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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

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Lecture 5

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  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).

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