Economics

Question 1

Homogeneity

Answer 1

Multiplying y and p by the same factor does not affect the budget constraint

If it does not affect motivations for choice within budget sets, choices should not be affected either

Marshal loan demands - homogeneous of degree 0

Question 2

Nonsatiation

Answer 2

Given any bundle - there is always some direction in which changing the bundle will make the consumer better off

Question 3

Well behaved preferences

Answer 3

Monotonicity: at least as much of both goods is better

Larger bundles are preferred to smaller bundles

IC’s slope downwards - MRS - marginal rate of substitution

Convenient: averages are preferred to extremes

Question 4

Convexity

Answer 4

Wealth preferred sets are convex or equivalently - MRS is diminishing

Question 5

Perfect substitutes

Answer 5

u(q₁, q₂) = aq₁ +bq₂

Constant MRS: -a/b

IC: parallel straight lines

Only preferences which are homeothermic and quasi linear

Question 6

Perfect complements

Answer 6

u(q₁, q₂) = min(aq₁, bq₂)

IC: L-shaped with kinks in the Rays though the origin of slope a/b

Homothetic preferences
Not quasilinear

Question 7

Cobb-Douglas

Answer 7

u(q₁, q₂) =a ln (q₁) + b ln (q₂)

IC: smooth

MRS: aq₂/bq₁ is diminishing

Question 8

Roy’s Identity

Answer 8

Shows that uncompensated demands can be deduced from the indirect function by differentiation

Question 9

Shepphard’s Lemma

Answer 9

Allows compensated demands to be decided from the expenditure function

Question 10

Technically Efficient

Answer 10

Production is technically efficient if:

q = f(z)

The greatest possible output is being produced given the inputs

Question 11

Marginal rate of technical substitution

Answer 11

MRT

The rate at which any input has to be increased as we decrease another holding output constant

This is the MRT between the two

Slope of isoquant

Question 12

Returns to scale

Answer 12

Concerned with the feasibility of scaling up and down production plans

DRTS: scaling up the input vector results in a less than proportionate increase in output

λf(z) > f(λz)

If production is homogenous - there are DRTS if α>1

Question 13

Budget line:

P1x1 + p2x2 ≤ m

Changes

Answer 13

Shift - income change

Slope change - price change - no of units of good 2 to give up for an additional good 1

Question 14

Numerate goods

Answer 14

Setting one of the prices of a good = 1

Question 15

Quantity Tax

Answer 15

Consumer pays an extra £1 for each unit of the good consumed

(p₁+t)x₁+ p₂x₂ ≤ m

Question 16

Ad Valorem Tax

Answer 16

Levied as a percentage

p₁(1+t)x₁ + p₂x₂ ≤ m

Question 17

Subsidy

Answer 17

Reduces the effective tax

quantity subsidy: (p₁-s)x₁ + p₂x₂ ≤ m

Ad Valorem subsidy: p(1-σ)x + p₂x₂ ≤ m

Question 18

Lump sum tax

Answer 18

Takes away a fixed amount of the consumers income => shifts budget line

p₁x₁ + p₂x₂ ≤ m -t

Question 19

Assumptions about preferences

Answer 19

Completeness:
Any 2 bundles can be compared

Reflectivity:
Any bundle is at least as good as itself

Transitivity:
If (x1,x2) ≥ (y1, y2) and (y1, y2) ≥ (z1, z2) then (x1, x2) ≥ (z1, z2)

Question 20

Indifference Curves

Answer 20

Graphically represent preferences

An IC is the locus of consumption bundles along which the consumer is indifferent

ICs cannot cross

Question 21

Marginal Rate of Substitution MRS

Answer 21

MRS - indicates how much the consumer is willing to give up of good 2 for an incremental increment of good 1

MRS if IC: gradient at any point

Question 22

Elasticity of substitution

Answer 22

Percentage change in the ratios of the two goods for a 1% increase in the MRS

Question 23

Homothetic preferences

Answer 23

If the MRS of an IC representing a particular type of preferences depends only on the ratio of the 2 goods, then those preferences are Homothetic

Question 24

Sufficiency and necessary conditions

Tangency between the budget constraint and IC is a necessary, not sufficient condition

