<p>Here is a simple model of consumer who spend on durable goods and non-durable goods:
Consumer lives for two periods. In period 1, consumer spends on a durable good (X) which he consumes for two periods. Rest of the income in period 1 is spend on a non-durable good (Y). In period 2, the entire income is spend on a non-durable good (Y).</p>
<p>Utility function of this consumer is assumed to be:
<span class="math-container">$U(x,y_1,y_2)=x^\alpha y_1+x^\alpha y_2$</span></p>
<p>Price of the durable good is <span class="math-container">$p_X$</span>, and of the non-durable good is <span class="math-container">$p_1$</span> in period 1, and <span class="math-container">$p_2$</span> in period 2.</p>
<p>Income of the consumer is <span class="math-container">$M$</span> in both the periods.</p>
<p>We are not allowing for saving or borrowing in period 1 in this simple model. Given the set-up, we know that <span class="math-container">$y_2=\dfrac{M}{p_2}$</span>. So, period 1's Utility maximization problem is:</p>
<p><span class="math-container">\begin{eqnarray*} \max_{x\geq 0, y_1\geq 0} &amp; \ x^\alpha\left(y_1+\dfrac{M}{p_2}\right) \\ \text{s.t. } &amp; p_Xx+p_1y_1 \leq M\end{eqnarray*}</span></p>
<p>Solving it, we get the demand for the durable good, <span class="math-container">$x$</span> as:
<span class="math-container">\begin{eqnarray*}x^d(p_X,p_1,p_2,M)=\frac{1}{p_X}\min\left\{\left(\dfrac{\alpha}{1+\alpha}\right)M\left(1+\dfrac{p_1}{p_2}\right), M\right\}\end{eqnarray*}</span></p>
<p>the demand for the non-durable good, <span class="math-container">$y_1$</span> as:
<span class="math-container">\begin{eqnarray*}y_1^d(p_X,p_1,p_2,M)=\max\left\{\frac{1}{p_1}\left(\dfrac{1}{1+\alpha}\right)M\left(1+\dfrac{p_1}{p_2}\right)-\dfrac{M}{p_2}, 0\right\}\end{eqnarray*}</span></p>
<p>Comparing elasticity of demand at the situation where <span class="math-container">$y_1^d&gt;0$</span> in optimum in this simple example, we get the absolute value of own-price elasticity of demand for <span class="math-container">$x$</span> is <span class="math-container">$1$</span>, and the absolute value of own-price elasticity of demand for <span class="math-container">$y_1$</span> is <span class="math-container">$\left(\frac{y_1^d+\dfrac{M}{p_2}}{y_1^d}\right)\left(\dfrac{p_2}{p_1+p_2}\right)$</span>.</p>

CC BY-SA 4.0
2023-12-14T02:35:48.047Z
2023-12-14T03:42:00.293Z
2023-12-14T03:42:00.293Z
Amit
<p>For the theory, House (JME several years ago), Barsky, House and Kimball (AER, circa 2006) Barsky, Boehm, House, and Kimball (working paper on SED website).  Johannes Wieland has a new paper on this, maybe not yet available.  </p>

<p>The key theoretical point (put somewhat loosely) is that purchases of an "idealized durable", one with a very low depreciation rate, should have a near-infinite intertemporal elasticity of substitution.  </p>

CC BY-SA 4.0
2019-08-06T17:16:28.653Z
Welcome to Econ.SE. It would be nice if you could supplement your answer with links to the articles mentioned herein.
Herr K.
CC BY-SA 4.0
2019-08-05T20:06:19.373Z
2019-08-05T20:06:19.373Z
Bob Barsky
<p>Some papers with estimates of consumer demand systems including non-durable and durable (usually clothes) goods:</p>

<p>Lewbel, A. (1997). Consumer demand systems and household equivalence scales. Handbook of Applied Econometrics Volume 2: Microeconomics, 155-185.</p>

