Always under construction. Most, if not all, linked files are in the PDF format.

- Important Notices
- About Myself
- Lecture Materials
- Latest Versions of Working Papers
- Published but Rarely Circulated Papers
- Books

- I do not take any student as a research fellow ("kenkyu-sei" in Japanese) of this institute unless I know him/her in person. Please do not email or ring me to make an inquiry on this matter. In any case, I shall not respond to any such message.

- Postal Mail:

Institute of Economic Research, Kyoto University

Yoshida-Honmachi, Sakyo-ku

Kyoto 606-8501 Japan - Telephone: +81 (0)75 753 7140 (Secretary) 7102 (Institute)
- Fax: +81 (0)75 753 7148
- (New!) Email: hara.chiaki.7x
**(at)**kyoto-u**(dot)**ac**(dot)**jp

where**(at)**should be replaced by @ and**(dot)**should be replaced by . . I am sorry for inconvenience but this is to avoid spam mails. - CV

- Homework 1 (in Japanese) (due on Wednesday 19 April, 2017)
- Homework 2 (in Japanese) (due on Monday 24 April, 2017)
- Homework 3 (in Japanese) (due on Monday 1 May, 2017)
- Homework 4 (in Japanese) (due on Wednesday 10 May, 2017)
- Homework 5 (in Japanese) (due on Wednesday 17 May, 2017)
- Homework 6 (in Japanese) (due on Wednesday 24 May, 2017)
- Homework 7 (in Japanese) (No need for submission)
- Lecture Notes revised by Ms Rusudan Kevkhishvili (in Japanese) (dated Wednesday 24 May 2017)
- Homework 8 and Answers (in Japanese) (No need for submission)

- Heterogeneous Impatience and Dynamic Inconsistency (Version: February 7, 2013)

This is a newer version than the Center for Intergenerational Studies, at the Institute of Economic Research of Hitotsubashi University, Discussion Paper Series No. 557.

**Abstract:**In a continuous-time equilibrium model of heterogeneous consumers, we formulate and prove the statement that the more heterogeneous the consumers are in their impatience, the more dynamically consistent the representative consumer is. We also characterize these orderings within some parameterized families of the distribution of the consumers' discount rates. We apply these results to the term structure of interest rates, and, in particular, to accommodate heterogeneous impatience in the model of Cox, Ingersoll, and Ross (1985)

**JEL Classification Codes:**D51, D53, D61, D81, D91, E43, G12.**Keywords:**Discount factor, discount rate, representative consumer, term structure of interest rates, cumulant-generating function. - Asset Prices, Trading Volumes, and Investor Welfare in Markets with Transaction Costs (Version: September 1, 2012)

This is a newer version than the Center for Intergenerational Studies, at the Institute of Economic Research of Hitotsubashi University, Discussion Paper Series No. 556.

**Abstract:**In a model of asset markets with transaction costs, we find a sufficient condition for an increase in transaction costs to increase buying prices, decrease selling prices, decrease the trading volume, and make all active investors worse off. The sufficient condition is met by all CARA utility functions. As for CRRA utility functions, it is met if and only if CRRA coefficients are less than or equal to one. We show that whenever some investor has a CRRA coefficient greater than one, an increase in transaction costs may well decrease buying prices and make buyers better off.

**JEL Classification Codes:**D51, D53, D61, D63, G11, G12.**Keywords:**General equilibrium, asset markets, transaction costs, Tobin tax, constant absolute risk aversion, constant relative risk aversion. - Heterogeneous Beliefs and Mispricing of Derivative Assets (Version: July 5, 2010)

**Abstract:**In an exchange economy under uncertainty populated by multiple consumers, we how the heterogeneity in the individual consumers' subjective beliefs affect the representative consumer's utility function. We derive a formula that indicates that the more heterogeneous the individual consumers' beliefs are, the higher probabilities the representative consumer's belief attaches to extreme events that would, in the absence of heterogeneous beliefs, have very low probabilities. We also explore an implication of this formula on derivative asset pricing.

**JEL Classification Codes:**D51, D53, D61, D81, D91, G12, G13.**Keywords:**Heterogeneous beliefs, derivative assets, representative consumer, monotone likelihood ratio condition, log super-modularity, Black-Scholes option pricing formula. - Effectively Complete Asset Markets with Multiple Goods and over Multiple Periods (Version: May 26, 2010)

This is a newer version than the KIER Discussion Paper Series No. 685.

**Abstract:**Following LeRoy and Werner (2001), we propose a definition of effectively complete asset markets in a model with multiple goods and multiple periods, and establish the first welfare theorem in such markets. As applications of the theorem, we derive the Pareto-efficiency of equilibrium allocation in economies with no aggregate risk and the mutual fund theorem. We also extend the sunspot irrelevance theorem of Mas-Colell (1992) to the model of multiple periods and the no-retrade theorem of Judd, Kubler, and Schmedders (2003) and Kubler and Schmedders (2003) to the case where the asset prices need not be time-invariant Markov processes.

**JEL Classification Codes:**D51, D52, D53, D61, D91, G11, G12.**Keywords:**Complete asset markets; effectively complete asset markets; first welfare theorem; aggregate risk; mutual fund theorem; sunspot; Markov environment. - Heterogeneous Beliefs in a Continuous-Time Model (Version: March 15, 2010)

This is the same version the KIER Discussion Paper Series No. 701.

