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Capitolo 5

Capitolo 5. Debiti, Prestiti e Vincoli di Bilancio. Figure 5.01. Dotazioni, ricchezza, e consumo. Figure 5.1. Figure 5.01. D. M (student, low Y 1 today, high Y 2 tomorrow). A. Y 2. (Professional athlete, high Y 1 P today, low Y 2 tomorrow). Y 1. B. Endowment,.

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Capitolo 5

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  1. Capitolo 5 Debiti, Prestiti e Vincoli di Bilancio

  2. Figure 5.01 Dotazioni, ricchezza, e consumo Figure 5.1

  3. Figure 5.01 D M (student, low Y1 today, high Y2 tomorrow) A Y2 (Professional athlete, high Y1 P today, low Y2 tomorrow) Y1 B Endowment, wealth... Endowments M, A and P for interest rate r imply the identical wealth OB. Consumption tomorrow 0 Consumption today Figure 5.1

  4. Vincolo di bilancio C2=Y2+(Y1 – C1 )(1+r) C1 + C2/(1+r) = Y1 + Y2/(1+r) Y1 + Y2/(1+r) =  (ricchezza) Prezzo obbligazione • semplice – Bot B(1+r)=100  B=100/(1+r) • Irredimibile p = a/r (a = cedola)

  5. Figure 5.01 D A Y2 Y1 B Endowment, wealth... and consumption possibilities Consumption tomorrow 0 Consumption today Figure 5.1

  6. Figure 5.02 Ereditare ricchezza o debiti Figure 5.2

  7. Figure 5.02 D´ D D´´ } } B Inheriting wealth or indebtedness All three intertemporal budget lines are parallel because the real interest rate is assumed unchanged. Consumption tomorrow B´´ B´ 0 Consumption today Figure 5.2

  8. Possibilità indebitamento (B) C1 + C2/(1+r) = Y1 + Y2/(1+r) + B1

  9. Figure 5.03 La funzione di produzione Figure 5.3

  10. Figure 5.03 Production function Output Note: in chapter 4, capital input assumed constant and labour input allowed to vary. Here we assume labour input is constant (full-employment) and capital input varies. 0 Capital stock Figure 5.3

  11. Figure 5.04 Tecnologia conveniente Figure 5.4

  12. Figure 5.04 R A Productive technology (profit making up to point A) Output Gain from borrowing K is Y i.e. next period F(K) with no K left over. Cost of borrowing K = (1+r)K i.e. next period pay back principal plus interest 0 Capital stock Figure 5.4

  13. Valore dell’impresa V=F(K)/(1+r)-K Max V F’(K)/(1+r)-1=0  MPK = (1+r) (il risultato dipende dal fatto che, considerando 2 periodi, assumiamo implicitamente che =1; tutto il K viene consumato alla fine del 2 periodo)

  14. Figure 5.05 Tecnologia non conveniente Figure 5.5

  15. Figure 5.05 R Losses Unproductive technology Output 0 Capital stock Figure 5.5

  16. Figure 5.05 R Profits Productive technology Output Technological innovation 0 Capital stock Figure 5.5

  17. Figure 5.06 L‘investimento aumenta la ricchezza Figure 5.6

  18. Figure 5.06 D This curved part is just a “backward” production function when we choose to use part of Y1 for production instead of consumption in the first period. A Y2 Y1 B Suppose we save from our original endowment? Consumption tomorrow 0 Consumption today Figure 5.6

  19. Figure 5.06 E A Y2 K Y1 Suppose we save K out of Y1... D It is as though our initial endowment point were really E instead of A. Consumption tomorrow C1 B 0 Consumption today Figure 5.6

  20. Figure 5.06 D´ E Intertemporal trade at interest rate r but without production. F A Y2 K Y1 B´ Investment increases wealth D Consumption tomorrow C1 B 0 Consumption today Figure 5.6

  21. K2 = I1 = Y1 – C1 • C2 = Y2 + F(K2) • Vincolo di bilancio • C1 + C2/(1+r) =  sostituendo al posto di C1 e C2 le espressioni precedenti si ha che •  = (Y1 – I1) + [Y2 + F(K2)]/(1+r) o anche •  = [Y1 + Y2 /(1+r)] + V

  22. Teorema Modigliani-Miller “Il valore dell’impresa è indipendente da come l’impresa è finanziata” • V = E + B (E = azioni; B = obbligazioni) •  = profitti • Rendimento impresa = / V= /(E+B) • Rendimento azionisti E= ( - rB)/E= (V-rB)/E= [(E+B)-rB]/V

  23. Costo totale del capitale TC= rB+ E=rB- (E+B)-rB= (E+B) • Costo del capitale medio AC=TC/(E+B)= (E+B)/(E+B)= 

  24. Figure 5.07 Corporate and household net saving, 1981-87 Figure 5.7

  25. Figure 5.08 Il vincolo di bilancio dello stato Figure 5.8

  26. Figure 5.08 Government budget constraint Figure 5.8

  27. D1 + G1 + G2/(1+rG) = T1 + T2/(1+rG)

  28. Figure 5.08 The case of no old debt (D1=0) Budget deficittomorrow Budget deficittoday 0 Government budget line Figure 5.8

  29. Figure 5.09 Ireland Italy Primary budget surpluses USA U.K. Figure 5.9

  30. Figure 5.10 Equivalenza Ricardiana Figure 5.10

  31. Figure 5.10 D A Y2 Y1 B Before the government gets its share of the pie... The original endowment, i.e. before government spending and taxes, is A. The national wealth is the present discounted value of A, =0B Consumptiontomorrow 0 Consumption today Figure 5.10

