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.

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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
- 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

- Lecture Notes (in Japanese) (revised on February 12, 2020)

- A Ranking over "More Risk Averse Than" Relations and its Application to the Smooth Ambiguity Model (Version: March 6, 2020)

This is a later version than the KIER Discussion Paper Series No. 1019.

**Abstract:**Given two pairs of expected utility functions, we formalize the notion that one expected utility function is more risk-averse than the other in the first pair to a greater extent than in the second pair. We do so by assuming that the utility functions are twice continuously differentiable and satisfy the Inada condition, and, in each of the two pairs, using the function that transforms the derivatives of one expected utility function to the derivatives of the other, rather than the function that transforms one expected utility function to the other. This definition allows us to interpret the quantitative results on the ambiguity aversion coefficients of the smooth ambiguity model of Klibanoff, Marinacci, and Mukerji (2005) in some cases not covered by the more-ambiguity-averse-than relation that they conceived.

**JEL Classification Codes:**C38, D81, G11.**Keywords:**Expected utility functions, risk aversion, ambiguity aversion, smooth ambiguity model. - Equilibrium Prices of the Market Portfolio in the CAPM with Incomplete
Financial Markets (Version: January 12, 2020)

This is a later version than the KIER Discussion Paper Series No. 1005.

**Abstract:**In the Capital Asset Pricing Model, we consider how introducing new assets will affect the prices of the existing ones. We prove that introducing new assets into financial markets increases the relative price of the market portfolio with respect to the risk-free bond if the elasticity of the marginal rates of substitution of the mean for standard deviation with respect to the latter is greater than one for every consumer; the relative price of the market portfolio decreases if the elasticity is less than one; and the relative price is left unchanged if the elasticity is equal to one.

**JEL Classification Codes:**D51, D52, G11, G12, G13.**Keywords:**Capital Asset Pricing Model, general equilibrium theory, incomplete asset markets, financial innovation, expected utility. . - Heterogeneous Impatience of Individual Consumers and Decreasing Impatience of the Representative Consumer (Version: May 12, 2019)

This is the same version as the KIER Discussion Paper Series No. 1009.

**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 apply this result to interest rate models, and, in particular, accommodate heterogeneous impatience in the model of Cox, Ingersoll, and Ross (1985) to come up with a new form of short-rate processes.

**JEL Classification Codes:**D51, D53, D61, D81, D91, E43, G12.**Keywords:**Discount factor, discount rate, representative consumer, decreasing impatience, cumulant-generating function, term structure of interest rates, short-rate processes. - Implied Ambiguity: Mean-Variance Efficiency and Pricing Errors (Version: October 9, 2018)

This is the same version as the KIER Discussion Paper Series No. 1004.

**Abstract:**We study the optimal portfolio choice problem for an ambiguity-averse investor having a utility function of the form of Klibanoff, Marinacci, and Mukerji (2005) and Maccheroni, Marinacci, and Ruffino (2013). We identify necessary and sufficient conditions for a given portfolio to be optimal for some ambiguity-averse investor. We also show that the smallest ambiguity aversion coefficient for the optimality of the given portfolio, which we term the implied ambiguity of the portfolio, is decreasing with respect to its Sharpe ratio. This relation can also be expressed in terms of the size of the pricing errors when the asset returns are regressed on the return of the portfolio. A numerical analysis is provided to find the ambiguity aversion implied by the U.S. equity market data.

**JEL Classification Codes:**D81, D91, G11, G12.**Keywords:**Ambiguity aversion, optimal portfolio, Sharpe ratio, beta, alpha, mutual fund theorem. - Asset Prices, Trading Volumes, and Investor Welfare in Markets with Transaction Costs (Version: September 1, 2012)

This is a later 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 later 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.

*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, may I suggest you contact Oxford University Press? Please do**not**direct any inquiry about its availability to me. Any comments on the contents of the manual are, however, more than welcome.