<p>Banks, J., Blundell, R., &amp; Lewbel, A. (1997). Quadratic Engel curves and consumer demand. The review of economics and statistics, 79(4), 527-539.</p>

<p>Crawford, I., Laisney, F., &amp; Preston, I. (2003). Estimation of household demand systems with theoretically compatible Engel curves and unit value specifications. Journal of Econometrics, 114(2), 221-241.</p>

CC BY-SA 3.0
2018-01-14T14:30:02.477Z
The last two references do not have any mention of elasticities of durable goods. Only non-durable (such as food and clothes). Clothes are not considered durable goods. Durable goods are cars, machinery, laptops, etc.
phdstudent
CC BY-SA 3.0
2018-01-12T15:08:59.573Z
2018-01-12T15:08:59.573Z
Pavel Obraztcov
<p>Does anyone know any seminal reference (either a paper in a top economics journal or a book) that compares own-price elasticities of demand for durable vs non-durable goods?</p>

<p>My intuition tells me that durable goods should be more elastic ... but not sure how to defend that statement without a reference.</p>

<p>Edit: </p>

<p>As requested I added some more content to the question. However, the question trying to find an answer to is merely an empirical question and therefore I do not have a specific model in mind. To be slightly more precise: </p>

<p>Consider a demand function for good $i$: $P_i = f(Q_i, X_i)$ where $P_i$ is the price of good $i$, $Q_i$ is the quantity and $X_i$ are other factors that influence demand. What I am looking are empirical estimates for $\frac{\partial Q_i}{\partial P_i} \frac{P_i}{Q_i}$ for two sectors: durable goods and non-durable goods. Now usually there is a problem in estimating this elasticity given the standard endogeneity problems. However, there are methods that have been used to disentangle such quantities. Two examples are: <a href="http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.554.3931&amp;rep=rep1&amp;type=pdf" rel="noreferrer">Berry,Levinson and Pakes (1995)</a> and <a href="https://www.google.co.uk/url?sa=t&amp;rct=j&amp;q=&amp;esrc=s&amp;source=web&amp;cd=2&amp;cad=rja&amp;uact=8&amp;ved=0ahUKEwi-rKrbnNDYAhUCIsAKHS2yBp8QFggyMAE&amp;url=https%3A%2F%2Fwww.aeaweb.org%2Farticles%3Fid%3D10.1257%2Faer.100.3.691&amp;usg=AOvVaw2s5HyohFkg3ulCDUGgRyWm" rel="noreferrer">Broda and Weinstein (2004)</a>.<br>
There are few anecdotal evidence of differences in elasticities for durable and non durable goods. One example taken from <a href="https://courses.lumenlearning.com/boundless-economics/chapter/price-elasticity-of-demand/" rel="noreferrer">here</a> is:</p>

<p><em>Duration of price change: For non-durable goods, elasticity tends to be greater over the long-run than the short-run. In the short-term it may be difficult for consumers to find substitutes in response to a price change, but, over a longer time period, consumers can adjust their behavior. For example, if there is a sudden increase in gasoline prices, consumers may continue to fuel their cars with gas in the short-run, but may lower their demand for gas by switching to public transportation, carpooling, or buying more fuel-efficient vehicles over a longer period of time. However, this tendency does not hold for consumer durables. The demand for durables (cars, for example) tends to be less elastic, as it becomes necessary for consumers to replace them with time.</em></p>

<p>But this is not an sufficient academic reference which is what I am looking for. </p>