  32. Figure 5.10 D D´ A Y2 A´ (Y2-G) (Y1-G) Y1 B´ B Bringing in the government Deducting the present value of government spending (equal to the present value of taxes by the government budget constraint), we have private wealth OB´ (= OB-B´B). For simplicity we assume identical G in both periods. Consumption tomorrow 0 Consumption today Figure 5.10

  33. I vincoli di bilancio dei settori pubblico e privato consolidati • C1 + C2/(1+r) = Y1 – T1 + [(Y2-T2)/(1+r)] • G1 + G2/(1+rG) = T1 + T2/(1+rG) • da cui si ottiene, assumendo che r=rG • C1 + C2/(1+r) = Y1 – G1 + [(Y2-G2)/(1+r)]

  34. Il settore privato internalizza il vincolo di bilancio del settore pubblico eliminando completamente le imposte dal vincolo di bilancio • Questa internalizzazione è nota come proposizione di equivalenza ricardiana: fintanto che Sett. Pubb e Sett Priv si indebitano e concedono prestiti allo stesso tasso gli spostamenti intertemporali si equivalgono

  35. Figure 5.10 Ricardian equivalence D The insight is that given the present value of government spending (i.e. the shift of private wealth to D´B´), it doesn’t matter for private wealth whether (i) there are low taxes and a deficit to be paid off later with higher taxes or (ii) higher taxes now so that taxes later are lower. D´ Consumption tomorrow A Y2 A´ (Y2-G) (Y1-G) Y1 B´ B 0 Consumption today Figure 5.10

  36. 3 modi di interpretare l’equivalenza ricardiana • La spesa totale non può superare la ricchezza della nazione. Dall’ultima relazione: C1 + C2/(1+r) = Y1 – G1 + [(Y2-G2)/(1+r)]  (C1+ G1)+[(C2+G2)/(1+r)] = Y1 + Y2/(1+r)

  37. Sempre dalla relazione: C1 + C2/(1+r) = Y1 – G1 + [(Y2-G2)/(1+r)] la ricchezza del settore privato è la differenza (in valore attuale) tra le dotazioni private e la spesa pubblica. Il profilo temporale delle imposte non produce alcun effetto sulla ricchezza privata; ciò che importa è la spesa pubblica

  38. C1 + C2/(1+r) = Y1 – G1 + [(Y2-G2)/(1+r)] quando il governo si indebita per finanziare il disavanzo emette obbligazioni, B. Il settore privato considera B come parte della loro ricchezza? A destra del segno di = tuttavia non compare alcun B. Infatti, +B+T in futuro. Per cui il debito pubblico non rappresenta ricchezza netta per il settore privato, in termini aggregati

  39. Casi nei quali l’equivalenza ricardiana perde validità • L’orizzonte temporale dei cittadini • r > rG  C1 + C2/(1+r) = Y1 – G1 + [(Y2-G2)/(1+r)] + [(r-rG)/(1+r)](G1 -T1) se r > rG  [(r-rG)/(1+r)](G1 -T1) >0 I minori costi di indebitamento dello Stato equivalgono alla concessione di un sussidio al settore privato (o quest’ultimo si indebita alle stesse condizioni dello Stato)

  40. Table 5.01 Public and private borrowing ratesMarch 2004: Long-term bonds (% per annum) Table 5.1

  41. Figure 5.11 • Vincoli all‘indebitamento Figure 5.11

  42. Figure 5.11 D A (Y2-G2) (Y1-G1) B Borrowing constraints If households are constrained from borrowing at all (but they can still save), they can choose only among the points along segment AD. Consumption tomorrow 0 Consumption today Figure 5.11

  43. Figure 5.11 D A (Y2-G2) A´ (Y2-T2) (Y1-G1) (Y1-T1) B One way to work around borrowing constraints... If the government is able to borrow at the interest rate r the government could reduce taxes today and raise taxes in the future (to pay for the tax saving this period plus interest). This increases budget segment of households to DA´. Consumption tomorrow 0 Consumption today Figure 5.11

  44. Figure 5.11 B´ Households face higher rate of interestif they borrow. D Consumption tomorrow A (Y2-G2) (Y1-G1) B 0 Consumption today Figure 5.11

  45. Figure 5.11 A´ (Y2-T2) (Y1-T1) B´´ Same way to ease the borrowing constraint of households D The government could reduce taxes today and raise taxes in the future (to pay for the tax saving this period plus interest). This increases budget segment of households to DA´B´´ from DAB´. Consumption tomorrow A (Y2-G2) (Y1-G1) B´ 0 Consumption today Figure 5.11

  46. Distorsione fiscale e le risorse inutilizzate: come reagiscono le persone ad un aumento delle tasse? Es. effetti sull’offerta di lavoro

  47. Figure 5.12 Ricardian equivalence in Denmark, 1981-2002 Fig. 5.12

  48. Il conto delle partite correnti e il vincolo di bilancio della nazione Il risparmio netto del paese rispetto al resto del mondo è determinato dal saldo delle PC (= saldo primario delle PC + reddito netto da investimenti esteri): PC = SPPC + rF F = posizione netta nei confronti del resto del mondo; F>0 (attività>passività)

  49. Vincolo di bilancio: SPPC1 + SPPC2/(1+r)=0, se F=0 oppure SPPC1 + SPPC2/(1+r)= -F1

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