1. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. Chapter 10 A Monetary Intertemporal Model: Money, Prices, and Monetary Policy

2. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-2 Chapter 10 Topics What is money? Monetary Intertemporal Model Real and nominal interest rates Neutrality of money Monetary policy: targets and rules

3. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-3 What is Money? Medium of exchange Store of value Unit of account

4. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-4 Table 10.1 Monetary Aggregates, July 2006 (in $Billions)

5. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-5 Equation 10.1 Inflation rate:

6. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-6 Equation 10.2 Fisher relation:

7. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-7 Equation 10.3 Approximate Fisher relation:

8. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-8 Figure 10.1 Real and Nominal Interest Rates, 1934-2006

9. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-9 Monetary Intertemporal Model Type of cash-in-advance model. Representative consumer, representative firm, and government. Consumers and firms require cash on hand to purchase goods, or can expend resources to use the services of banks to carry out transactions.

10. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-10 Timing of Events – Morning Session In the morning, consumers have money and bond balances, M - c and B - c, carried forward from last period. Pay taxes T in real terms. Buy bonds B c. Withdraw the remaining money, WD c.

11. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-11 Equation 10.4 Consumer’s currency withdrawal at the beginning of the day:

12. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-12 Timing of Events – Afternoon Session In the afternoon, the bank ATM machine is closed. No way to withdraw money any more. This makes the services of bank the only option. Receive wage income and dividend income. Choose a real amount X of the total real income to pay for consumption purchase. So PX is the nominal quantity of income spent on consumption via services of bank. Services of bank are costly, H(X) in real terms. Total expenditure of consumption purchase is a sum of PX and WD c. That is, PC = PX + WD c.

13. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-13 Equation 10.5 Consumer’s cash-in-advance constraint:

14. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-14 Timing of Events – Evening Session In the evening, carry forward what remains after all purchases are made and all income is received during the day.

15. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-15 Equation 10.6 Money balances held by the consumer at the bank at the end of the day: PY: income and dividend income.

16. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-16 Figure 10.2 The Cost of Banking Services

17. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-17 Equation 10.7 The marginal benefit for the consumer of using more banking services:

18. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-18 Equation 10.8 Consumer’s end-of-day money holdings:

19. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-19 Equation 10.9 Marginal cost for the consumer of using more banking services:

20. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-20 Equation 10.10 Determine the optimal choice of X:

21. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-21 Equation 10.11 Optimal choice of X, simplified:

22. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-22 Figure 10.3 The Consumer’s Optimal Choice of Banking Services

23. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-23 Figure 10.4 The Effect of an Increase in R on the Consumer’s Optimal Choice of Banking Services

24. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-24 Equation 10.12 The optimal choice of X is an increasing function of the nominal interest rate, R:

25. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-25 Representative Firm - Morning Begin with zero money balance (transfer to workers as wage and dividend income last period). Buy bond in the morning session. Withdraw the remaining money to pay for investment purchases.

26. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-26 Equation 10.13 Firm’s currency withdrawal at the beginning of the day:

27. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-27 Firm’s Behavior - Afternoon Use an amount X f of the total real revenue Y to pay for investment purchase via services of bank, which incurs real costs H (X f ). The total nominal purchase of investment goods, PI, is a sum of WD f + PX f.

28. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-28 Equation 10.14 Firms’ cash-in-advance constraint:

29. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-29 Firm’s Behavior - Evening Transfer what remains after all purchases are made.

30. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-30 Equation 10.15 Direct deposit made by the firm to the consumer’s bank:

31. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-31 Equation 10.16 Simplified direct deposit to the consumer: A = PY – PX f – H (X f )

32. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-32 Choice of Banking Services Like what happens to consumers, the optimal amount of banking service is determined by marginal costs = marginal benefits. The firms and consumers choose the same quantity of banking service.

33. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-33 Government Responsible for fiscal and monetary policy. Purchase G goods. Pay nominal interest and principal on government bond outstanding from last period. Finance G and payments by taxes, issuing new government bonds, and printing money.

34. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-34 Equation 10.17 Government budget constraint:

35. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-35 Competitive Equilibrium Consider only three markets: for current goods, for current labor, and money market. Focus on money market equilibrium.

36. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-36 Equation 10.18 Income-Expenditure identity:

37. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-37 Equation 10.19 Substitute using cash-in-advance constraints and government budget constraint:

38. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-38 Equation 10.20 Credit market clears in previous period:

39. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-39 Equation 10.21 Current credit market clears:

40. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-40 Equation 10.22 Money market clears in previous period:

41. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-41 Equation 10.23 In equilibrium, then:

42. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-42 Equation 10.24 Rewrite given the choice of banking services by the consumer and the firm:

43. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-43 Equation 10.25 “Money demand” relationship:

44. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-44 Equation 10.26 Nominal money demand function:

45. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-45 Equation 10.27 Nominal money demand using the Fisher relation:

46. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-46 Equation 10.28 Nominal money demand assuming the inflation rate equals zero (harmless assumption for our purposes here):

47. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-47 Equation 10.29 Money supply equals money demand:

48. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-48 Figure 10.5 The Nominal Money Demand Curve in the Monetary Intertemporal Model

49. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-49 Figure 10.6 The Effect of an Increase in Current Real Income on the Nominal Money Demand Curve

50. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-50 Figure 10.7 The Current Money Market in the Monetary Intertemporal Model

51. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-51 Figure 10.8 The Complete Monetary Intertemporal Model

52. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-52 Figure 10.9 A Level Increase in the Money Supply in the Current Period

53. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-53 The Neutrality of Money In the monetary intertemporal model, a level increase in the money supply increases the price level and the nominal wage in proportion to the money supply increase, but has no effect on any real macroeconomic variable.

54. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-54 Figure 10.10 The Effects of a Level Increase in M—The Neutrality of Money

55. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-55 Increase in Total Factor Productivity If z increases, this increases money demand (Y increases and r falls), which causes the price level to fall.

56. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-56 Figure 10.11 Short-Run Analysis of a Temporary Decrease in Total Factor Productivity

57. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-57 Figure 10.14 An Increase in the Cost of Banking Services

58. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-58 Figure 10.15 The Effect of an Increase in the Cost of Banking Services on the Choice of Banking Services

59. Copyright © 2008 Pearson Addison-Wesley. All rights reserved. 10-59 Figure 10.16 A Shift in the Demand for Money