Answer 24

Necessary condition:
FONCs of the consumers utility max problem

Sufficiency condition:
Requires the MRS to be decreasing in the quantity of good 1 consumed
The utility function must be quasi-concave (negative)

SOSC: requires that the bordered Hessian Matrix be negative definite → have principal minors that alternate in sign (starting negative)

Question 25

Properties of Indirect Utility Function

Answer 25

V(p₁, p₂, m):

• non-increasing in price
• increasing in income
• homogeneous of degree zero in prices and income
• quasi-convex in prices
• Roy’s Identity

Question 26

Effects of a price change

Answer 26

Substitution effect: prices of good 1 decreases
- rate at which good 1 and 2 are exchanged decreases ie. Giving up a unit of good 1 returns fewer good 2

Income effect: price of good 1 decreases
- purchasing power increases ie. If same level of utility is attained, then entire budget is not used

Question 27

Hicksian substitution

Answer 27

Changing relative prices while holding utility level constant

Question 28

Income effect

Answer 28

The residual hangs in the Qd from a ceteris paribus price change after accounting for the substitution effect

Question 29

Substitution vs income

Answer 29

Griffen Good: income effect > substitution effect

Quasilinear: substitution = total effect

Perfect Complements: income = total effect

Perfect Substitutes: substitution = total effect

Question 30

Compensating variation

Answer 30

The adjustment in income that returns the consumer to the original utility after an economic change has occurred

Question 31

Equivalent Variation

Answer 31

The adjustment in income that changes the consumer’s utility equal to the level that would occur IF the event had happened

Question 32

Properties of technology

Answer 32

Monotonicity:
If you increase the amount of at least one input - should be possible to products at to East as much as originally

Convenient in Isoquant:
If you have 2 ways to produce y units of output: their weighted average will produce at least Y units of output as well
If there are 2 feasible production plans that generate the same output - then so will a convex combination of them

Concavity of the Production Function:
The marginal product factor df/dx indicates the additional output possible from an infinitesimal increase in the use of the input

Question 33

Marginal rate of technical substitution

Answer 33

Rate at which a firm is willing to trade one factor input for another

–> slope of isoquant

Question 34

Marshallian vs Hicksian

Answer 34

Utility Maximisation

Question 35

Compensating Variation

Answer 35

The increase in income necessary to restore the consumers utility to its original level after a price change

Question 36

Equivalent Variation

Answer 36

The Decrease in income necessary before the price change to reduce the consumers utility to its new level

Question 37

The identities which link the Marshallian demand and Hicksian demand:

Answer 37

X₁(P1,P2,e(P1,P2,U) = h₁(P1,P2,U)

The demanded bundle that maximises expenditure is the same as the demanded bundle that minimises utility at wealth e(p1,p2,u)

h₁(p1,p2,v(1,p2,m)) = X₁(p1,p2,m)
The demanded bundle that maximises utility is the same that minimises e pen either at utility V(p1,p2,m)

Question 38

Link indirect utility and expenditure

Answer 38

The maximum level of utility attainable with minimum expenditure is U

The minimum level of expenditure necessary to reach optimal utility is m

Question 39

What does it mean to say a consumers choice behaviour satisfies WARP

Weak Axiom of Revealed Preferences

Answer 39

It means that if one bundle, say Bundle A, is directly revealed preferred to another bundle B under one set of prices, the. It cannot be that B is directly revealed preferred under a different set of Rouches. Ie. If A≻B, it cannot be that B≻A

Question 40

3 Axioms Consumer Preferences

Answer 40

Reflexivity : any bundle is at least as good as itself

Completeness : only 2 bundles can be compared and consumers either strictly prefer one over the other, weakly prefer one over the other or are indifferent

Rationality : people are rational - if x>y, y>z then x>z

Question 41

Concave prices

Answer 41

A function is concave if it’s Hessian matrix is negative semi-definite
Ie. The hessian matrix has a non-negative determinant and a first principal minor ai matrix with a negative determinant

Question 42

Restrictions on price effects

Answer 42

If price of some good goes up, then purchases of some good much be reduced so no good can be a Griffen good unless it has strong complements