Lecture 5

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# Lecture 5 - PowerPoint PPT Presentation

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

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
• 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
• 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
• Positive marginal utility
• Diminishing marginal utility of income
• Diminishing absolute risk aversion
• Increasing relative risk aversion
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

R

45o

-a/2b

R

R

P’

C

P

B

A

0

R

 = 1

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
• 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
• 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.
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 1 is withdrawn at the beginning of the period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
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
• 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
• 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
• 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
• 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
• 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).