tag:blogger.com,1999:blog-63793111339599345202024-03-05T13:15:25.818-08:00Ask The ProfStudents post questions they have from Microeconomics (Principles and Intermediate). The Prof helps them think it through.Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.comBlogger22125tag:blogger.com,1999:blog-6379311133959934520.post-89815838828556175172016-10-02T14:27:00.001-07:002016-10-02T14:27:15.042-07:00Getting the Excel FilesA student wrote in reference to this <a href="https://youtu.be/bos9X_m0Zas">YouTube video </a>on the Labor-Leisure choice:<br />
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<blockquote class="tr_bq">
<span data-sheets-userformat="{"2":513,"3":{"1":0},"12":0}" data-sheets-value="{"1":2,"2":"Hi Prof,\n\nYour video is great help.\nCan I get the excel worksheet with graphs to better understand. I wasn't able to find it on any posted links."}" style="font-family: arial,sans,sans-serif; font-size: 13px;">Hi Prof,</span><span data-sheets-userformat="{"2":513,"3":{"1":0},"12":0}" data-sheets-value="{"1":2,"2":"Hi Prof,\n\nYour video is great help.\nCan I get the excel worksheet with graphs to better understand. I wasn't able to find it on any posted links."}" style="font-family: arial,sans,sans-serif; font-size: 13px;"><br /></span><span data-sheets-userformat="{"2":513,"3":{"1":0},"12":0}" data-sheets-value="{"1":2,"2":"Hi Prof,\n\nYour video is great help.\nCan I get the excel worksheet with graphs to better understand. I wasn't able to find it on any posted links."}" style="font-family: arial,sans,sans-serif; font-size: 13px;">Your video is great help.</span><span data-sheets-userformat="{"2":513,"3":{"1":0},"12":0}" data-sheets-value="{"1":2,"2":"Hi Prof,\n\nYour video is great help.\nCan I get the excel worksheet with graphs to better understand. I wasn't able to find it on any posted links."}" style="font-family: arial,sans,sans-serif; font-size: 13px;">Can I get the excel worksheet with graphs to better understand. I wasn't able to find it on any posted links.</span></blockquote>
<span data-sheets-userformat="{"2":513,"3":{"1":0},"12":0}" data-sheets-value="{"1":2,"2":"Hi Prof,\n\nYour video is great help.\nCan I get the excel worksheet with graphs to better understand. I wasn't able to find it on any posted links."}" style="font-family: arial,sans,sans-serif; font-size: 13px;"><br /></span>
<span data-sheets-userformat="{"2":513,"3":{"1":0},"12":0}" data-sheets-value="{"1":2,"2":"Hi Prof,\n\nYour video is great help.\nCan I get the excel worksheet with graphs to better understand. I wasn't able to find it on any posted links."}" style="font-family: arial,sans,sans-serif; font-size: 13px;"><span style="font-family: Times; font-size: small;">My response:</span></span><br />
<span data-sheets-userformat="{"2":513,"3":{"1":0},"12":0}" data-sheets-value="{"1":2,"2":"Hi Prof,\n\nYour video is great help.\nCan I get the excel worksheet with graphs to better understand. I wasn't able to find it on any posted links."}" style="font-family: arial,sans,sans-serif; font-size: 13px;"><span style="font-family: Times; font-size: small;"><br /></span></span>
<blockquote class="tr_bq">
<span data-sheets-userformat="{"2":513,"3":{"1":0},"12":0}" data-sheets-value="{"1":2,"2":"Hi Prof,\n\nYour video is great help.\nCan I get the excel worksheet with graphs to better understand. I wasn't able to find it on any posted links."}" style="font-family: arial,sans,sans-serif; font-size: 13px;"><span style="font-family: Times; font-size: small;">In the description of that YouTube video, I updated the link to the <a href="https://drive.google.com/drive/folders/0Bz9kxuxY68EJOTczMWM3ZmMtNmExYS00NDFjLTg4NTQtYTRlMjE3MWE5MjIx">Excel Files</a>. You must download the files to use them and you need a functional version of Excel for that to work. </span></span></blockquote>
Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-66220688152114065752015-11-17T04:10:00.001-08:002015-11-17T04:10:55.861-08:00Estimating Demand ElasticityJoseph wrote:<br />
<br />
Dear Sir/Ma,<br />
<br />
I am a research student currently conducting a study to determent the price and income elasticity of demand for fuel products in Nigeria, using a Quadratic Almost Ideal Demand System. I am using a cross sectional data (Harmonized National Living Standard Survey, 2009) obtained from the statistical agency in Nigeria.
