economics_varian
TRANSCRIPT
MICHAELMAS TERM 2008:
MICROECONOMICS NOTES
Based on Hal Varian: Intermediate Microeconomics
Peter C. May Economics & Management Worcester College, Oxford
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C1: THE MARKET
- Optimization Principle: People try to choose the best patterns of consumption that they can afford
- Equilibrium Principle: Prices adjust until the amount that people demand of something is equal to the amount that is supplied
- Exogenous Variable: Determined outside the model; assumed to be fixed - Endogenous Variable: Determined within the model - Heterogeneity: Differences between individuals, not everyone the same; opposite to
homogeneity - Reservation Price: A person’s maximum willingness to pay for something, i.e. the
price at which the consumer is just indifferent between purchasing or not purchasing the product
- Demand Curve: Measures how much people wish to demand/consume at each price - Supply Curve: Measures how much people wish to supply/produce at each price - Equilibrium Price: Where demand = supply; imbalances are unsustainable
o If qD>qS → excess demand, price will go up! o If qD<qS → excess supply, price will go down!
- Pareto Efficiency: Situation when there is no way to make some group of people better off without making some other group worse off
C2: BUDGET CONSTRAINT
- Underlying principle: “Consumers choose the best bundle of goods they can afford” - Budget set: Consists of all bundle goods that the consumer can afford at the given
prices and income → affordable consumption bundles, e.g. p1x1 + p2x2 ≤ m - Budget line: The set of bundles that cost exactly m, e.g. p1x1 + p2x2 = m - Good 2 can represent a composite good that stands for everything else that the
consumer might want to consume other than good 1 x2
Rearranging budget line: x2 = m/p2 – p1/p2 × x1
- Slope of the budget line: Measures the rate at which the market is willing to substitute good 1 for good 2 → the opportunity cost of consuming good 1
- Changing variables: Increasing income → parallel shift outward of the budget line Increasing p1 → budget line becomes steeper, vertical intercept stays
the same Increasing p2 → budget line becomes flatter, horizontal intercept stays
the same
x1
Budget Line: Slope: - p1/p2
Vertical intercept = m/p2
Horizontal intercept = m/p1
→ Budget Set
- 3 -
- Numeraire price: when we set one of the prices to 1; numeraire good: good whose price has been set equal to one
- Quantity tax: To pay a fixed amount per unit → In QS equation: p changes to (p−t) - Value/ad valorem tax: Percentage tax → In QS equation: p changes to p×(1−t) - Lump sum tax: Fixed amount independent of units
C3: PREFERENCES
- Consumer preferences: Ranking consumption bundles as to their desirability (x1, x2) f (y1, y2) → consumer strictly prefers (x1, x2) to (y1, y2) (x1, x2) ≥ (y1, y2) → consumer weakly prefers (x1, x2) to (y1, y2) (x1, x2) ~ (y1, y2) → consumer is indifferent between (x1, x2) and (y1, y2)
- Assumptions about preferences: Complete: Any two bundles can be compared Reflexive: Any bundle is at least as good as itself, i.e. (x1, x2) ≥ (x1, x2) Transitive: If (x1, x2) ≥ (y1, y2) and (y1, y2) ≥ (z1, z2), then (x1, x2) ≥ (z1, z2)
- Positive monotonic transformations: Way of transforming a utility function and without re-ordering preferences; i.e. if u(x) is a utility function, and ƒ is an arbitrary positive monotonic transformation, then the transformation ƒ(u(x)) represents the same preferences (only ordinal!) → u(x)≥u(y), then ƒ(u(x))≥ƒ(u(y))
- Indifference curves: Graphical representation of preferences → bundles on the boundary of the weakly preferred set, i.e. bundles for which the consumer is just indifferent to (x1, x2)
- Indifference curves representing distinct levels of preference cannot cross! x2
- Examples of preferences: 1. PERFECT SUBSTITUTES
Two goods are perfect substitutes if the consumer is wiling to substitute one good for the other at a constant rate → e.g. consumer only cares about the total number of pencils, not about their colours
IC: Straight lines 2. PERFECT COMPLEMENTS
Goods that are always consumed together, e.g. right shoes and left shoes → Consumer always wants to consume the goods in fixed proportions to each other (not necessarily one-to-one)
IC: L-shaped 3. BADS
Commodity that the consumer doesn’t like, i.e. from which he gets negative utility
x1
A
B
C
In this case the consumer would be indifferent between A and C, as well as A and B, and therefore indifferent between B and C. BUT C must be strictly preferred to B
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IC: Slope up and to the right; direction of increasing preference is toward the direction of decreased consumption of the bad
4. NEUTRALS Goods from which the consumer gets no negative or positive utility, i.e.
he doesn’t care about it one way or the other IC: Vertical or horizontal lines
5. SATIATION When there is some overall best bundle for the consumer, i.e. there
exists a point from which on he gets negative utility from consuming more
IC: Surround the satiation point - Well-behaved preferences: 2 criteria
a) Monotonicity: More is better than less, i.e. if (x1, x2) is a bundle of goods and (y1, y2) is a bundle with at least as much of both goods and more of one, then (y1, y2) f (x1, x2)! → negative slope & preference increases to the right and up
b) Convexity: Averages are preferred to extremes; without convexity, consumers would prefer to specialize, i.e. only consume one good → Consumer weakly prefers the weighted average to either bundle
- ALSO: ICs are invariant to positive monotonic transformations - Marginal Rate of Substitution (MRS): Measures how much the consumer is willing
to give up of good 1 to acquire more of good 2, i.e. MRS2,1 = marginal rate of substitution of good 2 for good 1
- MRS = Slope of indifference curves → always negative - MRS also measures marginal willingness to pay: how much he will ‘pay’ some of good 1 in
order to buy some more of good 2 - Diminishing Marginal Rate of Substitution: For strictly convex indifference curves,
MRS decreases in absolute value as we increase x1, i.e. the amount of good 1 that the person is willing to give up for an additional amount of good 2 increases as the amount of good 1 increases!
