Weeks 1 and 2: Outline

1
Weeks 1 and 2 Outline

• 3 conditions for General Equilibrium
• Producer Optimization (Px/Py MRT)
• Consumer Optimization (Px/Py MRS)
• Market Clearing
• Goods Markets Xc Xp, Yc Yp
• Factor Markets Lx Ly L, Kx Ky K
• Get the production point, consumption point,
  input allocations and prices.
• Need to determine factor rewards.
• Competitive Factors paid their VMP.
• Know Prices, MPP. Wage VMPL P(MPL)

2
Important Relationships in GE

• Px/Py MRT MPLy/MPLx MPKy/MPKx
• Px/Py MRS
• Wage VMPL Px MPLx Py MPLy
• Rent VMPK Px MPKx Py MPKy
• Real Wage
• In terms of X Wage/Px MPLx (Py/Px) MPLy
• In terms of Y Wage/Py MPLy (Px/Py) MPLx

3
Producer Optimization

• STEP 1 Draw a PPF in XY space
• Maximum Y that can be produced given X
• What does the PPF look like?
• (a) Downward Sloping if MPL and MPK0. Will be
  satisfied for all production functions we use.
  Implies if increase good X then need more inputs
  for X. So must take some inputs from Y. Implies
  must reduce Y.

4
Producer Optimization

• (b) Concave if production functions satisfy
  Diminishing Marginal Returns. Implies as we keep
  putting more inputs into X production, output of
  X increases more and more slowly.
• dMPL/dL
• (c) Linear if production functions satisfy
  Constant Marginal Returns. Implies as we keep
  putting more inputs into X production, output of
  X continues to increase at the same rate.
• dMPL/dL 0 and dMPK/dK 0

5
Producer Optimization

• (d) How to draw the PPF?
• Give all inputs to X and none to Y. Plot this
  point.
• Give all inputs to Y and none to X. Plot this
  point.
• Now join the 2 points As a concave curve if the
  PPF is concave. Or, as a straight line if the PPF
  is linear.
• (e) What is the slope of the PPF? MRT

6
Consumer Optimization

• STEP 2 Draw community Indifference Curves in XY
  space.
• Think of a nice Cobb-Douglas utility function and
  draw this map.
• What is the slope of the ICs? MRS

Y
Slope of IC at point A or the MRS at point A
Indifference Curve
A
X
7
STEP 3 Prices

• From the 3 conditions for a GE
• MRT Px/Py MRS
• Implies the equilibrium is at the tangency point
  of the PPF and the IC
• The tangent is the price line.

8
STEP 4 Market Clearing

• Working with PPFs.
• On the PPF. Implies all inputs used. So get
  factor market clearing.
• IC tangent to PPF (On the PPF). Implies consumed
  goods equal produced goods. So get goods market
  clearing.

9
Example FT 2 (Section 2)

• 2 Goods Cloth and Wheat
• Only 1 input L
• Home Country
• 1 worker produces 4 bushels of wheat or 2 yards
  of cloth.
• Has total 25 workers.
• Foreign Country
• 1 worker produces 1 bushel of wheat or 1 yard of
  cloth.
• Has total 100 workers.
• How will we get the GE for each economy?

10
Home Country MPL

• 1L produces 4W or 2C w 4L, c 2L
• MPLW 4, MPLC 2.
• Both MPLW and MPLC positive. So downward sloping
  PPF.
• MPLW and MPLC same for all workers (given).
• dMPLW/dL 0, dMPLC/dL 0
• So CONSTANT Marginal Returns. So get a Linear
  PPF.

11
Home Country PPF points

• Give all L to W. Implies w 4L 4(25) 100.
• No inputs left for C. Implies c 2L 2(0) 0.
• Give all L to C. Implies c 2L 2(25) 50.
• No inputs left for W. Implies w 4L 4(0) 0.
• Plot (w1,c1)(100,0) and (w2,c2)(0,50).

12
Home Country Drawing the PPF

• Now plot the two PPF points. Put W on the x-axis
  and C on the y-axis. (Just to match FT, no other
  reason you can reverse if you want).
• Remember the PPF is downward sloping. Your
  plotted points should also tells you this.
• Now use the earlier derived fact that the PPF is
  linear. Draw a straight line to join the 2
  points.
• The PPF!