Currently, I face a challenge estimating the price elasticity of demand for fuel product because prices are constant across household units in the survey period (2009). The survey data contains information on expenditure of various fuel products, but no information is available on the price and quantities of fuel products purchased.
However, I obtained the price of each product in 2009, but it is constant across all households, as a uniform price is applicable in Nigeria. This poses a challenge in estimating the price elasticity of demand for fuel products. To circumvent this problem, some studies have used quantities of each product to divide expenditure of each product. This will create the needed variability in prices. This approach seems impossible to me since my data set has no quantity of fuel products purchased. I humbly write to seek for more clarification on how to obtain variability in prices of each product across various households units in the survey.
Thanks
Joseph O.
<br />
<br />
My response:<br />
<br />
I'm afraid I can't offer any further insight to what you've already said. I don't do empirical work and as you said, you don't have the data do produce estimates here. It seems to me the best you can do is some survey on what others have found. After a quick search I found <a href="http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2533136">this paper by Boshoff</a>. You are probably aware of it already. But in case not, on page 48 (page 6 of the pdf) there is a table with other estimates provided. And then, of course, there are his own estimates later in the paper. Those are for South Africa, not Nigeria. In the absence of data about your own country, however, you should find what else is known about gasoline demand elasticity elsewhere.Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-9237166533850695472015-05-09T05:51:00.003-07:002015-05-09T05:52:47.505-07:00Marginal Product of Labor in the Shapiro and Stiglitz Model<span style="font-family: arial, sans, sans-serif; font-size: 13px;">Dear Professor, </span><br />
<span data-sheets-userformat="[null,null,513,[null,0],null,null,null,null,null,null,null,null,0]" data-sheets-value="[null,2,"Dear Professor, \n\nThanks fir putting those lessons on youtube!\n\nI saw your video on the Shapiro Stiglitz Model and my doubt is regarding the comparative statistics of Marginal Productivity of Labour with unemployment and wages. \n\nAccording to my understanding, when unemployment increases, the wages should decrease as firms do not need to offer high wages to prevent workers from shirking, unemployment acts as a disciplining tool.\nHow does the Marginal Productivity of Labour vary with this? Does is it Increase as well?\n\nBest Regards\nUtkarsh Katyaayun"]" style="font-family: arial,sans,sans-serif; font-size: 13px;"><br />Thanks fir putting those lessons on youtube!<br /><br />I saw your video on the Shapiro Stiglitz Model and my doubt is regarding the comparative statistics of Marginal Productivity of Labour with unemployment and wages. <br /><br />According to my understanding, when unemployment increases, the wages should decrease as firms do not need to offer high wages to prevent workers from shirking, unemployment acts as a disciplining tool.<br />How does the Marginal Productivity of Labour vary with this? Does is it Increase as well?<br /><br />Best Regards<br />Utkarsh Katyaayun</span><br />
<span data-sheets-userformat="[null,null,513,[null,0],null,null,null,null,null,null,null,null,0]" data-sheets-value="[null,2,"Dear Professor, \n\nThanks fir putting those lessons on youtube!\n\nI saw your video on the Shapiro Stiglitz Model and my doubt is regarding the comparative statistics of Marginal Productivity of Labour with unemployment and wages. \n\nAccording to my understanding, when unemployment increases, the wages should decrease as firms do not need to offer high wages to prevent workers from shirking, unemployment acts as a disciplining tool.\nHow does the Marginal Productivity of Labour vary with this? Does is it Increase as well?\n\nBest Regards\nUtkarsh Katyaayun"]" style="font-family: arial,sans,sans-serif; font-size: 13px;"><br /></span>
<span data-sheets-userformat="[null,null,513,[null,0],null,null,null,null,null,null,null,null,0]" data-sheets-value="[null,2,"Dear Professor, \n\nThanks fir putting those lessons on youtube!\n\nI saw your video on the Shapiro Stiglitz Model and my doubt is regarding the comparative statistics of Marginal Productivity of Labour with unemployment and wages. \n\nAccording to my understanding, when unemployment increases, the wages should decrease as firms do not need to offer high wages to prevent workers from shirking, unemployment acts as a disciplining tool.\nHow does the Marginal Productivity of Labour vary with this? Does is it Increase as well?\n\nBest Regards\nUtkarsh Katyaayun"]" style="font-family: arial,sans,sans-serif; font-size: 13px;">My Response:</span><br />
