A general-equilibrium closed-form solution to the welfare costs of inflation (Forthcoming, Revista Brasileira de Economia)

This work presents closed-form solutions to Lucasís (2000) generalequilibrium expression for the welfare costs of ináation, as well as to the di§erence between the general-equlibrium measure and Baileyís (1956) partial-equilibrium measure. In Lucasís original work only numerical solutions are provided.

The n-dimensional bailey-divisia measure as a general-equilibrium measure of the welfare costs of inflation

This paper shows that in economies with several monies the Bailey-Divisia multidimensional consumers surplus formula may emerge as an exact general-equilibrium measure of the welfare costs of in ation, provided that preferences are quasilinear.

Bailey's measure of the welfare costs of infiation as a general-equilibrium measure

Lucas (2000) has ShO\nl t hat Baile,\"'s formula for t hc \\'elfare costs of inflatioIl caIl bc rcgardpd as an approximation to t hc gcneral-equilibriuIll IllCaSllH'S \\"hich emerge from thc Sidrauski anrl the shopping-time models, In this paper \\'c shm\' that Baile~"s mcaSllrc can bc cxactly obtairlf'd in tllf' Siclrauski geIleral-equilibri1lIn framp\\'ork under the assUIllption of quasilinpar prefpreIlC'cs, The rpslllt. based on ",heter or not \\'Palt h pffpcts are incorporatccl into t hp analysis, is also helpful in darif\'ing \\'hy Lucas' Illeasurp clerin'd from the Siclrauski model turns 01lt to be aIl upper bOllIlcl to Bailp~"s, T,,'o eXaInplcs arp used to illustratc t he main C'ondusions,

Infrastructure privatization in a neoclassical economy : macroeconomic impact and welfare computation

In this paper a competitive general equilibrium model is used to investigate the welfare and long run allocation impacts of privatization. There are two types of capital in this model economy, one private and the other initially public ("infrastructure"), and a positive externality due to the latter is assumed. A benevolent government can improve upon decentralized allocation internalizing the externality, but it introduces distortions in the economy through the finance of its investments. It is shown that even making the best case for public action - maximization of individuals' welfare, no• operation inefficiency and free supply to society of infrastructure services - privatization is welfare improving for a large set of economies. Hence, arguments against privatization based solely on under-investment are incorrect, as this maybe the optimal action when the financing of public investment are considered. When operation inefficiency is introduced in the public sector, gains from privatization are much higher and positive for most reasonable combinations of parameters .

A note on an application of Arrow's theorem: sufficient conditions for Lucas' inflation and welfare

Bellman's methods for dynamic optimization constitute the present mainstream in economics. However, some results associated with optimal controI can be particularly usefuI in certain problems. The purpose of this note is presenting such an example. The value function derived in Lucas' (2000) shopping-time economy in Infiation and Welfare need not be concave, leading this author to develop numerical analyses to determine if consumer utility is in fact maximized along the balanced path constructed from the first order conditions. We use Arrow's generalization of Mangasarian's results in optimal control theory and develop sufficient conditions for the problem. The analytical conclusions and the previous numerical results are compatible .

Speculative attacks on debts and optimum currency area: a welfare analysis

Traditionally the issue of an optimum currency area is based on the theoretical underpinnings developed in the 1960s by McKinnon [13], Kenen [12] and mainly Mundell [14], who is concerned with the benefits of lowering transaction costs vis-à- vis adjustments to asymmetrical shocks. Recently, this theme has been reappraised with new aspects included in the analysis, such as: incomplete markets, credibility of monetary policy and seigniorage, among others. For instance, Neumeyer [15] develops a general equilibrium model with incomplete asset markets and shows that a monetary union is desirable when the welfare gains of eliminating the exchange rate volatility are greater than the cost of reducing the number of currencies to hedge against risks. In this paper, we also resort to a general equilibrium model to evaluate financial aspects of an optimum currency area. Our focus is to appraise the welfare of a country heavily dependent on foreign capital that may suffer a speculative attack on its public debt. The welfare analysis uses as reference the self-fulfilling debt crisis model of Cole and Kehoe ([6], [7] and [8]), which is employed here to represent dollarization. Under this regime, the national government has no control over its monetary policy, the total public debt is denominated in dollars and it is in the hands of international bankers. To describe a country that is a member of a currency union, we modify the original Cole-Kehoe model by including public debt denominated in common currency, only purchased by national consumers. According to this rule, the member countries regain some influence over the monetary policy decision, which is, however, dependent on majority voting. We show that for specific levels of dollar debt, to create inflation tax on common-currency debt in order to avoid an external default is more desirable than to suspend its payment, which is the only choice available for a dollarized economy when foreign creditors decide not to renew their loans.