13
Home Country Slope of the PPF

• Slope of the PPF MRT MPLc/MPLw
• With linear PPFs, the slope is constant. So the
  MRT is constant.
• What is the slope? Remember it is a straight
  line.
• Slope (w2-w1)/(c2-c1) (50-0)/(0-100) - ½
• MRT ½
• Also note that the Slope (w2-w1)/(c2-c1)
  2(25)/4(25) MPLcL/MPLwL MPLc/MPLw.
• ½ yard of Cloth is the OPPORTUNITY COST of Wheat.
  Increase W by 1. Need ¼ L for 1W. So reduce ¼ L
  in C. ¼ L can produce ½ C. Reduces C by ½ yard.

14
Home Country GE

• Draw the ICs.
• Draw the tangency point.
• You will note that since the PPF is a straight
  line, the PPF is also the tangent and hence the
  price line.
• We already know the slope of the PPF so we know
  the prices too. The price ratio is Pw/Pc MRT
  ½ MRS.
• Tangency point is the production and the
  consumption point. It is on the PPF so get both
  labor and goods market clearing.

15
Home Country Wages

• We have the Prices.
• We have the MPLs.
• So what are the Wages? Remember there is perfect
  competition.
• Wage VMPL Pw MPLw Pc MPLc
• Real Wage in terms of Wheat Wage/Pw
• Real Wage in terms of Cloth Wage/Pc

16
Home Country Real Wages

• Wage VMPL Pw MPLw Pc MPLc
• Wheat Wage/Pw MPLw (Pc/Pw)MPLc
• Cloth Wage/Pc MPLc (Pw/Pc)MPLw
• Wheat Wage/Pw 4 (2)2
• Cloth Wage/Pc 2 (1/2)4

17
Foreign Country PPF

• Repeat the previous steps. Use the same axes. Now
  MPLw 1, MPLc 1.
• You will find that MRS Pw/Pc 1 MRT
  MPLc/MPLw Opportunity Cost of Wheat.
• Real Wages
• Wheat Wage/Pw 1 1(1)
• Cloth Wage/Pc 1 1(1)

18
Comparing Home and Foreign

• Opportunity Cost of Wheat lower at home
• Home ½
• Prices Wheat cheaper at home
• Pw/Pc Home ½
• Real Wages Both higher at home
• Wage/Pw Home 4 1 Wage/Pw Foreign
• Wage/Pc Home 2 1 Wage/Pc Foreign
• Reflects that Labor is more SCARCE at home

19
Comparative Advantage

• OCW lower at home
• Home OCW ½
• Home has a lower OCW. Home has a CA in Wheat.
• OCC 1/OCW lower in foreign
• Home OCC 2 1 Foreign OCC
• Foreign country has a CA in Cloth.

20
Price Changes and the PPF

• Suppose world prices are given to you.
• PPF procedure is the same. Technical.
• IC procedure is the same. Preferences.
• What about the tangency?
• If cannot trade then prices determined at home.
  Tangency procedure is the same. World prices do
  not affect you since the home country is a closed
  economy.

21
Price Changes and the PPF

• What about the tangency if the economy opens up
  to trade?
• Tangency procedure is not the same.
• Draw the post-trade world price line (assume this
  is given to you for now).
• Remember the PPF and ICs are the same.
• Find the tangency between the New Price Line and
  the original PPF. Gives the new PRODUCTION point.
• Find the tangency between the new price line and
  the highest IC of your original IC MAP. Gives the
  new CONSUMPTION point.

22
International Trade

• New Production Point (Xp,Yp)
• New Consumption Point (Xc,Yc)
• Look at the x-axis.
• If Xp Xc, then you are exporting good X.
• If Xp
• If Xp Xc, then you are not trading good X.
• Look at the y-axis. Repeat.

23
International Trade FT Ex.

• Suppose World Price after Trade Pw/Pc 2/3.
• Recall Home Pw/Pc ½ Foreign Pw/Pc 1.
• New Home Production Point
• PPF same as earlier.
• New Price Line is steeper.
• New tangency point of PPF and the new Price
  line must be on one of the corners.
• Look for the corner where the new price line is
  above the PPF.
• This is the New Production point (100,0)
• Home does not produce any cloth. Produces as much
  wheat as possible.
• Makes sense because OCW is lower at home.

