Economics Flashcards
Homogeneity
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
Nonsatiation
Given any bundle - there is always some direction in which changing the bundle will make the consumer better off
Well behaved preferences
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
Convexity
Wealth preferred sets are convex or equivalently - MRS is diminishing
Perfect substitutes
u(q₁, q₂) = aq₁ +bq₂
Constant MRS: -a/b
IC: parallel straight lines
Only preferences which are homeothermic and quasi linear
Perfect complements
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
Cobb-Douglas
u(q₁, q₂) =a ln (q₁) + b ln (q₂)
IC: smooth
MRS: aq₂/bq₁ is diminishing
Roy’s Identity
Shows that uncompensated demands can be deduced from the indirect function by differentiation
Shepphard’s Lemma
Allows compensated demands to be decided from the expenditure function
Technically Efficient
Production is technically efficient if:
q = f(z)
The greatest possible output is being produced given the inputs
Marginal rate of technical substitution
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
Returns to scale
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
Budget line:
P1x1 + p2x2 ≤ m
Changes
Shift - income change
Slope change - price change - no of units of good 2 to give up for an additional good 1
Numerate goods
Setting one of the prices of a good = 1
Quantity Tax
Consumer pays an extra £1 for each unit of the good consumed
(p₁+t)x₁+ p₂x₂ ≤ m
Ad Valorem Tax
Levied as a percentage
p₁(1+t)x₁ + p₂x₂ ≤ m
Subsidy
Reduces the effective tax
quantity subsidy: (p₁-s)x₁ + p₂x₂ ≤ m
Ad Valorem subsidy: p(1-σ)x + p₂x₂ ≤ m
Lump sum tax
Takes away a fixed amount of the consumers income => shifts budget line
p₁x₁ + p₂x₂ ≤ m -t
Assumptions about preferences
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)
Indifference Curves
Graphically represent preferences
An IC is the locus of consumption bundles along which the consumer is indifferent
ICs cannot cross
Marginal Rate of Substitution MRS
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
Elasticity of substitution
Percentage change in the ratios of the two goods for a 1% increase in the MRS
Homothetic preferences
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
Sufficiency and necessary conditions
Tangency between the budget constraint and IC is a necessary, not sufficient condition
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)
Properties of Indirect Utility Function
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
Effects of a price change
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
Hicksian substitution
Changing relative prices while holding utility level constant
Income effect
The residual hangs in the Qd from a ceteris paribus price change after accounting for the substitution effect
Substitution vs income
Griffen Good: income effect > substitution effect
Quasilinear: substitution = total effect
Perfect Complements: income = total effect
Perfect Substitutes: substitution = total effect
Compensating variation
The adjustment in income that returns the consumer to the original utility after an economic change has occurred
Equivalent Variation
The adjustment in income that changes the consumer’s utility equal to the level that would occur IF the event had happened
Properties of technology
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
Marginal rate of technical substitution
Rate at which a firm is willing to trade one factor input for another
–> slope of isoquant
Marshallian vs Hicksian
Utility Maximisation
Compensating Variation
The increase in income necessary to restore the consumers utility to its original level after a price change
Equivalent Variation
The Decrease in income necessary before the price change to reduce the consumers utility to its new level
The identities which link the Marshallian demand and Hicksian demand:
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)
Link indirect utility and expenditure
The maximum level of utility attainable with minimum expenditure is U
The minimum level of expenditure necessary to reach optimal utility is m
What does it mean to say a consumers choice behaviour satisfies WARP
Weak Axiom of Revealed Preferences
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
3 Axioms Consumer Preferences
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
Concave prices
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
Restrictions on price effects
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