C4: UTILITY
- Utility: Way to describe preferences - Utility function: Way of assigning a number to every possible consumption bundle
such that more-preferred bundles get assigned larger numbers than less-preferred bundles → represent/summarize a preference ordering
- A monotonic transformation of a utility function is a utility function that represents the same preferences as the original utility function → just a relabeling of indifference curves
- Ordinal utility: only the order matters - Cardinal utility: attaches significance to the magnitude of utility - Examples of utility functions:
Perfect substitutes: u(x1, x2) = ax1 + bx2 Perfect complements: u(x1, x2) = min{ax1, bx2} Quasilinear preferences: u(x1, x2) = v(x1) + x2 Cobb-Douglas preferences: u(x1, x2) = x1
c x2
d (simplest algebraic expression that generates well-behaved preferences)
- MRS= -MU1/MU2
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- Monotonic transformations don’t change the MRS because the MRS is measured along an indifference curve, and utility remains constant along an indifference curve
Mathematical Appendix
!
du ="u(x1,x2)
"x1dx1 +
"u(x1,x2)"x2
dx2 = 0
MRS =dx2dx1
= #
"u(x1,x2)"x1
"u(x1,x2)"x2
= #MU1
MU2
C5: CHOICE
- Underlying principle: “Consumers choose the best bundle of goods they can afford” → “Consumers choose the most preferred bundle from their budget sets”
- Optimal choice of the consumer is that bundle in the consumer’s budget set that lies on the highest indifference curve
- The optimal consumption position is where the indifference curve is tangent to the budget line
x2
- 3 exceptions: a) Indifference curve might not have a tangent line, e.g. when there is a kink at
the optimal choice b) If budget constraint is kinked and convex, there might be more than one
optimum c) When there is a boundary optimum (consuming 0 of one good)
- BUT: tangency condition is sufficient if preferences are strictly convex - Tangency condition: Slope of indifference curve = slope of budget line
!
MRS = "p1p2
- Examples of optimal choices:
Perfect substitutes: x1= Perfect complements: x1=x2=m/(p1+p2) Neutrals/Bads: x1=m/p1; x2=0 Cobb-Douglas preferences: x1=c/(c+d) × m/p1, x2=d/(c+d) × m/p2
x1 x1*
x2*
m/p1 when p1<p2 0 ≤ x1 ≤ m/p1 when p1=p2 0 when p1>p2
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- If everyone faces the same prices for two goods, then everyone will have the same MRS, and will thus be willing to trade off the two goods in the same way
C6: DEMAND
- Demand function: x1(p1, p2, m) - Normal goods: Demand increases when income increases → demand always changes
in the same way as income changes: Δx1/Δm > 0 - Inferior goods: Demand decreases when income increases, e.g. gruel, shacks, low-
quality goods; Δx1/Δm < 0 - Income Offer Curve: Connects together the demand bundles as we shift the budget
line outward - Engel Curve: How demand changes as we change income
- Income Offer Curves: x2
Blue line: x1 inferior, x2 normal Red line: both goods normal - Engel Curves:
m
Green line: x1 normal Orange line: x1 inferior
- Luxury good: Demand increases by a greater proportion than income - Necessary good: Demand increases by a smaller proportion than income - Homothetic preferences: Preferences only depend on the ratio of good 1 to good 2
→ consumer prefers (tx1, tx2) to (ty1, ty2) for any positive value of t - If preferences are homothetic, then the income offer curves are straight lines through
the origin - Ordinary good: Demand increases when the price decreases Δx1/Δp1 < 0 → demand
curve slopes downwards - Giffen good: Demand increases when the price increases Δx1/Δp1 > 0 → demand
curve slopes upwards - Price offer curve: Connecting the optimal points when let p1 change while we hold p2
constant - Demand curve: How demand for a good changes as we change its price → plot of the
demand function x1(p1, p2, m) while holding p2 and m fixed
x1
x1
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- Price Offer Curves:
x2
Red line: both goods ordinary Blue line: x1 Giffen, x2 ordinary
- Demand Curves: p1
Orange line: x1 ordinary Green line: x1 Giffen
- Substitutes: Goods that, to some degree, substitute for each other, e.g. pens and pencils → Δx1/Δp2 > 0
- Complements: Goods that tend to be consumed together, albeit not always, e.g. shoes and socks → Δx1/Δp2 < 0
- Inverse demand function PD(Q): Measures the price at which a given quantity will be demanded
- The height of the demand curve at a given level of consumption measures the marginal willingness to pay for an additional unit of the good at that consumption level; p1=p2×|MRS|
C7: REVEALED PREFERENCE
- Principle of Revealed Preference: Let (x1, x2) be the chosen bundle when prices are (p1, p2), and let (y1, y2) be some other bundle such that p1x1 + p2x2 ≥ p1y1 + p2y2 → (x1, x2) f (y1, y2)
x2
X Y x1
- Indirectly Revealed Preferences: (Transitivity assumption) → If we know that (x1, x2) is directly revealed preferred to (y1, y2), and (y1, y2) is directly revealed preferred to (z1, z2), then we can conclude that (x1, x2) is indirectly revealed preferred to (z1, z2)!
x1
x1
- 8 -
- Weak Axiom of Revealed Preference (WARP): If (x1, x2) is directly revealed preferred to (y1, y2), and the two bundles are not the same, then it cannot happen that (y1, y2) is directly revealed preferred to (x1, x2)
- Strong Axiom of Revealed Preference (SARP): If (x1, x2) is revealed preferred (either directly or indirectly) to (y1, y2), and the two bundles are not the same, then it cannot happen that (y1, y2) is revealed preferred (directly or indirectly) to (x1, x2)
- WARP and SARP are necessary conditions that consumer choices have to obey if they are to be consistent with the economic model of optimizing choice
C8: SLUTSKY EQUATION
- When the price of a good changes, there are two effects: 1. Substitution effect – change in demand due to the change in the rate of
exchange between the two goods 2. Income effect – change in demand due to more/less purchasing power
- There are 2 decompositions: SLUTSKY: Adjusting to same purchasing power, but different level of
utility HICKS: Adjusting to same utility level, but different purchasing power
Slutsky
- Graphically: First pivot the budget line around the original demanded bundle and then shift the pivoted line out to the new demanded bundle
- Mathematical Description:
!
Substitution Effect "#x1s = x1( $ p 1, $ m ) % x1(p1,m), $ m = m + x1#p1
Income Effect "#x1n = x1( $ p 1,m) % x1( $ p 1, $ m )
Total Change "#x1 = #x1s + #x1
n
Substituting #x1m = %#x1
n
#x1 = #x1s %#x1
m
#x1#p1
=#x1
s
#p1%#x1
m
#p1
y
x
A
B
C
y*
2y*
ySS
Income Effect
Substitution Effect
Equations of Lines: 1) Original BC: pxx + pyy = m → (x*, y*) 2) Pivoted Line: pxx + 0.5pyy = pxx* + 0.5pyy* 3) Final BC: pxx + 0.5pyy = m
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- Slutsky Equation:
!