24
International trade Consumption

• New Home Consumption Point
• IC MAP same as earlier.
• New Price Line is steeper.
• Find the New Tangency Point.
• This is the New Consumption Point.
• With nice preferences, the New Consumption Point
  will be to the Left of the Autarky Tangency
  Point.
• Example New (40,40) Autarky (50,25)

25
International trade Home

• New Production Point (100,0)
• New Consumption Point (40,40)
• Look at the x-axis.
• 100 40. So Xp Xc, then you are exporting good
  X which is Wheat.
• Look at the y-axis.
• 0 which is Cloth.
• Makes sense. Buying Cloth from the foreign
  country since its OCC is lower there. Selling
  Wheat to the foreign country since your OCW is
  lower.

26
Gains from Trade

• Is the IC higher with Trade or in Autarky?
• If higher, then consumers are better off.
• So economy has got a welfare gain by opening the
  economy to trade.
• What is the GFT?

27
Home GFT

• Real Wages in Autarky at Home
• Wage VMPLw Pw MPLw Pw 4 VMPLc Pc MPLc
  Pc 2
• Wage/Pw 4
• Wage/Pc 2
• New Trade Price is Pw/Pc 2/3
• New VMPLw / VMPLc (Pw MPLw)/(Pc MPLc)
  (Pw/Pc)(MPLw/MPLc) (2/3)(4/2) 4/3 1.3
• VMPLw is higher that VMPLc. So all workers want
  to move to the Wheat industry.

28
Real Wages at Home after Trade

• Home only producing Wheat now. So we can only
  define VMPLw and not VMPLc.
• Wage VMPLw Pw MPLw Pw 4
• Real Wage
• Wheat Wage/Pw VMPLw/Pw
• Pw MPLw/ Pw MPLw 4.
• Cloth Wage/Pc VMPLw/Pc Pw MPLw/Pc (Pw/Pc)
  MPLw (2/3) 4 8/3.

29
Home GFT

• Trade Wage/Pw 4 Autarky Wage/Pw
• Trade Wage/Pc 2.67 2 Aut Wage/Pc
• Workers are at least as well-off after trade.
• In fact, here they are better-off.
• Note that the GFT comes from the higher ability
  to purchase Cloth (the imported good which was
  cheaper in the Foreign country).

30
International Trade Foreign

• Repeat the same for the foreign country.
• New Production Point (100,0)
• New Consumption Point is to the right of the
  Autarky Tangency Point. Say, new (60,60) and old
  (50,50).
• BOTH countries Gain from trade.
• Imports Wheat and Exports Cloth.
• Wage VMPLc
• Real Wage
• Wheat Wage/Pw VMPLc/Pw (Pc/Pw) MPLc (3/2)
  1 3/2 1.5
• Cloth Wage/Pc VMPLc/Pc MPLc 1 1

31
Foreign GFT

• Trade Wage/Pw 1.5 1 Aut Wage/Pw
• Trade Wage/Pc 1 Aut Wage/Pc
• Workers are at least as well-off after trade.
• In fact, here they are better-off.
• Higher ability to purchase Wheat.

32
Home Export Supply of W

• At Aut Home Price (Pr,X) (1/2, 0)
• At Trade Price (Pr,X) (2/3, 60)
• Think of an increase in Trade Price. The price
  line is steeper now and consumption moves more to
  the left. So Homes Export Supply Curve is Upward
  sloping.
• Why? Cloth cheaper. Substitute into cloth.
  (Assuming that extra income from wheat does not
  dominate the substitution). Also Foreign country
  wants to sell more Cloth since they are getting a
  better price.
• Homes Export Supply Curve is Convex.
• Why? If Price (Pw/Pc) increases by the same
  amount again, then want to consume less Wheat.
  Due to the law of Diminishing Marginal Utility,
  you now dont want to give up as much of Wheat as
  earlier because youre already consuming less of
  it.
• Similarly, by the law of Diminishing Marginal
  Returns, if you keep putting in more resources
  into Wheat production, the output of Wheat will
  rise more slowly.
• What about linear PPFs (with CONSTANT Marginal
  Returns)?

33
Home Export Supply of W

• At Aut Home Price (Pr,X) (1/2, 0)
• At Trade Price (Pr,X) (2/3, 60)
• At Price 2/3 Say, (Pr,X) (1, 80)
• At Price between ½ and 2/3 Say, (Pr,X) (0.55,
  55). Check this yourself.

34
Linear PPF Export Supply

• What else at Autarky price ½ ?
• When Price is ½ , workers get the same wages in
  both Wheat and Cloth (Just like in Autarky). This
  is because the slope of a linear PPF is ½ at all
  points.
• So can produce anywhere on the PPF and continue
  to consume at the desirable Consumption Point
  (which is the original consumption).