<span data-sheets-userformat="[null,null,513,[null,0],null,null,null,null,null,null,null,null,0]" data-sheets-value="[null,2,"Dear Professor, \n\nThanks fir putting those lessons on youtube!\n\nI saw your video on the Shapiro Stiglitz Model and my doubt is regarding the comparative statistics of Marginal Productivity of Labour with unemployment and wages. \n\nAccording to my understanding, when unemployment increases, the wages should decrease as firms do not need to offer high wages to prevent workers from shirking, unemployment acts as a disciplining tool.\nHow does the Marginal Productivity of Labour vary with this? Does is it Increase as well?\n\nBest Regards\nUtkarsh Katyaayun"]" style="font-family: arial,sans,sans-serif; font-size: 13px;"><br /></span>
<span data-sheets-userformat="[null,null,513,[null,0],null,null,null,null,null,null,null,null,0]" data-sheets-value="[null,2,"Dear Professor, \n\nThanks fir putting those lessons on youtube!\n\nI saw your video on the Shapiro Stiglitz Model and my doubt is regarding the comparative statistics of Marginal Productivity of Labour with unemployment and wages. \n\nAccording to my understanding, when unemployment increases, the wages should decrease as firms do not need to offer high wages to prevent workers from shirking, unemployment acts as a disciplining tool.\nHow does the Marginal Productivity of Labour vary with this? Does is it Increase as well?\n\nBest Regards\nUtkarsh Katyaayun"]" style="font-family: arial,sans,sans-serif; font-size: 13px;">First, I'm sorry this has taken a while. I didn't see the question until this morning. </span><br />
<span data-sheets-userformat="[null,null,513,[null,0],null,null,null,null,null,null,null,null,0]" data-sheets-value="[null,2,"Dear Professor, \n\nThanks fir putting those lessons on youtube!\n\nI saw your video on the Shapiro Stiglitz Model and my doubt is regarding the comparative statistics of Marginal Productivity of Labour with unemployment and wages. \n\nAccording to my understanding, when unemployment increases, the wages should decrease as firms do not need to offer high wages to prevent workers from shirking, unemployment acts as a disciplining tool.\nHow does the Marginal Productivity of Labour vary with this? Does is it Increase as well?\n\nBest Regards\nUtkarsh Katyaayun"]" style="font-family: arial,sans,sans-serif; font-size: 13px;"><br /></span>
<span data-sheets-userformat="[null,null,513,[null,0],null,null,null,null,null,null,null,null,0]" data-sheets-value="[null,2,"Dear Professor, \n\nThanks fir putting those lessons on youtube!\n\nI saw your video on the Shapiro Stiglitz Model and my doubt is regarding the comparative statistics of Marginal Productivity of Labour with unemployment and wages. \n\nAccording to my understanding, when unemployment increases, the wages should decrease as firms do not need to offer high wages to prevent workers from shirking, unemployment acts as a disciplining tool.\nHow does the Marginal Productivity of Labour vary with this? Does is it Increase as well?\n\nBest Regards\nUtkarsh Katyaayun"]" style="font-family: arial,sans,sans-serif; font-size: 13px;">The Shapiro-Stiglitz model is quite conventional on the productivity side. There is a production function for each firm. That determines output based on the number employees hired (assuming they don't shirk). The unemployment rate in the market doesn't impact productivity at an individual firm at all, if the workers put for effort. In other words, the marginal product of labor curve looks just like the it does for a neoclassical firm in intermediate microeconomics.</span><br />
<span data-sheets-userformat="[null,null,513,[null,0],null,null,null,null,null,null,null,null,0]" data-sheets-value="[null,2,"Dear Professor, \n\nThanks fir putting those lessons on youtube!\n\nI saw your video on the Shapiro Stiglitz Model and my doubt is regarding the comparative statistics of Marginal Productivity of Labour with unemployment and wages. \n\nAccording to my understanding, when unemployment increases, the wages should decrease as firms do not need to offer high wages to prevent workers from shirking, unemployment acts as a disciplining tool.\nHow does the Marginal Productivity of Labour vary with this? Does is it Increase as well?\n\nBest Regards\nUtkarsh Katyaayun"]" style="font-family: arial,sans,sans-serif; font-size: 13px;"><br /></span>