**Abstract:**In an exchange economy under uncertainty populated by consumers having constant and equal relative risk aversion but heterogeneous probabilistic beliefs, we analyze the nature of the representative consumer's probabilistic belief and discount rates. We prove a formula that implies that the representative consumer's discount rates are raised or lowered by belief heterogeneity depending on whether the constant relative risk aversion is greater or smaller than one. We also show that the representative consumer's discount rates may be a hyperbolic function of time even when the individual consumers' discount rates are equal to one another, as long as their beliefs are heterogeneous.

**JEL Classification Codes:**D51, D53, D81, D91, G12, G13, Q51, Q54.**Keywords:**Representative consumer, expected utility, hyperbolic discounting, constant relative risk aversion, Ito's Lemma, Girsanov's Theorem. - Necessary and Sufficient Conditions for the Efficient Risk-Sharing Rules and the Representative Consumer's Utility Function (Incomplete Version: March 22, 2007.)

**Abstract:**We show that for every collection of increasing risk-sharing rules and for every increasing and concave expected utility function, there exists a collection of increasing and concave expected utility functions for which the given risk-sharing rules are efficient and the given utility function coincides with the corresponding representative consumer's utility function. We then determine the smallest class of utility functions that contains not only all functions exhibiting constant relative risk aversion but also all functions derivable as the representative consumer's utility function from such utility functions; and also fully characterize the efficient risk-sharing rules in this class. Furthermore, we show that in a two-consumer economy, assuming that the two have the same utility function imposes no additional restriction on the efficient risk-sharing rules.

**JEL Classification Codes:**D51, D61, D81, G12, G13.**Keywords:**Risk-sharing rule, representative consumer, pricing kernel, expected utility, risk aversion, Inada condition, complete markets. - Boundary Behavior of
Excess Demand Functions without the Strong Monotonicity Assumption
(Version: April 5, 2004)
**Abstract:**We give a theorem on the existence of an equilibrium price vector for an excess demand correspondence, which may have been derived from consumers with non-monotone preference relations.

- Report on Economic
Theory of Desirable Futures Contracts,
*Sakimono Torihiki Kenkyu*(Futures Trading Research) vol. 10, no.1-14 (December 2006), pp. 119-131 (in Japanese).**Abstract:**This paper surveys recent results on the general equilibrium theory of pecuniary externalities that arise when new securities become available for trade in incomplete financial markets. - Unlinked Allocations
in an Exchange Economy with One Good and One Bad, published in
*Kyokyuroku*(Workshop Proceeding) no. 1337 (August 2003), pp. 70-80, Research Institute for Mathematical Sciences, Kyoto University.**Abstract:**We consider an exchange economy with two commodities, of which one is a good, which generates utility to all consumers, and the other is a bad, which causes disutility to all consumers. We look into "unlinked" allocations, that is, allocations at which almost every consumer consumes either the good or the bad, but not both, and ask under what conditions there exist unlinked and individually rational allocations and also unlinked and envy-free allocations. We also examine efficient and equilibrium allocations, taking special care of the cases where the so called minimum condition is violated. - Theory of Corporate Debt
Issues under Asymmetric Information: Informativeness of Security Prices of
Linear Rational Expectations Equilibrium in Incomplete Markets, published
in
*Yucho Shikin Kenkyu*(Postal Saving Research) vol. 12 (September 2003), pp. 1-31 (in Japanese).**Abstract:**This paper analyzes the informativeness of security prices of linear rational expectations equilibrium. In particular, it characterizes the information conveyed by equilibrium prices in terms of the trading volumes of the informed trader. The model of the paper deserves special attention in two respects. First, the dimensions of risk factors affecting security payoffs, initial endowments, and noisy signals are completely arbitrary. Second, there is a limited participation constraint, in the sense that some uninformed traders can access some but not all of security markets.

*Recent Advances in Financial Engineering 2010*, World Scientific, Singapore, 2011, coedited with Masaaki Kijima, Yukio Muromachi, Hidetaka Nakaoka, and Katsumasa Nishide.

The table of contents can be obtained from its web site.*Recent Advances in Financial Engineering 2009*, World Scientific, Singapore, 2010, coedited with Masaaki Kijima, Keiichi Tanaka, and Yukio Muromachi.

The table of contents can be obtained from its web site.*Introduction to Microeconomics*, coauthored with Shin-Ichi Takekuma, Koichi Kaneko, Tadanobu Tanno, Hiroshi Ogawa, and Shinji Yamashige, Diamond Inc, 2005 (in Japanese).

My contribution is "Chapter 5: Analysis of security markets" on pp. 160-215.

The table of contents can be obtained from its web site.*Solution Manual to Mas-Colell, Whinston, and Green's 'Microeconomic Theory'*, coauthored with Steve Tadelis and Ilya Segal, Oxford University Press, 1997.

My contribution is for Parts 1 and 4.

I have no authority to distribute this manual. Neither do I have any spare copy. If you are a course instructor, please contact Oxford University Press through their web site. Please do**not**direct any inquiry about its availability to me. Any comments on the contents of the manual are, however, more than welcome.