"x1"p1
="x1
s
"p1#"x1
m
"mx1 →
- Normal goods: Income effect works in the same direction as substitution effect
!
"x1"p1
="x1
s
"p1#"x1
m
"mx1
(-) = (-) - (+) → Demand increases as price decreases - Inferior goods: Income effect works in the opposite direction as substitution effect,
but is smaller
!
"x1"p1
="x1
s
"p1#"x1
m
"mx1
(-) = (-) - (-) → Demand increases as price decreases - Giffen goods: Income effect works in the opposite direction as substitution effect, and
outweighs it
!
"x1"p1
="x1
s
"p1#"x1
m
"mx1
(+) = (-) - (-) → Demand decreases as price decreases
- Perfect complements: 0 substitution effect, income effect = total effect - Perfect substitutes: 0 income effect, substitution effect = total effect if change from
good 1 to good 2, or 0 substitution effect, income effect = total effect if no change - Quasilinear preferences: 0 income effect, substitution effect = total effect
Hicks
- Graphically: Adjust budget constraint to new prices and find the point where it is tangent to the original indifference curve
- The Law of Demand: If the demand for a good increases when income increases, then the demand for that good must decreases when its price increases! → normal goods must have downward sloping demand curves
In this equation, the substitution effect is always negative, i.e. works in the opposite direction of the price
y
A
B
C
y*
2y*
ySH
Income Effect
Substitution Effect
- 10 -
C9: BUYING AND SELLING (ENDOWMENTS)
- Suppose consumer starts off with an endowment (ω1, ω2) → BC: p1x1 + p2x2 = p1ω1 + p2ω2
- The budget line always passes through the endowment and has a slope of -p1/p2 - Gross demand: Amount that the consumer ends up consuming - Net demand: Amount that the consumer buys/sells - Net demand = Gross demand – Endowment - If x1* > ω1 → Net Buyer of x1 - If x1* < ω1 → Net Seller of x1 - Price changes → Pivot the budget line around the endowment - Income effect can be subdivided into:
ORDINARY INCOME EFFECT – change in purchasing power due to change in price of good
ENDOWMENT INCOME EFFECT – change in purchasing power due to change in value of endowment
- Endowment Slutsky Equation:
!
"x1"p1
="x1
s
"p1+ (#1 $ x1)
"x1m
"m
EXAMPLE: Labour Supply
- Assumptions: non-labour income (M), consumption (C), wage rate (w), price level (p) and labour in hours (L):
pC = M + wL pC – wL = M pC + w(LMAX – L) = M + wLMAX
- Leisure (R): R = LMAX – L and the endowments RE = LMAX and CE = M/p, thus M = pCE:
pC + wR = pCE + wRE → Endowment BC with p1 = p, p2 = w, x1 = C, x2 = R, 1 ω1= CE, ω2 = RE
- Slutsky Decomposition for the effect on leisure R of an increase in wage w:
mRRR
wR
wR M
ES
!
!"#+
!
!=
!
! )(
(?) = (– ) + (–) × (+) [assuming leisure is a normal good] o When Substitution Effect > Total Income Effect → Total effect negative
(leisure decreases and labour increases as the wage rate increases) o When Total Income Effect > Substitution Effect → Total effect positive
(leisure increases and labour decreases as the wage rate increases) RESULT: Backward-bending labour supply curve!
C10: INTERTEMPORAL CHOICE
- Two budget constraints for intertemporal consumption:
o Present Value Budget Constraint:
!
c1 +c21+ r
=Y1 +Y21+ r
o Future Value Budget Constraint:
!
c1(1+ r) + c2 =Y1(1+ r) +Y2 - Slope = – (1+r)
- 11 -
- Borrower: c1 > Y1; Lender: c1 < Y1 - Two propositions:
If a person is a lender and the interest rate rises, he or she will always remain a lender
If a person is a borrower and the interest rate rises, he or she will always be worse off
- In order to take inflation into account: real interest rate →
!
1+ " =1+ r1+ #
, where ρ = real
interest rate, r = nominal interest rate and π = inflation rate - A consumer who can borrow and lend at a constant interest rate should always prefer
an endowment with a higher present value to one with a lower present value!
C14: CONSUMER SURPLUS
- Consumers’ and Producers’ Surplus:
P
Supply curve Demand curve
- The change in consumers’ surplus associated with a price change has a roughly trapezoidal shape → change in utility associated with the price change
- 2 more ways to measure the monetary impact of a price change on consumer: a) Compensating Variation – How much money would you have to
give the consumer after the price change to make him just as well off as before the price change
b) Equivalent Variation – How much money would you have to take away from the consumer before the price change to make him just as well off as after the price change
*CV & EV negative in this case
Q Q*
P*
x1 x1
x2 x2
CV
EV
COMPENSATING VARIATION
EQUIVALENT VARIATION
GREEN AREA – Consumers’ surplus BLUE AREA – Producers’ surplus
- 12 -
- CV = m(p1’, p2’, u’) – m(p1’, p2’, u) - EV = m(p1, p2, u’) – m(p1, p2, u) - If utility is Quasilinear, CV, EV and CS are all equal
C15: MARKET DEMAND
- Market demand curve = sum of the individual demand curves → ATTENTION: When adding linear demand curves, there may be kinks in the market demand curve
- Extensive margin: Decision whether or not to enter the market - Intensive margin: Decision to increase/decrease consumption - Elasticity: Measures of responsiveness:
o Price Elasticity of Demand (PED): Measures the responsiveness of the quantity demanded to a change in price
!
"x1 ,p1 =#x1#p1
$p1x1
→ for downward sloping demand curves: negative
o Cross Price Elasticity of Demand (XED): Measures the responsiveness of the quantity demanded to a change in the price of another good
!
"x1 ,p2 =#x1#p2
$p2x1
→ for complements: -ve, for substitutes: +ve
o Income Elasticity of Demand (MED): Measures the responsiveness of the quantity demanded to a change in income
!
"x1 ,m =#x1#m
$mx1
→ inferior goods: -ve, normal goods: +ve, between 0
- Independent in demand: 0 cross price elasticity (XED) for all other goods - Necessities: Income elasticity of demand between 0 and 1 - Luxury goods: Income elasticity of demand above 1 - How the absolute values of PED changes along a linear demand curve:
P
- Elasticity and Marginal Revenue:
!
