1 / 30

Lecture 5

Lecture 5. The Micro-foundations of the Demand for Money - Part 2. State the general conditions for an interior solution for a risk averse utility maximising agent Show that the quadratic utility function does not meet all these conditions

christmas
Download Presentation

Lecture 5

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lecture 5 The Micro-foundations of the Demand for Money - Part 2

  2. State the general conditions for an interior solution for a risk averse utility maximising agent • Show that the quadratic utility function does not meet all these conditions • Examine the demand for money based on transactions costs • Examine the precautionary demand for money • Examine buffer stock model of money

  3. The Tobin model of the demand for money • Based on the first two moments of the distribution of returns • Generally a consistent preference ordering of a set of uncertain outcomes that depend on the first n moments of the distribution of returns is established only if the utility function is a polynomial of degree n. • Restricting the analysis to 2 moments has weak implication of quadratic utility function

  4. Arrow conditions • Positive marginal utility • Diminishing marginal utility of income • Diminishing absolute risk aversion • Increasing relative risk aversion

  5. Arrow conditions

  6. Quadratic Utility Function U Max U U(R) R

  7. Alternative specifications • Set b > 0 - but this is the case of a ‘risk lover’ • A cubic utility function implies that skewness enters the decision process - not easy to interpret. • But the problems with the quadratic utility function are more general

  8. A Paradoxical Result

  9. Equation of a circle R 45o -a/2b R

  10. The Opportunity Set

  11. R P’ C P B A 0 R  = 1

  12. Implications • Slope of opportunity set is greater than unity • wealth effect will dominate substitution effect • for substitution effect to dominate r <g • bond rate will have to be lower the volatility of capital gains/losses

  13. Transactions approach • Baumol argued that monetary economics can learn from inventory theory • Cash should be seen as an inventory • Let income be received as an interest earning asset per period of time. • Expenditure is continuous over the period so that by the end of the period all income is exhausted

  14. Assumptions • Let Y = income received per period of time as an interest earning asset • Let r = the interest yield • Expenditure per period is T • Suppose agent makes 2 withdrawals within the period - one at beginning and one before the end.

  15. More ? • Suppose 0 <  < 1 is withdrawn at the beginning of the period • Interest income foregone = (average cash balance during the fraction  of the period) x (the interest rate for the fraction of the period ) • (Y/2)(r) = ½ 2rY

  16. More • Later (1- )Y is withdrawn to meet expenditure in the remainder of the period (1- ) time • Thus agent gives up ½(1- )2rY • Let total interest foregone = F • F =½ 2rY + ½(1- )2rY • What value of  minimises F?

  17. Minimisation

  18. Both withdrawals must be of equal size Y Y/2 t t=½

  19. Optimal withdrawal • Calculate optimal size of each withdrawal • Gives optimal number of withdrawals • The average cash held over the period is M/2 • Interest income foregone is r(M/2) • assume that each withdrawal incurs a transactions cost ‘b’

  20. Optimal money holding

  21. Elasticities

  22. Miller & Orr • 2 assets available- zero yielding money and interest bearing bonds with yield r per day • Transfer involves fixed cost ‘g’ - independent of size of transfer. • Cash balances have a lower limit or cannot go below zero • Cash flows are stochastic and behave as if generated by a random walk

  23. Miller & Orr continued • In any short period ‘t’, cash balances will rise by (m) with probability p • or fall by (m) with probability q=(1-p) • cash flows are a series of independent Bernoulli trials • Over an interval of n days, the distribution of changes in cash balances will be binomial

  24. Properties • The distribution will have mean and variance given by: • n = ntm(p-q) • n2 = 4ntpqm2 • The problem for the firm is to minimise the cost of cash between two bounds.

  25. Buffer stocks and Disequilibrium Money

  26. In period T at the Terminal date MT+1 = MT

  27. Generalising for an error-correction mechanism

  28. Disequilibrium Money causes adjustments in all markets

  29. Conclusion • Post Keynesian development in the demand for money have micro-foundations but they are not solid micro-foundations. • The Miller-Orr model of buffer stocks money demand allows for disequilibrium and threshold adjustment. • The macroeconomic implication is the disequilibrium money model. • The disequilibrium money model builds on the real balance effect of Patinkin and has long lag adjustment of monetary shocks • Equilibrium models have rapid adjustment of monetary shocks (rational expectations).

More Related