all the profit will be distributed among the acting firms until there are no profits

149
Q

profit function

A

pi (p,w) = max pq - wy

150
Q

1st order condition of profit max

A

p = MC(q*)

151
Q

2nd order condition of profit max

A

d^2C(q) / dq^q >= 0 or MC(q) is increasing

152
Q

in SR if firm decides to produce nothing then…

A

they will still have fixed costs so are making a loss

153
Q

monopoly profit max equation

A

MC = MR

154
Q

monopoly in practice

A

a monopoly cannot exploit all consumers because it cannot differentiate between consumers so it will set one price and those consumers who wish to buy above that price will be served, the others will not. revenue depends on quantity supplied with determines the price

155
Q

crusoe production - at prices (p,w) : pi(p,w) = px2 - wl, iso-profits =

A

x2 = pi/p + (w/p)l

156
Q

budget line in general equilibrium with production

A

= pi/p + (w/p)l

157
Q

marginal rate of production transformation (MRPT) in a PPF

A

= - MCx1 / MCx2

158
Q

benefits of general equilibrium

A

preferences and technology exogenous; under perfect information and price taking assumption; prices endogenous and so is WEA

159
Q

limits of general equilibrium

A

externalities; lack of information; market power; public goods; efficiency not equal to optimal distribution

160
Q

an allocation is feasible if

A

it respects the initial endowments of both consumers

161
Q

An allocation is unblocked if

A

no two consumers can mutually improve their utility through trade from this allocation

162
Q

walrasian equilibrium

A

an allocation where all markets clear (demand equals supply) and marginal rates of substitution for all consumers are equal to the price ratio

163
Q

general formulation of the First Welfare Theorem for an exchange economy

A

Consumers: n consumers with continuous and quasi-concave utility functions Ui(xi), where xi = (xi1, xi2) represents the consumption bundle of goods 1 and 2 for consumer i.
Endowments: Each consumer has an initial endowment ei = (e1i, e2i) of both goods.
Production Efficiency: There are no production possibilities, meaning the economy solely focuses on exchange of existing endowments.
Competitive Equilibrium: There exists a price vector p = (p1, p2) for the two goods and consumption bundles xi for each consumer such that:
Market Clearing: Aggregate demand for each good equals aggregate supply, z(p*)=0
Individual Optimization: Each consumer maximizes their utility Ui(xi) given their budget constraint p * xi <= p * ei.
Theorem: Under the above assumptions, the competitive equilibrium (p, x) is Pareto efficient.

164
Q

general formulation of the Second Welfare Theorem for an exchange
economy

A

Consumers: n consumers with continuous and quasi-concave utility functions Ui(xi), where xi = (xi1, xi2) represents the consumption bundle of goods 1 and 2 for consumer i.
Endowments: Each consumer has an initial endowment ei = (e1i, e2i) of both goods.
Pareto Efficiency: There exists an efficient allocation (x, y) for all consumers, where no other allocation can make someone better off without harming another.
Redistribution: There exists a feasible redistribution of endowments e’i = (e’1i, e’2i) for each consumer such that the sum of redistributed endowments remains the same as the original total: ∑ni=1 e’1i = ∑ni=1 ei1 and ∑ni=1 e’2i = ∑ni=1 ei2.
Theorem: Under the above assumptions, there exists a price vector p = (p1, p2) and consumption bundles xi for each consumer such that:
Competitive Equilibrium: The allocation (x, y) is a competitive equilibrium for the economy with redistributed endowments

165
Q

a utility function of 3 goods that is quasi linear and homogenous of degree 1

A

U(x1, x2, x3) = x1 + sqrt(x2x3)

166
Q

can a utility function of 2 goods be quasi linear and homogenous of degree 1

A

no

167
Q

expenditure function def

A

represents the minimum cost required to achieve a certain level of utility. E(p,u) = min p*x subject to U(X) >= u

168
Q

the duality result holds under what assumptions and why

A

holds under the assumptions of rationality, continuity, and strict convexity of preferences. These assumptions ensure a unique solution to the consumer’s optimization problem and a well-defined relationship between the indirect utility and expenditure functions

169
Q

duality result

A

V(p,w)=u <-> E(p,u)=w. the indirect utility evaluated at utility level u is equal to income w if and only if the expenditure function is equal to income.

170
Q

income effect def

A

describes how an increase in income or purchasing power can change the quantity of goods consumers demand

171
Q

substitution effect def

A

the decrease in sales for a product that can be attributed to consumers switching to cheaper alternatives when its price rises

172
Q

income and substitution effect on normal goods

A

both work in the same direction; a decrease in the relative price of the good will increase quantity demanded both because the good is now cheaper than substitute goods, and because the lower price means that consumers have a greater total purchasing power and can increase their overall consumption

173
Q

income and substitution effect on normal goods

A

work in opposite directions

174
Q

income and substitution effect on Giffen goods

A

positive income effect and negative substitution effect

175
Q

example of preferences that are represented by a continuous utility function that allows for fat indifference curves

A

perfect complements: U(x) = min{ax1, bx1}

176
Q

marshallian demand derived from

A

utility maximisation problem

177
Q

hicksean demand derived from

A

expenditure minimisation problem