R(q) = p(q) " q# R (q) = MR(q) = p(q) + # p (q) " q
MR(q) = p(q) " (1+dpdq
qp) = p(1+
1$)
→
!
MR = p(1" 1#)
Q
∞ elastic
1
inelastic
0
- 13 -
- Demand with constant elasticity, e.g. q = Apε or ln(q) = ln(A) + εln(p) - Linear demand curve: MR has the same y-intercept and is twice as steep (MR=a-bq) - Another expression for elasticity, e.g. PED:
!
"x1 ,p1 =d ln x1d ln p1
C16: EQUILIBRIUM
- Equilibrium Price: D(p*)=S(p*) - With tax: PS=PD – t → D(PD)=D(PS) - Deadweight Loss of a Tax: Net loss in consumers’ surplus plus producers’ surplus that
arises from imposing the tax → measures the value of the output that is not sold due to the presence of the tax
P Supply + tax
Supply BLUE AREA: Deadweight loss RED AREA: TAX REVENUE Demand
- Pareto Efficiency: No way to make any person better off without hurting anybody else
- Pareto efficient amount of output to supply in a single market is that amount where demand and supply curves cross → only point where the amount that demanders are willing to pay for an extra unit of output equals the price at which suppliers are willing to supply an extra unit of output
C18: TECHNOLOGY
- Factors of production: Inputs to production → land, labour, capital, entrepreneurship & raw materials (measured in flow units)
- Technological constraints → only certain combinations of inputs are feasible ways to produce a given amount of output
- Production set: All combinations of inputs and outputs that comprise a technologically feasible way to produce
- Production function ƒ(x1, x2): Boundary of the production set → measures the maximum possible output that you can produce from a given amount of input
- Isoquants: Set of all possible combinations of inputs 1 and 2 that are just sufficient to produce a given amount of output
- Properties of technology: o MONOTONIC: If you increases the amount of at least one of the inputs, it
should be possible to produce at least as much output as you were producing originally → free disposal: the firm can costlessly dispose of any inputs, having extra inputs around can’t hurt it; HENCE: MP is always positive!
Q
- 14 -
o CONVEX: if you have two ways to produce y units of output, (x1, x2) and (z1, z2), then their weighted average will produce at least y units of output
- Marginal product MP1(x1, x2): The extra output per extra unit of an input, holding all other inputs fixed
→
!
MP1 ="f (x1,x2)
"x1# 0
- Diminishing marginal product: We typically assume that the total output will go up at a decreasing rate as we increase the amount of only one factor, holding all others equal
- Technical Rate of Substitution TRS(x1, x2): (=MRTS) How much extra of factor 2 you need if you give up a little of factor 1 → Measures the slope of an isoquant
→
!
TRS = "MP1MP2
e.g. Y(L, K) → TRS=−MPL/MPK - Diminishing TRS: As we increase the amount of factor 1, and adjust factor 2 so as to
stay on the same isoquant, the TRS declines → Convexity - 2 time periods:
o Short run: Time period where at least one input is fixed (e.g. fixed amount of land)
o Long run: All the factors of production can be varied - Returns to scale: The factor by which output changes as we change the scale of
production (e.g. multiply all inputs by a constant factor) o CONSTANT RETURNS TO SCALE: ƒ(tx1, tx2) = tƒ(x1, x2) o DECREASING RETURNS TO SCALE: ƒ(tx1, tx2) < tƒ(x1, x2) o INCREASING RETURNS TO SCALE: ƒ(tx1, tx2) > tƒ(x1, x2)
C19: PROFIT MAXIMIZATION
- Profits = Revenues – Costs → (Π=TR-C)
→
!
" = piyi # $ ixii=1
m
%i=1
n
%
- All costs measured using appropriate market prices → measure of opportunity costs - Economic Costs/Opportunity Costs = Explicit Costs (easily identified and accounted
for cash outflows) + Implicit costs (Opportunity Cost of forgoing an alternative) - Accounting profit = Total Revenue − Explicit Costs - Economic profit = Total Revenue − Economic Costs - Economic Profit → Entering/Staying in the market; Economic Loss → Leaving the
market; 0 Economic Profit → Equilibrium! - Fixed factor: Amount is independent of the level of output → even if output = 0 - Variable factor: Amount changes as the level of output varies - Quasi-fixed factors: Must be used in a fixed amount (i.e. independent of output), as
long as output is positive
Short-run profit maximization:
!
maxx1
pf (x1,x 2) "#1x1 "#2x 2
pMP1 =#1
→ The value of the marginal product of a factor should equal its price
- 15 -
- Graphical representation of short-run profit maximization:
!
" = py #$1x1 #$2x 2
y(x1) ="p
+$2
px 2 +
$1p
x1
y
!
- The firm chooses the input and output combination that lies on the highest isoprofit
line (tangency condition: MP1=ω1/p)
Long-run profit maximization:
!
maxx1 ,x2
pf (x1,x2) "#1x1 "#2x2
!
pMP1 ="1pMP2 ="2
→ Factor demand curves: measure the relationship between the price of a factor and the profit maximizing choice of that factor
- Inverse factor demand curve: Measures the price of a factor for some for some given
quantity of inputs to be demanded
ω1
pMP1(x1, x2*) = price × marginal product of good 1 (MP decreases as x1 increases)
- Implication: Each factor demand function must be a decreasing function of its price - If pMP1>ω1 → firm should increase factor 1; if pMP1<ω1 → firm should decrease
factor 1 - Important relationship between competitive profit maximization and returns to scale:
o If the firm’s production function exhibits constant returns to scale and the firm is making positive profits in equilibrium, then doubling the outputs would double profits → contradict the assumption that previous output was profit-maximizing
o RESULT: If a competitive firm exhibits constant returns to scale, then its long-run maximum profits must be zero!
x1
Isoprofit lines slope = ω1/p
y=ƒ(x1, x̄ 2) → production function
y*
x1*
x1
- 16 -
o Also: it is implausible to have decreasing returns to scale everywhere, since subdividing the output would always increase profits
y
→ The supply function of a competitive firm must be an increasing function of the price of output (upward sloping supply curve!)
C20: COST MINIMZATION
- Cost function: C(ω1, ω2, y) → measures the minimum costs of producing a given level of output at given factor prices
- Isocost lines: Every point on an isocost curve has the same cost (C)
!
