Understanding The Standard Model in Applied Economics

1. PubPol/Econ 541 Classes 15, 16 The Standard Model by Alan V. Deardorff University of Michigan 2023

2. Quiz Q5 Q6 Q7 Mean 8.97 7.60 7.73 Median 9 7 7.5 Max 10 10 10 Min 8 5.5 6 S.D. 0.64 1.69 1.35 Class 15: The Standard Model 2

3. Pause for News Class 15: The Standard Model 3

4. Announcements • Paper 2 – Due Nov 8 • Meetings with me: – If your group wants to meet with me by Zoom, email me with a couple of suggested times for me to select from, including on the weekend if that’s what you prefer. • I’ll miss this week’s Thursday office hour (Nov 2) Class 15: The Standard Model 4

5. Outline • Relative supply • Relative demand • International equilibrium – Small country Two country world • Effects of growth • Effects of trade barriers Class 15: The Standard Model 5

6. The Standard Model* • Assumes – Two goods, cloth C and food F • Outputs: QC, QF • Prices: PC, PF – Takes as given: • Production possibilities – Represented by Production Possibility Frontier (PPF) • Preferences for consumption – Represented by community indifference curves – Assumed to be “homothetic” (see below) *Name given to this model by Krugman and Obstfeld (1991) and subsequent editions. Class 15: The Standard Model 6

7. The Standard Model • Also assumes (as before) – Homogeneous products – Perfect competition – No distortions (externalities, etc.) – Zero costs of trade (transport, etc.) except when we add tariffs • Also (and not needed before) – Balanced trade Class 15: The Standard Model 7

8. The model • Includes as special cases – The Ricardian model (but linear PPF) – Heckscher-Ohlin Model – Specific factors model Class 15: The Standard Model 8

9. Outline • Relative supply • Relative demand • International equilibrium – Small country – Two country world • Effects of growth • Effects of trade barriers Class 15: The Standard Model 9

10. Production Possibilities QF • Curvature – Ricardian Model: Not curved – Heckscher-Ohlin Model: due to industries’ different factor intensities – Specific Factors Model: due to diminishing returns to non- specific factor PPF = “Production Possibility Frontier” Why “Frontier”? Because it could certainly produce less, • If it produced inefficiently • Or if resources were not fully employed QC Class 15: The Standard Model 10

11. Prices QF • Price lines = iso-value lines: V = PCQC+PFQF • or QF = V/PF– (PC/PF)QC V3 –PC/PF V2 V1 QC Class 15: The Standard Model 11

12. Equilibrium Production Tangency implies maximum value QF • Supplies depend on price ratio, or “relative price”: SC = SC (PC/PF) SF = SF (PC/PF) SF0 –PC0/PF0 SC0 QC Class 15: The Standard Model 12

13. Equilibrium Production QF • Thus “Relative Supply”, RS = SC/SF, also depends on relative price, RP = PC/PF: RS= RS(RP) SF0 RP0 SC0 QC SF/SC=1/RS Class 15: The Standard Model 13

14. How Supplies Depend on Prices QF • ΔRP = Δ(PC/PF) > 0 => ΔSC> 0 ΔSF< 0 ΔRS > 0 RP1 RP0 SF0 SF1 SC0 SC1 QC ΔRP = Δ(PC/PF) > 0 Class 15: The Standard Model 14

15. Relative Supply RP = PC/PF • It follows that RS as a function of RP – thus RS(RP) – is upward sloping RS(RP) RP1 • Note: There is no reason for this to be a straight line. But it could curve either way. RP0 RS0 RS1 RS= SC/SF Class 15: The Standard Model 15

16. 16 Figure 6.2 How an Increase in the Relative Price of Cloth Affects Relative Supply In panel (a), the isovalue lines become steeper when the relative price of cloth rises. As a result, the economy produces more cloth and less food. Panel (b) shows the relative supply curve associated with the production possibilities frontier TT. The rise in the relative price of cloth leads to an increase in the relative production of cloth.

