Neoclassical Trade Theory: Tools to Be Employed

Appleyard & Field (& Cobb): Chapters 5–7

Basic Concepts for the Consumer Theory• Bundle = combination of goods (that are

being consumed)• If a consumer gets the same amount of

utility from bundle A as from bundle B, she is indifferent between A and B

• Indifference curve is a set of all bundles that yield the same utility

• Slope of the indifference curve = marginal rate of substitution (MRS) = the increase of one good needed to compensate the loss of another goodo diminishing MRS declining marginal utility

convex indifference curve concave utility function

Indifference Curve (two goods)

Good Y

Good X103

12

4Indifference curve 1

Indifference curve 2

Higher utility

Budget Constraint and the Equilibrium

• Budget constraint (budget line) = maximum combinations of goods that can be bought with a fixed level of income (given the prices)

• Consumer maximizes her utility given her income and prices consumer chooses the highest indifference curve available

• In equilibrium: MRS = MUY/MUX = PX/PY

Good Y

Good Xx*

y*

Budget Constraint: PX*X+PY*Y= income Y=income/PY – PX/PY*XThat is, slope of the budget constraint = –PX/PY

Indifference Curve: MUX*X+MUY*Y=initial utility Y = (initial utility)/MUY-MUX/MUY*XThat is, slope of the indifference curve = -MUX/MUY

Equilibrium: PX/PY=MUX/MUY=MRS

The Consumer Equilibrium

Marginal Utility & Product• Marginal utility = the additional utility from

consuming an additional (very small) unit of a good.o Typically we assume that this is decreasing as

consumption of a good increases, e.g. increasing the consumption of water from zero to one litre a day increases utility more than a change of consumption from 1000 to 1001 litre a day.

• Marginal product = additional output from using an additional (very small) unit of factor of production.o Typically we assume that if you keep the other factors of

production constant, the marginal product is decreasing, e.g. you have 10 shovels (capital), then increasing the number of workers from 9 to 10 increases output more than increasing the workers from 10 to 11.

Production: Capital and Labour

Capital (K)

Labour (L)

High K/L ratio

Capital (K)

Labour (L)

Low K/L ratio

Basic Concepts for the Production Theory

• Isoquant = combinations of inputs that produce the same level of output

• Slope of the isoquant = Marginal rate of technical substitution (MRTS) = the increase of an input needed to maintain the level of output after a decrease of another input

• Isocost = combination of factors that can be bought for given input costs

Producer Equilibrium

Capital

LabourL*

K*

Isocost: PK*K+PL*L=cost of production K=(cost of production)/PK – PL/PK*L

Isoquant: MPPK*K+MPPL*L=output K = (output)/MPPK-MPPL/MPPK*K

Equilibrium: MRTS=MPPL/MPPK=PL/PK

(Firm chooses inputs to minimize the cost for given output)

Isoquant

Isocost

Generalizing for the Whole Economy• Community Indifference Curve

o If a give amount of good X is taken away from the economy how much of good Y is needed to put all consumers back to their initial utility level?

• Production Possibilities Frontiero What can be produced given the resources of the

economy (≈ budget constraint of the country)

• Instead of thinking about individuals, we now use the same ideas to think about whole countries. Note, however, that while this gives us the great gain of being able to use the powerful framework of the decision theory, one should be cautious of thinking about countries as if they were individuals. This point will be discussed in more detail later in the course.

Production Possibilities Frontier (PPF): Constant Opportunity Cost

Good Y

Good X

40

10

20

20

Good Y

Good X

40

10

15

20

PPF: Increasing Opportunity Cost

5

22

Why?1. Rising marginal cost2. Specific factors3. Different factor intensities

Autarky Equilibrium

Good XX*

Y*

Good Y

Equilibrium: MRT = PX/PY = MRS

ProductionPossibilities

Slope = -Marginal Rate of Transformation (MRT)

Community Indifference Curveslope = -MUY/MUX = -MRS

Slope = -PX/PY

Gains from TradeAssuming:1. Costless factor

mobility2. Full employment

of factors of production

3. The indifference curve can show welfare changes

For more discussion, see Appleyard and Field around page 93-95.