The consistency of welfare judgements with a representative consumer

This paper is about economies with a representative consumer. In general a representative consumer need not exist, although there are several well known sets of sufficient conditions under which Qne will. It is common practice, however, to use the representative consumer hypothesis without specifically assuming any of these. We show, firstly, that it is possible for the utility of the representative consumer to increase when every actual consumer is made worse off. This shows a serious shortcoming of welfare judgements based on the representatíve consumer. Secondly, in economies where this does not occur, there exists a social welfare function, which we construct, which is consistent with welfare judgements based on the utility of the representative consumer. Finally we provide a converse to Samuelson' s 1956 representative consumer result, which relates it to Scitovsky's community indifference curves.

An intra-household approach to the welfare costs of inflation

The literature on the welfare costs of in‡ation universally assumes that the many-person household can be treated as a single economic agent. This paper explores what the heterogeneity of the agents in a household might imply for such welfare analyses. First, we show that allowing for a single-unity or for a multi-unity transacting technology impacts the money demand function and, therefore, the welfare costs of in‡ation. Second, we derive su¢cient conditions that make the welfare assessments which depart directly from the knowledge of the money demand function (as in Lucas (2000)) robust under this alternative setting. Third, we compare our general-equilibrium measure with Bailey’s (1956) partial-equilibrium one.

Two additions to Lucas's "inflation and welfare"

This work adds to Lucas (2000) by providing analytical solutions to two problems that are solved only numerically by the author. The first part uses a theorem in control theory (Arrow' s sufficiency theorem) to provide sufficiency conditions to characterize the optimum in a shopping-time problem where the value function need not be concave. In the original paper the optimality of the first-order condition is characterized only by means of a numerical analysis. The second part of the paper provides a closed-form solution to the general-equilibrium expression of the welfare costs of inflation when the money demand is double logarithmic. This closed-form solution allows for the precise calculation of the difference between the general-equilibrium and Bailey's partial-equilibrium estimates of the welfare losses due to inflation. Again, in Lucas's original paper, the solution to the general-equilibrium-case underlying nonlinear differential equation is done only numerically, and the posterior assertion that the general-equilibrium welfare figures cannot be distinguished from those derived using Bailey's formula rely only on numerical simulations as well.

An intra-household approach to the welfare costs of inflation (Revised Version, Forthcoming 2006, Estudos Econômicos)

The literature on the welfare costs of ináation universally assumes that the many-person household can be treated as a single economic agent. This paper explores what the heterogeneity of the agents in a household might imply for such welfare analyses. First, we show that allowing for a one-person or for a many-person transacting technology impacts the money demand function and, therefore, the welfare costs of ináation. Second, more importantly, we derive su¢ cient conditions under which welfare assessments which depart directly from the knowledge of the money demand function (as in Lucas (2000)) are robust (invariant) under the number of persons considered in the household. Third, we show that Baileyís (1956) partial-equilibrium measure of the welfare costs of ináation can be obtained as a Örst-order approximation of the general-equilibrium welfare measure derived in this paper using a many-person transacting technology.

Os dois métodos da teoria econômica

Economic theory deals with a complex reality, which may be seen through various perspectives, using different methods. Economics’ three major branches – development economics, macroeconomics, and microeconomics – cannot be unified because the former two use preferentially a historical-deductive, while the later, an essentially hypothetical-deductive or aprioristic method. Smith, Marx and Keynes used an essentially the method of the new historical facts, while Walras, an aprioristic one to devise the neoclassical general equilibrium model. The historical-deductive method looks for the new historical facts that condition the economic reality. Economic theory remains central, but it is more modest, or less general, as the economist that adopt principally this method is content to analyze stabilization and growth in the framework of a given historical phase or moment of the economic process. As a trade off, his models are more realistic and conducive to more effective economic policies, as long as he is not required to previously abandon, one by one, the unrealistic assumptions required by a excessively general theory, but already starts from more realistic ones

Bailey's rule for the welfare of inflation: a theoretical foundation

This paper demonstrates that for a very general class of monetary models (the Sidrauski type models and the cash-in-advance models), Bailey’s rule to evaluate the welfare efect of infation is in deed accurate. The result applies for any technology or preference, if the long-run capital stock does not depend on the ination rate. In general, a dynamic version of Bailey’s rule is established. In particular, the result extends to models in which there is a banking sector that supplies money substitutes services. A dditionally, it is argued that the relevant money demand concept for this issue- the impact of in ination under welfare- is the monetary base.