C ="1x1 +"2x2
x2 =C"2
#"1"2
x1
- Cost-minimization problem: Find the point on the isoquant that has the lowest possible isocost line associated with it:
x2
- Tangency condition: Slope of production isoquant = slope of isocost lines:
!
"MP1MP2
= TRS = "#1#2
- Conditional Factor Demands (or derived factor demands): x1(ω1, ω2, y) using the
equation above → measure the relationship between the prices and of output and the optimal factor choice of the firm conditional on the firm producing a given level of output y (in short: give the cost-minimizing choices for a given level of output) → always downward sloping (Δω1Δx1≤0)
- Average cost function: cost per unit to produce y units of output (AC=C(ω1, ω2, y)/y - Relationship between returns to scale and cost function:
x1
If the output price increases, the isoprofit lines become flatter (since slope = ω1/p) → increase in supply from y* to y’
y*
x1*
y’
x1
Isoquant ƒ(x1, x2)=y
Isocost lines Slope=-ω1/ω2
OPTIMAL CHOICE
- 17 -
o CONSTANT RETURNS TO SCALE: AC(ω1, ω2, y) = C(ω1, ω2, 1) → constant AC o DECREASING RETURNS TO SCALE: AC(ω1, ω2, y) > C(ω1, ω2, 1) → rising AC o INCREASING RETURNS TO SCALE: AC(ω1, ω2, y) < C(ω1, ω2, 1) → falling AC
- Short run cost function:
!
cs(y,x 2) ="1x1s("1,"2,x 2,y) +"2x 2
→ Minimum cost of producing output y = cost associated with using the cost-minimizing choice of inputs, where factor 2 is fixed
- Long run cost function:
!
c(y) ="1x1("1,"2,y) +"2x2("1,"2,y) → Minimum cost of producing output y = cost associated with using the cost-minimizing choice of inputs
- Relationship between short and long run cost functions:
!
c(y) = cs(y,x2(y))x1("1,"2,y) = x1
s("1,"2,x2(y),y)
→ The cost-minimizing amount of the variable factor in the long run is that amount that the firm would choose in the short run if it happened to have the cost-minimizing amount of the fixed factor
- Fixed costs: Costs associated with the fixed factors → there are no fixed costs in the long run!
- Sunk costs: Payment that is made and cannot be recovered - At the given level of output, a profit-maximizing firm will always minimize costs
BECAUSE: Profits = TR−TC, and if the firm wasn’t minimizing costs it would always be able to increase profits!
- If MP1/ω1 > MP2/ω2 → Increase amount of factor 1 and decrease amount of factor 2 to decrease costs
- CONDITIONAL FACTOR DEMANDS x1(ω1, ω2, y) give the cost-minimizing choices for a given level of output; the PROFIT MAXIMIZING FACTOR DEMANDS (pMP1(x1, x2)=ω1 solved for x1) give the profit-maximizing choices for a given price of output
C21: COST CURVES
- AC(y) = C(y)/y = CV(y)/y + F/y = AVC + AFC - MC(y) = ΔCV(y)/Δy = C’(y) → MC(1) = AVC(1) - Properties:
o AVC curve may initially slope down but need not, HOWEVER, it will eventually rise, as long as there are fixed factors that constrain production
o AC curve will initially fall due to declining AFC, BUT then rise due to increasing AFC → U-shape
o MC curve passes through the minimum of both the AC and the AVC curve:
!
AC(y) =C(y)
y" A # C (y) =
y # C (y) $C(y)y 2
= 0" # C (y) =C(y)
y
→MC=AC at minimum of AC
!
AVC(y) =C(y) " F
y# AV $ C (y) =
y $ C (y) " (C(y) " F)y 2
= 0# $ C (y) =C(y) " F
y
→MC=AVC at minimum of AVC
- 18 -
- The area under the MC curve = Total Variable Costs!
!
MC(y)dy = TVC(y) = CV (y)0
y"
- The optimal division of output between two plants must have the MC of producing output at plant 1 = MC of producing output at plant 2
→ MCP1=MCP2 - Long run cost function = Short run cost function adjusted to/evaluated at the optimal
choice of the fixed factors: C(y)=cS(y, k(y)) - Firm must be able to do at least as well by adjusting plant size as by having it fixed:
C(y)≤cS(y, k*) - At y*: C(y*)=cS(y*, k*) → optimal choice of plant size is k* - HENCE: short run average cost curve must be TANGENT to the long run average cost
curve! - Thus, the LAC is the lower envelope of the SAC:
Q
Costs
MC AC
AVC
Q
Costs
MC
BLUE AREA: Total Variable Costs
Q
Costs
LAC
SACs
- 19 -
- Relationship between long-run and short-run marginal costs with continuous levels of the fixed factor:
C22: FIRM SUPPLY
- Firm faces: a) Technological constraints (production function) b) Economic constraints (cost function)
- Perfect competition: Market structure with many small firms producing a homogeneous product → firm = PRICE TAKER: price independent of own level of output; HOMOGENEOUS PRODUCT: Regardless of the number of firms in the market, if consumers are well informed about prices, the only equilibrium price is the lowest price offered
- Demand curve faced by a competitive firm:
- In a perfectly competitive industry, supply decision: p=MC(y); MC curve of a competitive firm is precisely its supply curve
- Two exceptions: o When there are two levels of output where p=MC, the profit-maximizing
quantity supplied can lie only on the upward sloping part of the MC curve o Shutdown-condition – Firm is better off going out of business when:
!
"F ># = py "CV (y) " F →
!
CV (y)y
= AVC > p
- IN THE SHORT RUN: The supply curve is the upward sloping part of the MC curve that
lies above the AVC curve
Q
Costs
LAC
SAC
LMC SMC
y*
P
p*
Q
Demand Curve: • 0 above p* • Horizontal at p* • Entire market demand curve below p*
- 20 -
- Profits: Difference between total revenue and total costs → Π(y) = y×p(y) − y×AC(y) = y×(p(y) − AC(y)) or Π(y) = py − cV(y) − F
- Producer’s surplus: Profits + Fixed costs → PS = py − cV(y) = Π(y) + F - 3 ways to measure PS:
1) Total Revenue – Total Variable Costs 2) Area above the MC curve and below the price 3) Area to the left of the supply curve
1) Total Revenue – Total Variable Costs:
3) Area to the left of the supply curve
- Long Run supply curve: p = MCl(y) = MC(y, k(y)) → In contrast: Short run supply curve p = MCS(y) = MC(y, k) involves holding k fixed! - Typically, long run supply curve will be more elastic than short run supply curve - Shutdown condition in the long-run: p ≥ AC(y) → LRS curve is the upward sloping
part of the long run marginal cost curve that lies above the LRAC (not LRAVC)!
