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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

Lecture 5

The Micro-foundations of the Demand for Money - Part 2

slide2
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
the tobin model of the demand for money
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
arrow conditions
Arrow conditions
  • Positive marginal utility
  • Diminishing marginal utility of income
  • Diminishing absolute risk aversion
  • Increasing relative risk aversion
alternative specifications
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
equation of a circle
Equation of a circle

R

45o

-a/2b

R

slide11

R

P’

C

P

B

A

0

R

 = 1

implications
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
transactions approach
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
assumptions
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.
slide15
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
slide16
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?
optimal withdrawal
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’
miller orr
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
miller orr continued
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
properties
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.
conclusion
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).