Good XXA

YA

Good Y

XPXC

YP

YC

Imp

ort

s

Exports

(PX/PY)FT

(PX/PY)A

Equilibrium: MRT = (PX/PY)FT = MRS

Consumption and Production Gains

Good X

Good Y (PX/PY)FT

(PX/PY)A consumption gain

production gain

Mutual Gains

Good XXA

YA

Good Y

XPXC

YP

YC

Imp

ort

s

Exports

(PX/PY)FT

(PX/PY)A

Good XXA

YA

Good Y

XP XC

YP

YCExp

ort

s

Imports

(PX/PY)FT

(PX/PY)A

Country 1 Country 2

Note that the graphs are not drawn accurately. In a two-country model, the amount of imports of good Y from Country 1 must equal the amount of exports of good Y to Country 2 (and similarly for good X…)

Identical PPF, Different Preferences

Good X

Good Y(PX/PY)A

(PX/PY)FT

(PX/PY)A

Defining Central Concepts for Neoclassical Trade Theory

• Terms of Trade = PX/PM

o the world price of a country's exports relative to the world price of its imports

o PX/PY in the two-country-two-goods-model

o terms of trade “improve” when this index rises, i.e. for the same amount of exports the country will get a larger amount of imports

• Offer Curve = reciprocal demand curve indicating country’s quantity of imports and exports at all terms of trade

Other Concepts Called “Terms of Trade”

• Income Terms of Trade = (PX/PM)*QX

o Index of total export earnings PX*QX

divided by price of imports country’s ability to import

• Single Factoral TOT=(PX/PM)*OX

o O=productivity index. Intuition: the amount of imports available for unit of work effort

• Double Factoral TOT=(PX/PM)*(OX /OM)

Deriving the Offer Curve

Good X

Good

Y

XPXC

YP

YC

(PX/PY)1

Good X

Good

Y

XPXC

YP

YC

(PX/PY)2

Exports1

Exports2

Imp

ort

s 1Im

port

s 2

Exports of good X

Imp

ort

s of

good

Y

Exports2

Exports1

Imp

ort

s 1

Imp

ort

s 2

(PX/PY)2 = TOT2

(PX/PY)1 = TOT1

Offer Curve

Potential price lines: PX*QX=PY*QY QY=(PX/PY)*QX

i.e. given the prices, the value of exports equals the value of imports

Note that there is a mistake in A&FFigure 4 page 99 (in the 4th ed.)

Putting the Offer Curves to One Graph

Exports of good X

Imp

ort

s of

good

Y

(PX/PY)2

(PX/PY)1

Offer Curve

Exports of good Y

Imp

ort

s of

good

X

(PX/PY)2

(PX/PY)1

Offer Curve

Country 1 Country 2

Imports of good X

Exp

orts o

f good

Y

Offer Curve

Trading Equilibrium:The determination of international prices

Good X: Exports from country 1

Imports to country 2

Good

Y:

Imp

ort

s to

cou

ntr

y 1

exp

ort

s fr

om

cou

ntr

y 2

(PX/PY)E = TOTE (PX/PY)’

Country 1’s offer curve

Country 2’s offer curve

Shift of Offer Curves (1)• Assume that in

Country 1 there is shift in preferences and the taste for imports (good Y) increases

• That is, for every terms of trade, country 1 is willing to trade more

• That is, the offer curve shifts rightwards

Exports of good X

Imp

ort

s o

f g

oo

d Y

(PX/PY)2

(PX/PY)1OC0

OC1

Shift of Offer Curves (2)

New equilibrium:

• More trade• New terms of

trade = new relative prices

• (PX/PY)E’ < (PX/PY)E o i.e. the

relative price of good Y increase

Good X: Exports from country 1

Imports to country 2

Go

od

Y:

Imp

ort

s to

co

un

try

1 ex

po

rts

fro

m c

ou

ntr

y 2

(PX/PY)E = TOTE

Country 1’s offer curves

Country 2’s offer curve

(PX/PY)E’ = TOTE’

Improvement in Terms of Trade:Substitution, Production and Income Effects

• Improvement in Terms of Trade relative price of the exported good X increases relative price of the imported good Y decreaseso Substitution effect: consumers shift

their purchases towards the imported goods

o Production effect: producers start producing more exports

o Income effect (terms-of-trade effect): real income of the home country rises (more demand for both X and Y)