CC BY-SA 3.0
2018-01-11T15:21:02.350Z
Can you make your question formally precise?
Michael Greinecker
CC BY-SA 3.0
2018-01-11T15:32:46.977Z
I have added some more content to the question, but I am not sure what you are exactly after.
phdstudent
CC BY-SA 3.0
2018-01-11T15:39:04.840Z
Well, I didn't even know you wanted to get empirical estimates from your original question.
Michael Greinecker
CC BY-SA 3.0
2018-01-11T15:40:14.093Z
Oh. I see. My apologies. In any case a theoretical estimate would also do the trick actually. Usually if there is a paper with a theory estimate almost for sure one can find an empirical paper that tested the theoretical framework.
phdstudent
CC BY-SA 4.0
2020-12-27T23:10:41.303Z
Maybe this is interesting https://www.nber.org/system/files/working_papers/w25840/w25840.pdf I think it has been accepted for publication.
Jesper Hybel
CC BY-SA 4.0
2021-12-23T13:40:33.817Z
The gasoline-car example is a rather special case.  What it illustrates is that when a durable and a non-durable are complements, the non-durable will tend to be price-inelastic in the short term and price-elastic in the longer term.
Adam Bailey
<elasticity>
Elasticity of Durable Goods vs Non-Durable Goods
phdstudent
# Elasticity of Durable Goods vs Non-Durable Goods

(Asked by: username_0 on 2018-01-11)

Does anyone know any seminal reference (either a paper in a top economics journal or a book) that compares own-price elasticities of demand for durable vs non-durable goods?

My intuition tells me that durable goods should be more elastic ... but not sure how to defend that statement without a reference.

Edit:

As requested I added some more content to the question. However, the question trying to find an answer to is merely an empirical question and therefore I do not have a specific model in mind. To be slightly more precise:

Consider a demand function for good $i$: $P\_i = f(Q\_i, X\_i)$ where $P\_i$ is the price of good $i$, $Q\_i$ is the quantity and $X\_i$ are other factors that influence demand. What I am looking are empirical estimates for $\frac{\partial Q\_i}{\partial P\_i} \frac{P\_i}{Q\_i}$ for two sectors: durable goods and non-durable goods. Now usually there is a problem in estimating this elasticity given the standard endogeneity problems. However, there are methods that have been used to disentangle such quantities. Two examples are: [Berry,Levinson and Pakes (1995)](http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.554.3931&rep=rep1&type=pdf) and [Broda and Weinstein (2004)](https://www.google.co.uk/url?sa=t&rct=j&q=&esrc=s&source=web&cd=2&cad=rja&uact=8&ved=0ahUKEwi-rKrbnNDYAhUCIsAKHS2yBp8QFggyMAE&url=https%3A%2F%2Fwww.aeaweb.org%2Farticles%3Fid%3D10.1257%2Faer.100.3.691&usg=AOvVaw2s5HyohFkg3ulCDUGgRyWm).  
There are few anecdotal evidence of differences in elasticities for durable and non durable goods. One example taken from [here](https://courses.lumenlearning.com/boundless-economics/chapter/price-elasticity-of-demand/) is:

*Duration of price change: For non-durable goods, elasticity tends to be greater over the long-run than the short-run. In the short-term it may be difficult for consumers to find substitutes in response to a price change, but, over a longer time period, consumers can adjust their behavior. For example, if there is a sudden increase in gasoline prices, consumers may continue to fuel their cars with gas in the short-run, but may lower their demand for gas by switching to public transportation, carpooling, or buying more fuel-efficient vehicles over a longer period of time. However, this tendency does not hold for consumer durables. The demand for durables (cars, for example) tends to be less elastic, as it becomes necessary for consumers to replace them with time.*

But this is not an sufficient academic reference which is what I am looking for.

**Tags:** elasticity
> **Comments:**
> **username_1**: Can you make your question formally precise?  
> **username_0**: I have added some more content to the question, but I am not sure what you are exactly after.  
> **username_1**: Well, I didn't even know you wanted to get empirical estimates from your original question.  
> **username_0**: Oh. I see. My apologies. In any case a theoretical estimate would also do the trick actually. Usually if there is a paper with a theory estimate almost for sure one can find an empirical paper that tested the theoretical framework.  
> **username_2**: Maybe this is interesting https://www.nber.org/system/files/working_papers/w25840/w25840.pdf I think it has been accepted for publication.  
> **username_3**: The gasoline-car example is a rather special case.  What it illustrates is that when a durable and a non-durable are complements, the non-durable will tend to be price-inelastic in the short term and price-elastic in the longer term.  