Q
Costs
MC AC
AVC
Supply Curve: • 0 below p=AVC • Horizontal at p=AVC • MC curve above p=AVC
p=AVC
Q
P
MC AC
AVC
p*
q* Q
P
MC AC
AVC
p*
q*
Q
P
MC AC
AVC
p*
q*
2) Area above MC Curve and below Price
- 21 -
- If constant returns to scale → LRS curve: horizontal line at cmin, level of constant AC! - Long run cases:
o If constant AC with or without free entry: LRS curve flat, profit = 0, number of firms indeterminate
o Increasing AC: a) restricted entry – LRS curve slopes up, positive accounting profits but 0 economic profit; or b) free entry – infinite number of firms producing infinitesimal output (implausible)
o Decreasing AC: incompatible with perfect competition o U-shaped AC: a) restricted entry – like SR situation, profits can persist; or b)
free entry – profits driven down to a minimal level, if market large relative to firms within it the LR industry supply curve is almost flat
C23: INDUSTRY SUPPLY
- Industry supply curve = sum of individual demand curves:
!
S(p) = Si(p)i=1
n
"
S1
S2
S1+S2
- Short run industry equilibrium: If p* = AC → 0 profits If p* < AC → negative profits (loss) If p* > AC → positive profits
- Long run industry equilibrium (given free entry & exit) If positive profits made in the short run, new firms will enter, driving
down prices until p* = AC → 0 profits If negative profits made in the short run, some firms will exit, so prices
rise until p* = AC → 0 profits - If there is free entry and exit, then the long run equilibrium will involve the maximum
number of firms consistent with nonnegative profits! - Approximate long run supply curve:
S1
S2 S3 S4
P
Q
→ Horizontal addition KINKED
P We can eliminate portions of the supply curves that can never be intersections with a downward sloping market demand curve in the long run → If there are a reasonable number of firms in the long run, the equilibrium price cannot get far from minimum average costs!
Q
Approximate supply curve p* = min(AC)
p*
Example: If S1(p)=p−10 and S2(p)=p−15 → p1(q)=q+10, p2(q)=q+15, by drawing we can see that kink at p=15
- 22 -
- The more firms there are in a given industry, the flatter is the long run industry supply
curve - HENCE, in the long run in a perfectly competitive industry without barriers to entry,
profits cannot go far from 0! - If a firm is making positive profits, it means that people value the output of the firm
more highly than they value the inputs! - If there are forces preventing the entry of firms into a profitable industry, the factors
that prevent entry will earn economic rents; the rent earned is determined by the price of the output of that industry
- Economic Rent: Payments to a factor of production that are in excess of the minimum payment necessary to have that factor supplied → Rent = p*y* − cV(y*) = PS
- Equilibrium rent will adjust to be whatever it takes to drive profits down to 0 - EXAMPLES:
o Convenience stores near the campus do not have high prices because they have to pay high rents, but they are able to charge high prices and earn high profits, so that landowners in turn are able to charge high rents!
o If a New York City cab operator appears to be making positive profits in the long run after carefully accounting for the operating and labour costs, he still does not make economic profits because he does not take into account the price/value of the licence!
- TAXATION in the short and long run: SRS1
D
- In the short run: part of the tax burden falls on consumers, and part of the tax burden falls on producers, BUT: in the long run, the ENTIRE tax burden falls on the consumer!
- 0 profits in the long run → industry will stop growing since there is no longer an inducement to enter
C24: MONOPOLY
- Monopoly: When there is only one supplier in the industry → PRICE MAKER: monopolist recognizes its influence over the market price and chooses that level of price and output that maximized its overall profits
- Properties: o Monopolist faces the total market demand curve, which slopes downward due
to diminishing marginal utility o Monopolist has to take into account the effect of its changes in output on the
inframarginal units, which could have been sold at the old price
P
Q
GREEN AREA: Consumer tax burden RED AREA: Producer tax burden
SRS0 LRS0
LRS1 t
PD’’
PS’’=PS=PD
PD’
PS’
- 23 -
o Entry into the industry is completely blocked; barriers to entry can include patents, extensive economies of scale and control over supplies or outlets through vertical integration
- HENCE: Whilst perfectly competitive firm has the condition MR=p because it behaves as if the impact of its output (qi) decision on price (p) was 0, a monopolist takes into account that increasing q brings about a fall in p, hence MR<p (demand)
!
TRPC (y) = p " y # MRPC (y) = pTRM (y) = p(y) " y # MRM (y) = p(y) + $ p (y) " y
!
MR(y) = p(y) " 1# 1$(y)
%
& '
(
) * + MR < p
- Monopolist’s profit-maximization problem:
!
maxyr(y) " c(y)# optimization condition MR(y) = MC(y)
MR(y) = p(y) $ 1" 1%(y)
&
' (
)
* + = MC(y)# p(y) =
MC(y)1"1/%(y)
- Mark-up Price: Compared to perfect competition, the monopolist sells its product at a market price that is a mark-up over marginal cost:
!
11"1/#(y)
→
- Market power: The more price inelastic (the closer ε(y) to -1) demand is, the greater the mark-up on the price and the market power of the monopolist!
- Monopolist produces less than the competitive amount of output (QM instead of Q*)
at a higher price (pM instead of p*) and is therefore Pareto inefficient - Total Welfare = Consumer Surplus + Producer Surplus; maximized when p=MC, but
the monopolist produces where p>MC → DEADWEIGHT LOSS DUE TO MONOPOLY (there are consumers who would derive benefits from the additional output that are greater than the marginal costs of producing these units)
- Reason: Monopolist would always be ready to sell an additional unit at a lower price than it is currently charging if it did not have to lower the price of all the other inframarginal units that it is currently selling
PRICE
OUTPUT
D=AR
MC
MR
Q* QM
p*
pM
→ Deadweight Loss due to Monopoly
Move from PC to M: - Loss in CS: A+B - Loss in PS: C - Gain in PS: A
Monopolist will never choose to operate where demand is inelastic (MR would be negative!)
