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The Optimality of the Friedman Rule

Author: YuXiuZhi
Tutor: LiYong
School: Jilin University
Course: Applied Mathematics
Keywords: Friedman rule optimality imperfect competition endogenous discount factor
CLC: F820
Type: Master's thesis
Year: 2010
Downloads: 23
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Abstract

In the 1970s,Modern monetary economists headed by Friedman focused on the amount of currency in circulation of the economy and the impact of inflation on the economy.This school concluded the optimal condition that the nominal interest rate equals 0 on the condition of the cost of holding money to the private should be the same as the cost of the country increase money,namely, the Friedman rule.Many economists have questioned this theory,but more scholars agreed with the view of Friedman and proved and improved the theory constantly.This paper is a guideline on the optimality of the Friedman rule,Chapter I in-troduces the background of the Friedman rule presented and the recent state,and pre-sented the main results of scholars briefly.Chapter II gives the mathematical models of the company,the family, and the central bank and the government firstly,and then discuss the optimality of the Friedman rule in a growing economy with imperfect competition,concluded that if capital generates production externality, there exists a wedge between returns to money and to capital, driving the Friedman rule is not op-timal.However, in the absence of capital externality, the Friedman rule may be valid even under imperfect competition.Chapter III examines the optimality of the Friedman rule in the utility (MIU) and cash-credit models with endogenous discount factor.We consider two types of endogenous discount factors:the utility in the discount factor (UIDF) and the components in the discount factor (CIDF). The CIDF model is pre-sumed as a generalized model of UIDF. Combination the two endogenous discount factors andtwomonetary models,we have studied four cases. The main results of this paper are follows.A zero inflation tax is optimal in the MIUmodels regardless of the type of endogenous discount factor because in the MIU model the Friedman rule indi-cates an infinite money supply and eliminates the effects of the endogenous discount factor.In the cash-credit model, the zero inflation tax is optimal for the UIDF but not for the CIDF.We have concluded that the result from the UIDF model is a special case, even though the UIDF model is the most commonly used endogenous discount factor model.Then we discuss the optimality of the Friedman rule in a shopping time model with an endogenous discount factor.The shopping time model assumes that agents al-locate their time between leisure, labor, and shopping. While they can save their shop-ping time by using money for transactions, they must bear the opportunity cost of real balance holdings. The Friedman rule recommends that the government supply as large an amount of money as possible in order to equate the marginal benefit and marginal excess burden of real balance holdings in constant discount factor models. Moreover, similar to the MIU model with endogenous discount factors, it is easy to check the optimality of the Friedman rule in shopping time models with UIDF and CIDF.The optimality of the Friedman rule is a classic result in monetary economics. However, that conclusion relied on the hypothesis that the Ramsey planner had access to a complete set of distorting tax instruments. Some papers showed that if policy-makers were unable to implement some conceivable distorting taxes, then the opti-mal monetary policy would prescribe positive nominal interest rates.In chater four, we investigated the relation between the optimality of the Friedman rule and the set of distorting tax instruments available to a benevolent planner. We carried out the study in a two-sector (tradable and non-tradable goods) deterministic small open economy framework.We introduced money by assuming that a fraction of people’s purchases of non-tradables had to be paid in cash.We showed that the Friedman rule was optimal whenever the Ramsey planner could select the tax rate on the consumption of the good that requires money to be purchased. A positive nominal interest rate corresponds to a tax on the sector that requires money to carry out transactions. However, as other authors have established, this type of taxation is inefficient. Hence, if the Ramsey planner can select at least one distorting tax instrument that burdens that same sector, then the Friedman rule will be optimal.

The Optimality of the Friedman Rule

Abstract

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