Assorted topics in monetary economics

Esta tese é uma coleção de quatro artigos em economia monetária escritos sob a supervisão do Professor Rubens Penha Cysne. O primeiro desses artigos calcula o viés presente em medidas do custo de bem-estar da inflação devido a não se levar em conta o potencial substitutivo de moedas que rendem juros, como depósitos bancários.[1] O segundo se concentra na questão teórica de se comparar os escopos dos tradicionais modelos money-in-the-utility-function e shopping-time através do estudo das propriedades das curvas de demanda que eles geram.[2] O terceiro desses trabalhos revisita um artigo clássico de Stanley Fischer sobre a correlação entre a taxa de crescimento da oferta monetária e a taxa de acumulação de capital no caminho de transição.[3] Finalmente, o quarto diz respeito à posição relativa de cada uma de seis medidas do custo de bem-estar da inflação (uma das quais é nova) em relação às outras cinco, e uma estimativa do erro relativo máximo em que o pesquisador pode incorrer devido a sua escolha de empregar uma dessas medidas qualquer vis-à-vis as outras.[4] This thesis collects four papers on monetary economics written under the supervision of Professor Rubens Penha Cysne. The first of these papers assesses the bias occuring in welfare-cost-of-inflation measures due to failing to take into consideration the substitution potential of interest-bearing monies such as bank deposits.[1] The second one tackles the theoretical issue of comparing the generality of the money-in-the-utility-function- and the shopping-time models by studying the properties of the demand curves they generate.[2] The third of these works revisits a classic paper by Stanley Fischer on the correlation between the growth rate of money supply and the rate of capital accumulation on the transition path.[3] Finally, the fourth one concerns the relative standing of each one of six measures of the welfare cost of inflation (one of which is new) with respect to the other five, and an estimate of the maximum relative error one can incur by choosing to employ a particular welfare measure in place of the others.[4] [1] Cysne, R.P., Turchick, D., 2010. Welfare costs of inflation when interest-bearing deposits are disregarded: A calculation of the bias. Journal of Economic Dynamics and Control 34, 1015-1030. [2] Cysne, R.P., Turchick, D., 2009. On the integrability of money-demand functions by the Sidrauski and the shopping-time models. Journal of Banking & Finance 33, 1555-1562. [3] Cysne, R.P., Turchick, D., 2010. Money supply and capital accumulation on the transition path revisited. Journal of Money, Credit and Banking 42, 1173-1184. [4] Cysne, R.P., Turchick, D., 2011. An ordering of measures of the welfare cost of inflation in economies with interest-bearing deposits. Macroeconomic Dynamics, forthcoming.

Infrastructure privatization in a neoclassical economy: macroeconomic impact and welfare computation

In this paper a competi tive general equilibrium model is used to investigate the welfare and long run allocation impacts of privatization. There are two types of capital in this model economy, one private and the other initially public ("infrastructure"), and a positive extemality due to the latter is assumed. A benevolent governrnent can improve upon decentralized allocation intemalizing the extemality, but it introduces distortions in the economy through the finance of its investments. It is shown that even making the best case for public action - maximization of individuais' welfare, no operation inefficiency and free supply to society of infrastructure services - privatization is welfare improving for a large set of economies. Hence, arguments against privatization based solely on under-investment are incorrect, as this maybe the optimal action when the financing of public investment are considered. When operation inefficiency is introduced in the public sector, gains from privatization are much higher and positive for most reasonable combinations of parameters.

Moral hazard and nonlinear pricing in a general equilibrium model

The paper analyzes a two period general equilibrium model with individual risk and moral hazard. Each household faces two individual states of nature in the second period. These states solely differ in the household's vector of initial endowments, which is strictly larger in the first state (good state) than in the second state (bad state). In the first period households choose a non-observable action. Higher leveis of action give higher probability of the good state of nature to occur, but lower leveIs of utility. Households have access to an insurance market that allows transfer of income across states of oature. I consider two models of financiaI markets, the price-taking behavior model and the nonlínear pricing modelo In the price-taking behavior model suppliers of insurance have a belief about each household's actíon and take asset prices as given. A variation of standard arguments shows the existence of a rational expectations equilibrium. For a generic set of economies every equilibrium is constraíned sub-optímal: there are commodity prices and a reallocation of financiaI assets satisfying the first period budget constraint such that, at each household's optimal choice given those prices and asset reallocation, markets clear and every household's welfare improves. In the nonlinear pricing model suppliers of insurance behave strategically offering nonlinear pricing contracts to the households. I provide sufficient conditions for the existence of equilibrium and investigate the optimality properties of the modeI. If there is a single commodity then every equilibrium is constrained optimaI. Ir there is more than one commodity, then for a generic set of economies every equilibrium is constrained sub-optimaI.