35
Linear PPF Export Supply of W

• What else at Autarky price ½ ?
• Consumption Point (50,50).
• Maximum Wheat Production 100
• Maximum Wheat X Prod Cons 100 -
  50 50
• Get a New Point (Pr,X) (1/2, 50)
• Already know Aut Point (Pr,X) (1/2, 0)
• Can also choose anything in the middle so join
  these 2 points to get a Straight Line at Autarky
  Price ½.

36
Foreign Excess Demand (Import Demand) of Wheat

• Usual Excess Demand Function
• Downward sloping for Price not equal to 1.
• Convex for Price not equal to 1. (Law of DMU
  still holds which gives the convex shape).
• But the Constant MR changes the shape at Foreign
  Autarky Price 1
• Straight line segment at Price 1 Foreign
  Autarky Price.
• Special property of Linear PPFs.
• Think of the Autarky Price in the case of a
  concave PPF No straight line portion.

37
Foreign Import Demand (Excess Demand) of Wheat

• At Pw/Pc 1 (Same as Foreigns Autarky Price)
• Continue to consume at A
• Can produce anywhere on the PPF
• If produce all C, then Import Dd of W
• Cons Prod
• 50 (A) 0 (No W) 50
• If produce all W, then Export Supply of W
• Prod Cons
• 100 (all W) 50 (A) 50

All C Prod Point
Cloth
Pw/Pc1
100
Cons Point
A
All W Prod Point
Wheat
50
100
Max IM Dd of W at Pw/Pc 1
Max Ex Ss of W at Pw/Pc 1
38
Foreign Import Demand (Excess Demand) of Wheat

• At Pw/Pc 1 (Autarky Price)
• Continue to consume at A
• Can produce anywhere on the PPF
• If produce all C, then Import Dd of W Cons
  Prod 50 (A) 0 (No W) 50
• If produce all W, then Export Supply of W Prod
  Cons 100 (all W) 50 (A) 50
• At Pgreen point , Consume at pink tangency point).
• At Pat green point, Consume at blue tangency point)

New Prod Point for P P
New Cons Point for P
100
New Cons Point for P
P
A
P
Pw/Pc1
50
100
IM Dd of W at P
IM Dd of W at P
39
Foreign Import Demand (Excess Demand) of Wheat
Plot the points we just derived. The graph should
look like this.
Convince yourself that this quadrant looks like
this.
Pw/Pc
1
P
P
50
50
Excess Ss of Wheat
Excess Dd of Wheat
40
Equilibrium Trade Patterns

• Intersection of Home X Ss and Foreign M Dd of
  Wheat.
• Home X Ss Foreign M Dd
• Market Clearing
• Wheat produced in the world Wheat consumed in
  the world.
• Home Prod Foreign Prod Home Cons Foreign
  Cons
• Home Prod Home Cons Foreign Cons Foreign
  Prod
• Home X Ss Foreign M Dd

41
Equilibrium Terms of Trade

• ToT Price of Exports / Price of Imports
• Home exports W so its ToT Pw/Pc 2/3
• Can we say something about ToT?
• Recall the Average Cost of producing W at Home
  Amount paid to 1 worker Wage at Home
• Similarly, AC of producing Cloth in Foreign
  Wage in Foreign

42
Equilibrium Terms of Trade

• Here AC AVC.
• If Price
• Home produces W if Pw ACw Wage/MPLw
• Foreign produces C if Pc ACc Wage/MPLc
• Suppose Pw 1.
• Wage at Home Pw MPLw 4.
• Wage in Foreign Pw MPLw 1.
• Home Pc ACc 2. Pw/Pc ½.
• Foreign Pc ACc 1. Pw/Pc 1.
• ½

43
Equilibrium Terms of Trade

• ToT Price of Exports / Price of Imports
• Home exports W so its ToT Pw/Pc 2/3
• Can we say something about ToT?
• Recall the Average Cost of producing W at Home
  Amount paid to 1 worker Wage at Home
• Similarly, AC of producing Cloth in Foreign
  Wage in Foreign

44
Equilibrium Terms of Trade

• Here AC AVC.
• If Price
• Home produces W if Pw ACw Wage/MPLw
• Foreign produces C if Pc ACc Wage/MPLc
• Suppose Pw 1.
• Wage at Home Pw MPLw 4.
• Wage in Foreign Pw MPLw 1.
• Home Pc ACc 2. Pw/Pc ½.
• Foreign Pc ACc 1. Pw/Pc 1.
• ½