A
B C
- 24 -
- Minimum Efficient Scale (MES): Output that minimizes average costs - Natural Monopoly: Occurs when a firm cannot operate at an efficient level of output
without losing money, often because there are large fixed costs and small marginal costs (ECONOMIES OF SCALE) or high costs of duplication or need for standardization → MES beyond demand curve; e.g. public utilities
- When do monopolies occur? → Depends on MES RELATIVE to market demand! o If demand is large relative to MES, a competitive market is likely to result o If demand is small relative to MES, a monopolistic industry structure is likely
- HENCE, shape of the AC curve, which in turn is determined by the underlying technology, is one important aspect that determines whether a market will operate competitively or monopolistically
- Theory of contestable markets: What determines firms’ behaviour most is not current level of competition, but degree to which potential competitors could enter market → if barriers to entry and exit are low, even a monopolist might be forced to charge low prices because high profits would act as signal for other firms to enter market
- Taxes: o PURE PROFIT TAX → No effect on a choice of output, only decrease profit o QUANTITY TAX
If linear demand curve and constant marginal cost: price rises by ½ of the tax
If constant elasticity demand curve: price rises by more than the amount of the tax
- Summary: Why does monopolist always set its price above MC?
!
TR = p(y) " y # MR = $ p (y) " y + p(y) = MCHence p(y) = MC % $ p (y) " y where $ p (y) " y < 0# p(y) > MC
- Problems of regulating monopolies: o Determining the true MC for the firm o Making sure that all customers are served o Ensuring that the monopolist will not make a loss at the new price and output
level
PRICE
OUTPUT
D=AR
MC
MR
Q* QM
p*
pM
AC
If a natural monopolist is forced to operate at the socially efficient level of output (Q*) it will make a loss (BLUE AREA); monopolist would make 0 profit/loss
- 25 -
- Economic & technological conditions that are conducive to the formation of monopolies:
o Large fixed costs and small marginal costs o Large minimum efficient scale relative to the market o Ease of collusion (cartels)
C25: MONOPOLY BEHAVIOUR
- Monopolists have an incentive to use their market power for Price Discrimination (charging different prices for different units/customers) in order to increase profits (by decreasing the effect of the inframarginal units)
- 3 Types: 1) First-degree price discrimination = Perfect price discrimination: Selling each
unit of the good to the individual who values it most highly at the maximum price this individual is willing to pay for it (at each consumer’s reservation price) → Entire CS is shifted to PS!
RESULTS: The effect on the inframarginal units disappears Producers ends up getting the entire surplus generated in the market Producer earns supernormal profits Perfectly PD monopolist is Pareto efficient, producing where p=MC
DANGERS: High-willingness-to-pay person can pretend to be the low-willingness-
to-pay-person → monopolist must be able to separate the individuals Costs of price discriminating may be very high
2) Second-degree price discrimination = Non-linear price discrimination: Price
per unit depends on how much you buy! → Give the consumer an incentive to self select (in practice, monopolist often encourages self-selection by adjusting the quality of the good)
B A C
3) Third-degree price discrimination: Most common form; monopolist charges
different prices to different groups of people
WILLINGNESS TO PAY
X0 X1
The high-demand consumer would prefer buying X0 at price A, leaving him with a surplus B instead of X1 at a price A+B+C, leaving him with 0 surplus. However, if the monopolist offers X1 at a price A+C, then the high-demand consumer would buy X1, giving him utility of A+B+C and paying A+C, leaving him with a surplus B → This generally yields more profit to the monopolist! (Economies of Scale)
QUANTITY
High demand consumer
Low demand consumer
- 26 -
!
maxy1 ,y2
p1(y1)y1 + p2(y2)y2 " c(y1 + y2)
MR1(y1) = MC(y1 + y2), MR2(y2) = MC(y1 + y2)
# MC(y1 + y2) = p1 $ 1"1%(y1
&
' (
)
* + = p2 $ 1"
1%(y2
&
' (
)
* +
p1p2
=1"1/%(y2)1"1/%(y1)
Hence, if |ε2|>|ε1|, i.e. group 2’s demand curve is more price elastic than group 1’s demand curve, then 1−1/|ε2|>1−1/|ε1| so p1>p2
→ The higher the PED, the lower the price under 3rd degree price discrimination! - Bundling: Selling several goods together; REASON: Price is determined by the
purchaser who was the lowest willingness to pay → bundling means reducing the dispersion of willingness to pay and therefore increasing the lowest willingness to pay
- Two-part tariffs (or Disneyland Dilemma)
- Monopolistic Competition: Industry structure in which there is product differentiation, so each firm has some degree of monopoly power, but there is also free entry and exit, so that profits are driven to 0 in the long run!
QUANTITY
Demand curve
PRICE
MC
X*
p*
A B
If the owners of the park set a price of p* per ride, then x* rides will be demanded → consumer surplus = orange area and area A is the profits earned. HOWEVER, if the owners set the price p=MC per ride, they can then increase profits by charging the entire triangle (orange + A + B) as the entrance fee
PRICE
OUTPUT
D=AR
QMC
pMC
AC
3 Observations: - Although profits are 0, the
situation is still Pareto inefficient → there is an efficiency argument for expanding output
- Firms will always operate to the left of the MES
- Monopolistic competition can result in too much or too little product differentiation
- 27 -
C27: OLIGOPOLY
- Oligopoly: When few firms dominate the industry, e.g. newspaper or airline industry - Duopoly: When there are only two suppliers - Results:
o Firms are interdependent; a firm’s behaviour will dependent on the behaviour of its competitors → strategic interdependence
o Each firm is a PRICE MAKERS, and also recognizes that its actions have a noticeable effect on the prices that other firms can receive
o No single equilibrium price/quantity, but several ways to model strategic interdependence
- 5 ways: o Sequential:
Stackelberg Duopoly/Quantity leadership – Sequential quantity setting
Price leadership – Sequential price setting o Simultaneous:
Cournot Duopoly – Simultaneous quantity setting Bertrand Duopoly – Simultaneous price setting
o Cartel Stackelberg Duopoly
- Sequential quantity setting: o Follower maximizes profits by setting its quantity in terms of unknown
quantity of leader o Then, the leader maximizes its profits taking into account the decision of the
follower → Asymmetric: one firm is able to make its decision before the other firm!