17. Pause for Discussion Class 15: The Standard Model 17

18. Questions (Not asked before) • If the relative price of C goes up, the isovalue line gets steeper. Is there a way to see this without deriving it or remembering the equation? • Does this model display upward sloping supply? How does it differ, in this respect, from the partial equilibrium model we have seen before? • In partial equilibrium, supply slopes up because marginal cost rises. Is that true here? Class 15: The Standard Model 18

19. Outline • Relative supply • Relative demand • International equilibrium – Small country – Two country world • Effects of growth • Effects of trade barriers Class 15: The Standard Model 19

20. Preferences QF • Represented by a family of indifference curves for the whole country: • Called “community indifference curves” • Their shapes are like those of individual consumers in micro- econ, but these are for the whole country. QC Class 15: The Standard Model 20

21. Preferences QF • If we knew the budget line, then we would use it to find demand, from – Tangency between budget line and an indifference curve • That’s the most preferred bundle of the two goods that consumers can afford. QC Class 15: The Standard Model 21

22. Equilibrium Demand QF • Given prices, income is the value of production. • So the budget line is the price line tangent to the PPF. • And demand is then given by its tangency with an indifference curve. D0 DF0 SF0 S0 DC0 SC0 QC Class 15: The Standard Model 22

23. Trade QF • For arbitrary prices, RP0, demand will not equal supply • Their difference will be trade: • Exports: SC–DC=XC • Imports: DF–SF=MF Trade Triangle D0 DF0 MF0 SF0 S0 RP0 XC0 DC0 SC0 QC We can use this as the complete model for the small-country case, and we will. But for the large country we’ll need Relative Demand. Class 15: The Standard Model 23

24. Relative Demand QF • We will use this first, however, to find Relative Demand: RD = DC/DF D0 DF0 SF0 S0 RP0 DC0 SC0 QC DF/DC=1/RD Class 15: The Standard Model 24

25. How Demands Depend on Prices RP1 QF • ΔRP = Δ(PC/PF) > 0 => ? • With no assumption on preferences (indifference curves) we can say little about how prices affect demand • (Recall “income and substitution effects” from microeconomics) D1 RP0 D0 DF0 RP0 DC0 QC Class 15: The Standard Model 25

26. Homothetic Preferences QF • So we assume: each indifference curve is a radial expansion or contraction of all others • Thus: – Ratio of demands depends only on ratio of prices – Change in income (with prices fixed) does not change relative demand RD = DC/DF QC Class 15: The Standard Model 26

27. How Demands Depend on Prices RP1 QF • With homotheticity: • ΔRP = Δ(PC/PF) > 0 => ΔDF> 0 ΔRD < 0 • But we still don’t know ΔDC>,=,< 0 • That’s why we now work with relative supply and demand. D1 DF1 RP0 D0 DF0 RP0 DC1 DC0 QC Class 15: The Standard Model 27

28. Relative Demand RP = PC/PF • It follows that RD(RP) is downward sloping RP1 • Note: Again, there’s no reason for this to be a straight line. It could curve either way. RP0 RD RD1 RD0 RD= DC/DF Class 15: The Standard Model 28

29. Autarky Equilibrium RP = PC/PF • Combine RS and RD RS RPaut RD RQaut RQ= QC/QF Class 15: The Standard Model 29

30. Pause for Discussion Class 15: The Standard Model 30

31. Questions (Not asked before) • Does this display downward sloping demand? How does it differ, in this respect, from the partial equilibrium model we have seen before? • As shown above, demand for C falls when its relative price rises. How could it be otherwise? • How will RPautand RQautchange with shifts in RS & RD? With changes in production possibilities and preferences? Class 15: The Standard Model 31

32. How Demands May Depend on Prices RP1 QF As RP rises, consumers still substitute away from cloth. But now they can buy more of both goods (the income effect), and with a tighter curvature of the indifference curves, they do, buying more cloth and more food. RP0 D1 DF1 D0 DF0 RP0 DC0 DC1 QC Class 15: The Standard Model 32

33. Outline • Relative supply • Relative demand • International equilibrium – Small country – Two country world • Effects of growth • Effects of trade barriers Class 15: The Standard Model 33

34. Small Country Trade • Suppose that the country is too small to matter for both PC and PFin the world market. Then RPW= PCW/PFWis given Class 15: The Standard Model 34

