IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this paper or follow this series

Optimal Dynamic Choice of Durable and Perishable Goods

  • Peter Bank
  • Frank Riedel

We analyze the life cycle consumption choice model for multiple goods, focusing on the distinction between durables and perishables. As an approximation of the fact that rather high transaction costs and market imperfections prevail in markets for used durables, we assume that investment in durables is irreversible. In contrast to the additive model with one perishable good, the optimal consumption plan is not myopic. Instead, it depends on past as well as on (expected) future prices. The optimal stock level of the durable good is obtained by tracking a certain \emph{shadow level}: The household purchases just enough durables to keep the stock always above this shadow level. It is shown that this shadow level is given by a backward integral equation that replaces the Euler equation. For the perishable good, the `usual' Euler equation determines the optimal choice in terms of the optimal stock of durables. Since the optimal stock level aggregates past as well as future prices, the consumption of perishables ceases to be myopic as well. The solutions show that durables play an important part in intertemporal consumption decisions. In fact, major purchases of durables are being made early in life, whereas no durables are bought in the retirement years. Through substitution and complementarity effects, this has a significant impact on the consumption of perishable goods. On the technical side, the paper provides a new approach to singular control problems that might be widely applicable in other contexts like irreversible investment, price rigidities etc. We present a numerical algorithm that allows one to calculate the shadow level for arbitrary period utility functions and time horizons. Explicit solutions are given for the case of a homogeneous Markov setup with infinite time horizon and Cobb--Douglas type period utilities. This setup includes prices driven by Brownian motion and/or Poisson processes.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.wiwi.uni-bonn.de/bgsepapers/bonedp/bgse29_2003.pdf
Download Restriction: no

Paper provided by University of Bonn, Germany in its series Bonn Econ Discussion Papers with number bgse29_2003.

as
in new window

Length: 36
Date of creation: Dec 2003
Date of revision:
Handle: RePEc:bon:bonedp:bgse29_2003
Contact details of provider: Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Hindy, Ayman & Huang, Chi-fu & Kreps, David, 1992. "On intertemporal preferences in continuous time : The case of certainty," Journal of Mathematical Economics, Elsevier, vol. 21(5), pages 401-440.
  2. Domenico Cuoco & Hong Liu, . "Optimal Consumption of a Divisible Durable Good," Rodney L. White Center for Financial Research Working Papers 20-98, Wharton School Rodney L. White Center for Financial Research.
  3. Sanford J. Grossman & Guy Laroque, 1987. "Asset Pricing and Optimal Portfolio Choice in the Presence of Illiquid Durable Consumption Goods," NBER Working Papers 2369, National Bureau of Economic Research, Inc.
  4. Jérôme B. Detemple & Christos I. Giannikos, 1995. "Asset and Commodity Prices with Multiattribute Durable Goods," CIRANO Working Papers 95s-47, CIRANO.
  5. Hindy, Ayman & Huang, Chi-fu, 1993. "Optimal Consumption and Portfolio Rules with Durability and Local Substitution," Econometrica, Econometric Society, vol. 61(1), pages 85-121, January.
  6. Damgaard, Anders & Fuglsbjerg, Brian & Munk, Claus, 2003. "Optimal consumption and investment strategies with a perishable and an indivisible durable consumption good," Journal of Economic Dynamics and Control, Elsevier, vol. 28(2), pages 209-253, November.
  7. Mankiw, N. Gregory, 1982. "Hall's consumption hypothesis and durable goods," Journal of Monetary Economics, Elsevier, vol. 10(3), pages 417-425.
  8. Peter Bank & Frank Riedel, 1998. "Non-Time Additive Utility Optimization - the Case of Certainty," GE, Growth, Math methods 9811002, EconWPA.
  9. Harry Mamaysky, 2001. "Interest Rates and the Durability of Consumption Goods," Yale School of Management Working Papers ysm224, Yale School of Management, revised 01 Jan 2002.
  10. Merton, Robert C., 1971. "Optimum consumption and portfolio rules in a continuous-time model," Journal of Economic Theory, Elsevier, vol. 3(4), pages 373-413, December.
  11. Akerlof, George A, 1970. "The Market for 'Lemons': Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, MIT Press, vol. 84(3), pages 488-500, August.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:bon:bonedp:bgse29_2003. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (BGSE Office)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.