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## 3 answers

### Answer by username_4 on 2023-12-14. Score: 1

Here is a simple model of consumer who spend on durable goods and non-durable goods:
Consumer lives for two periods. In period 1, consumer spends on a durable good (X) which he consumes for two periods. Rest of the income in period 1 is spend on a non-durable good (Y). In period 2, the entire income is spend on a non-durable good (Y).

Utility function of this consumer is assumed to be:
$U(x,y\_1,y\_2)=x^\alpha y\_1+x^\alpha y\_2$

Price of the durable good is $p\_X$, and of the non-durable good is $p\_1$ in period 1, and $p\_2$ in period 2.

Income of the consumer is $M$ in both the periods.

We are not allowing for saving or borrowing in period 1 in this simple model. Given the set-up, we know that $y\_2=\dfrac{M}{p\_2}$. So, period 1's Utility maximization problem is:

\begin{eqnarray\*} \max\_{x\geq 0, y\_1\geq 0} & \ x^\alpha\left(y\_1+\dfrac{M}{p\_2}\right) \\ \text{s.t. } & p\_Xx+p\_1y\_1 \leq M\end{eqnarray\*}

Solving it, we get the demand for the durable good, $x$ as:
\begin{eqnarray\*}x^d(p\_X,p\_1,p\_2,M)=\frac{1}{p\_X}\min\left\{\left(\dfrac{\alpha}{1+\alpha}\right)M\left(1+\dfrac{p\_1}{p\_2}\right), M\right\}\end{eqnarray\*}

the demand for the non-durable good, $y\_1$ as:
\begin{eqnarray\*}y\_1^d(p\_X,p\_1,p\_2,M)=\max\left\{\frac{1}{p\_1}\left(\dfrac{1}{1+\alpha}\right)M\left(1+\dfrac{p\_1}{p\_2}\right)-\dfrac{M}{p\_2}, 0\right\}\end{eqnarray\*}

Comparing elasticity of demand at the situation where $y\_1^d>0$ in optimum in this simple example, we get the absolute value of own-price elasticity of demand for $x$ is $1$, and the absolute value of own-price elasticity of demand for $y\_1$ is $\left(\frac{y\_1^d+\dfrac{M}{p\_2}}{y\_1^d}\right)\left(\dfrac{p\_2}{p\_1+p\_2}\right)$.


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### Answer by username_5 on 2019-08-05. Score: 0

For the theory, House (JME several years ago), Barsky, House and Kimball (AER, circa 2006) Barsky, Boehm, House, and Kimball (working paper on SED website). Johannes Wieland has a new paper on this, maybe not yet available.

The key theoretical point (put somewhat loosely) is that purchases of an "idealized durable", one with a very low depreciation rate, should have a near-infinite intertemporal elasticity of substitution.

> **Comments:**
> **username_6**: Welcome to Econ.SE. It would be nice if you could supplement your answer with links to the articles mentioned herein.  

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### Answer by username_7 on 2018-01-12. Score: -1

Some papers with estimates of consumer demand systems including non-durable and durable (usually clothes) goods:

Lewbel, A. (1997). Consumer demand systems and household equivalence scales. Handbook of Applied Econometrics Volume 2: Microeconomics, 155-185.

Banks, J., Blundell, R., & Lewbel, A. (1997). Quadratic Engel curves and consumer demand. The review of economics and statistics, 79(4), 527-539.

Crawford, I., Laisney, F., & Preston, I. (2003). Estimation of household demand systems with theoretically compatible Engel curves and unit value specifications. Journal of Econometrics, 114(2), 221-241.

> **Comments:**
> **username_0**: The last two references do not have any mention of elasticities of durable goods. Only non-durable (such as food and clothes). Clothes are not considered durable goods. Durable goods are cars, machinery, laptops, etc.  

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