- Reaction function: Tells us how each firm will react to the other’s choice of output, e.g. y2=f2(y1)
Reaction curve of Firm 1 (leader) Reaction curve of Firm 2 (follower) Isoprofit lines
X2
X1 QL
QF
Knowing the reaction curve of the follower (blue line), the leader will choose the output on the highest isoprofit line on his reaction curve → QL and QM
Output if firm 1 was a monopolist
- 28 -
Sequential Price Setting - Characteristics:
o One firms sets its price, and the other firm chooses how much it wants to supply at that price
o The leader takes into account the behaviour of the follower when it makes its decision
o Follower takes the price as being outside of its control since it has already been set by the leader; Follower’s optimization problem:
!
maxy2
py2 " c2(y2)# p = MC2(y2)
o If the follower supplies S(p), the leader will face a residual demand curve: R(p)=D(p)−S(p) → Optimization: MRRES(y1)=MC1(y1)
Cournot Duopoly
- Simultaneous quantity setting: o Two firms are simultaneously trying to decide what quantity to produce o Equilibrium: Situation where each firm finds its beliefs about the other firm to
be confirmed; each firm optimally chooses to produce the amount of output that the other firm expects it to produce
o Reaction functions: y1 = ƒ1(y2e) and y2 = ƒ2(y1
e) Reaction curve of Firm 1 (leader) Reaction curve of Firm 2 (follower)
X2
X1 QC
QC
Equilibrium: where the two reaction curves cross! → Only equilibrium; at any other point one of the firms would not maximize its profits Example: Point A is not equilibrium because firm 1 could increase profits by moving to point B!
A B
QL QT
p*
Demand curve facing the leader → market demand curve – the follower’s supply curve (increasing MC for follower!) The leader equates his marginal revenue (MRRES(q)) and marginal cost (MC) to find his optimal quantity QL. The total amount supplied at the chosen price p* is QT, so the follower supplies the quantity QT−QL
MC of leader
Market demand curve
QUANTITY
Residual demand
MR of leader
Follower’s supply
PRICE
- 29 -
- If both firms have identical, constant marginal costs (c), then we can mathematically deduce:
!
Y = y1 + y2
MR1(y1) = p(Y ) " 1# s1$(y1)
%
& '
(
) * = MC = c
p(Y ) =c
1# si /$(yi)if si = 0.5
p(Y ) =c
1#1/2 " $(yi)<
c1#1/$(yi)
- If more than 2 firms: each firm has a small market share → price will be very close to MC (industry will be nearly competitive)
Bertrand Duopoly
- Simultaneous price setting: o Both firms are setting the prices and letting the market determine the quantity
sold o At any price above p=MC, each firm has an incentive to offer a price just
below its competitor, thereby getting the total market demand and earning higher supernormal profits!
o Graphically:
- If both firms offer a price p0, each one produces Q0/2 and firm 1 makes profits represented by the red box. However, it has an incentive to offer a price just below p0, e.g. p1, getting the total market demand and increasing profits to the blue box → Only equilibrium where p=MC!
Cartel
- A cartel consists of a number of firms colluding to restrict output and maximize industry profit (e.g. OPEC) → behave like a monopolist
- If collusion is possible, the firms do better to choose the output that maximizes total industry profits and then divide up the profits among themselves
Cournot duopolists sell at a lower price and therefore, the sum of their individual outputs is greater than the output of a monopolist → smaller deadweight loss!
QUANTITY QUANTITY
PRICE PRICE
p0 p1
Q0/2 Q0 Q1
D
MC MC
D
- 30 -
Reaction curve of Firm 1 (leader) Reaction curve of Firm 2 (follower)
Mathematically:
!
maxy1 ,y2
p(y1 + y2) " y1 + y2[ ] # c1(y1) # c2(y2)
$p(y1 + y2)$y1
y2 +$p(y1 + y2)
$y1y1 + p(y1 + y2) #MC1(y1) = 0
$p(y1 + y2)$y2
y1 +$p(y1 + y2)
$y2y2 + p(y1 + y2) #MC2(y2) = 0
% MC1(y1) = MC2(y2)
- HENCE: the two marginal costs will be equal in equilibrium; if one firm has a cost advantage, it will necessarily produce more than the other in equilibrium!
- A cartel will typically be unstable in the sense that each firm will be tempted to sell more than it has agreed upon if it believes that the other firms will not respond, i.e. TEMPTATION TO CHEAT → need for punishment strategy!
!
"1(y1) = p(y1 + y2) # y1 $ c1(y1)%"1
%y1= p(y1 + y2) +
%p(y1 + y2)%y1
y1 $MC1(y1)
%"1
%y1+%p(y1 + y2)
%y1y1 = 0&%"1
%y1= $
%p(y1 + y2)%y1
y1 where%p(y1 + y2)
%y1y1 < 0
&%"1
%y1> 0
- THUS: if firm 1 believes that firm 2 will keep its output fixed, then it will believe that it can increase profits by increasing its own production!
- Example for punishment strategy: “If I discover you cheating by producing more that your amount, I will punish you by producing the Cournot level of output forever”
o Present value of cartel behaviour: Πm+Πm/r o Present value of cheating: Πd + Πc/r, where Πd = profit from cheating (only
once) → Strategy useful if present value of cartel behaviour > present value of cheating
!
"m +"m
r>"d +
"c
r# r <
"m $"c
"d $"m
> 0
RESULT: As long as interest rate (r) is sufficiently small, i.e. the prospect of future punishment is sufficiently important, it will pay the firms to stick to their quotas
Cartel will produce somewhere along the red dotted line!
QUANTITY
PRICE
- 31 -
C31: EXHANGE
- Partial equilibrium analysis: How demand and supply are affected by the price of a particular good
- General equilibrium analysis: How demand and supply conditions in several markets determine the prices of several goods
o Simplest model: Pure exchange economy - Assumptions for pure exchange economy:
1) Competitive markets → Producers & Consumers = Price takers 2) 2 goods, 2 consumers 3) 2 stages:
a. Start with fixed endowments b. Trade; no production involved → quantities supplied = fixed
Edgeworth Box
- Allows us to depict the endowments, possible allocations and preferences of 2 consumers in one diagram
- Feasible allocation: When total amount consumed = total amount available
!
xA1 + xA
2 ="A1 +"A
2
xB1 + xB
2 ="B1 +"B
2
Person A
GOOD 2
GOOD 1
Endowment
x1A ω1A
x1B ω1B
x2B
ω2B
x2A
ω2A
Contract Curve B’s IC
A’s IC
Person B
GOOD 2
GOOD 1
Width = total amount of good 1 available Height = total amount of good 2 available