35. Small-Country Trade Equilibrium RP = PC/PF • RP0W > RPautimplies – RS0> RD0 – Country » Exports good C » Imports good F RS RP0W RPaut • RP1W< RPautimplies – RS1< RD1 – Country » Exports good F » Imports good C RP1W RD RS1 RD0 RS0 RD1 RQ= QC/QF Class 15: The Standard Model 35

36. Small-Country Trade Equilibria Trade Triangle Trade Triangle QF QF D0 RP1W S1 RD0 D1 RS1 S0 RP0W RS0 RD1 QC QC Class 15: The Standard Model 36

37. Pause for Discussion Class 15: The Standard Model 37

38. Questions (Not asked before) • Looking at the figures, where can you see the “gains from trade”? • Suppose that you knew that events in other countries were going to “worsen” your country’s terms of trade. – How will that hurt your country? – Would your country therefore be better off if it did not trade at all? Class 15: The Standard Model 38

39. Worsening of Terms of Trade QF QF RP0W RP1W D0 D1 S0 S1 Saut=Daut Saut=Daut D1 D0 S1 RP0W S0 RP1W QC QC Class 15: The Standard Model 39

40. Outline • Relative supply • Relative demand • International equilibrium – Small country – Two country world • Effects of growth • Effects of trade barriers Class 15: The Standard Model 40

41. Two-Country World • Additional assumption: – Preferences are the same in the two countries – Since they are also homothetic, • If the two countries’ consumers face the same relative prices (as they will with free trade)… • …then they will consume the two goods in the same proportions. Class 15: The Standard Model 41

42. World Relative Supply & Demand • For international equilibrium, we need world relative supply and demand (of 2 countries) • These cannot be gotten by just adding up those for the individual countries • Instead, they are weighted averages of the separate countries • QCW = QC+ QC* • QFW = QF+ QF* QC+ QC* => RQW = QF+ QF* QF QC QF* QC* = + QF+ QF* QF QF+ QF* QF* RQW = βQFRQ + (1–βQF)RQ* where βQF = QF+ QF* QF Class 15: The Standard Model 42

43. World Relative Supply & Demand • Thus: RSW = βSFRS + (1–βSF)RS* where βSF = SF+ SF* SF RDW = βDFRD + (1–βDF)RD* where βDF = DF+ DF* DF Class 15: The Standard Model 43

44. World Relative Supply RP = PC/PF World relative supply is a weighted average; it thus lies between the domestic and foreign relative supplies (Strictly speaking, these need not be straight and should not be parallel) • RS* RSW RSW’ RS • βSF The larger is the home share of supply, βSF = , the closer RSWwill be to home relative supply RS. • SF SF+ SF* • RQ= QC/QF Class 15: The Standard Model 44

45. World Relative Demand RP = PC/PF • Because preferences are identical and homothetic in the two countries, RD is the same in both. • So world relative demand is the same as well. RDW=RD=RD* RQ= QC/QF Class 15: The Standard Model 45

46. International Market Equilibrium RP = PC/PF • Int’l market equilibrium is the relative price that equates world relative supply to world relative demand. RS* RSW RS RP0 • As drawn, the home (no *) country is assumed to be the larger relative supplier of good C. • So home exports C. RDW RQ0 RQ= QC/QF Class 15: The Standard Model 46

47. 47 Figure 6.5a Equilibrium Relative Price with Trade and Associated Trade Flows

48. Movement Autarky to Free Trade RP = PC/PF RS* • Home: – RP rises – RQ rises – Exports cloth – Imports food • Foreign: – RP falls – RQ falls – Imports cloth – Exports food RSW RS RPaut* RP0 RPaut RDW RQ0 RQ= QC/QF Class 15: The Standard Model 48

49. International Market Equilibrium RP = PC/PF • The next slide shows production, consumption, and trade in this free-trade equilibrium RS* RSW RS RP0 RDW RQ0 RQ= QC/QF Class 15: The Standard Model 49

50. International Market Equilibrium QF* Foreign QF Home SF* DF* DF SF QC* DC SC QC SC* DC* Class 15: The Standard Model 50