<span data-sheets-userformat="[null,null,513,[null,0],null,null,null,null,null,null,null,null,0]" data-sheets-value="[null,2,"Dear Professor, \n\nThanks fir putting those lessons on youtube!\n\nI saw your video on the Shapiro Stiglitz Model and my doubt is regarding the comparative statistics of Marginal Productivity of Labour with unemployment and wages. \n\nAccording to my understanding, when unemployment increases, the wages should decrease as firms do not need to offer high wages to prevent workers from shirking, unemployment acts as a disciplining tool.\nHow does the Marginal Productivity of Labour vary with this? Does is it Increase as well?\n\nBest Regards\nUtkarsh Katyaayun"]" style="font-family: arial,sans,sans-serif; font-size: 13px;">All the interaction is on the incentive side. There, as you say, if the unemployment rate is higher, which means future job acquisition is lower once unemployed. So the efficiency wage need not be as great then. </span>Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-38788117918194442192014-06-06T10:07:00.000-07:002014-06-06T10:07:00.710-07:00A question about health insurance James asked:<br />
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<blockquote class="tr_bq">
<span style="font-family: arial, sans, sans-serif; font-size: 13px;">I saw your Youtube video on Demand for Insurance and it led me to here. With that said, there are many articles written about health coverage choice e.g.</span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">National Institute of Health: http://economics.mit.edu/files/7870</span><span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">Beginning on page 5 and,<br /> </span><span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">Urban institute: http://www.urban.org/UploadedPDF/412471-Health-Insurance-Policy-Simulation-Model-Methodology-Documentation.pdf</span><span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">Beginning on page 12.</span><span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">RAND Compare has an overly complex model, but for discussion purposes, will use NIH's example.</span><span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">NIH is taking into consideration (i) Risk aversion utility maximization (ii) expected healthcare needs (iii) variance in OOP cost from a set of health plans with consideration of variance in premiums for the health plans.<br /> </span><span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">Is there a model or someone who can help me create a supplemental excel model that reflects the NIH's Model? In this model, they are using limited data such as Age, Income, and gender to impute a cost (lognorm function?)<br /> </span><span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">There is so much written about this subject, however, I am having a very hard time modeling what is being discussed. If you could point me in a direction to someone who can help or may be interested in taking this on as a project, I would appreciate your feedback.</span></blockquote>
<span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span>
<span style="font-family: arial, sans, sans-serif; font-size: 13px;">My response:</span><br />
<span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span>
<br />
<blockquote>
<span style="font-family: arial, sans, sans-serif; font-size: 13px;">The video of mine that you mention just considers risk aversion and then only in the two-state case: loss or no-loss. So it is done very simply in that model. I have another video on <a href="https://www.youtube.com/watch?v=55jIRXzir6I">adverse selection</a>, that looks at the problem graphically in a simple model and one on <a href="https://www.youtube.com/watch?v=hXEk5NUhItc&feature=youtu.be">moral hazard</a> that does it algebraically. (It is really a model of the principal and agent, but that is essentially the same as an insurance model with moral hazard.)</span> </blockquote>
<blockquote>
<span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">The MIT paper that you mention puts all these factors together in one model by considering two periods, where in the second period there is moral hazard, given the insurance policy choice in the first period. Then, understanding the second period solution, they fold it back and look at the selection problem in the first period. And the do this noting that demographic characteristics of the insurance purchaser will impact both the moral hazard and the selection problems. This is substantially more complex then any of my videos. It is also more realistic. </span> </blockquote>
<blockquote>
<span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">Whether you can build an Excel model that imitates the MIT paper, I'm not sure. But why would you want to do that? To understand the MIT paper because it is too hard to work through the equations that are presented there? Please not that papers published in the AER are meant for an audience of professional economists and assume the reader has crossed a prior threshold of understanding - both on the issues and the math modeling. I would not teach this paper to an undergraduate class. </span></blockquote>
Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com3tag:blogger.com,1999:blog-6379311133959934520.post-4874353771571755432014-04-26T10:16:00.003-07:002014-04-26T10:16:28.116-07:00Comparative AdvantageDanny wrote:<br />
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<blockquote class="tr_bq">
Hi professor, </blockquote>
<blockquote class="tr_bq">
For example, given two countries and two outputs such as trains and planes, when determining which has the comparative advantage, do you compare within the country itself or between countries? That is, should you be comparing whether producing one particular good has a lower opportunity cost than the other in that same country? Or comparing whether producing one particular good has a lower opportunity cost in another country relative to your own country? </blockquote>
<blockquote class="tr_bq">
In other words, are the comparisons of opportunity costs performed horizontally or vertically? I am confused. </blockquote>
<blockquote class="tr_bq">
For an example, please see:
https://www.youtube.com/watch?v=z9SAzSm24qg&index=7&list=PLA46DB4506062B62B
At 2:00mins, the instructor suggests comparing between countries, however, isn't comparative advantage and opportunity costs compared within the same country? Or is it because the introduction of trade changes it around? Not really sure. </blockquote>
<blockquote class="tr_bq">
Thanks for any help</blockquote>
<br />
My response:<br />
<br />
<blockquote class="tr_bq">
The question that might help you to understand this is this. Suppose trade between the two countries can occur and is costless. Then an efficient production plan that produced a given amount of trains would maximize the number of airplanes produced. How should production be divided across the two countries to attain an efficient production plan? </blockquote>
<blockquote class="tr_bq">
If the efficient production plan entails one country specializing in production, for example say that country A produces Trains only while country B produces Trains and Planes, with the result an efficient plan, then we say that country A has a comparative advantage in producing Trains. </blockquote>
<blockquote class="tr_bq">
Further, if you considered a different efficient production plan with a bit less production of Trains and a bit more production of planes, then the way to get from the first to the second is by having country B reduce its production of trains and increase its production of planes and have country A continue to specialize in the production of trains. </blockquote>
<br />Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-37707739820472888192014-04-26T09:55:00.000-07:002014-04-26T09:55:04.219-07:00The effect of a tax<div class="tr_bq">
Danny wrote:</div>
<br />
<br />
<blockquote class="tr_bq">
Hi Professor, </blockquote>
<blockquote class="tr_bq">
In regards to taxes, I have seen that in your video, that you name the vertical axes either the selling price or the buyer price and am I correct in saying that depending on whether the tax is levied on buyers or sellers is what determines what you name your vertical axes and thus determines which curve you shift. I have never seen it been done this way. I've always seen the vertical axes to just be denoted price. </blockquote>
<blockquote class="tr_bq">
Since the burden of the tax is shared (doesn't have to be equally shared of course right) between buyers and sellers, does it really matter what curve you shift (demand or supply) when either the buyer pays the tax or the seller pays the tax? Is it correct to shift either one of the curves?
The way my lecturer has demonstrated it is to draw a tax wedge between the supply and demand curves,however I get confused to how this is used or can be used to answer questions. Because there will be two intersections given a particular quantity with both the supply and demand curve, so how do you know which one to look at?<br /> <br />My lecturer has said he does not prefer shifting the supply or demand curves because that is not actually what is happening, it is just 'construction lines' to depict the tax levy and drawing a tax wedge is much more simpler and achieves the same thing, however I have difficulty grasping the tax concept. </blockquote>
<blockquote class="tr_bq">
Furthermore, my lecturer and other online videos suggest that the price to the buyer is equal to the price to the producer PLUS the tax? (Pb = Ps + Tax) </blockquote>
<blockquote class="tr_bq">
However isn't that only correct if we are assuming that the consumer PAYS the tax? What if the producer pays the tax, does that mean this equation (Pb = Ps + Tax) is invalid? And rather it should be the price to the producer equals the price to the consumer plus the tax? </blockquote>
<blockquote class="tr_bq">
Or because the tax burden is shared between buyers and sellers, that it doesn't really matter? So in these cases, how do you know which curve to be shifting or to be looking at when determining the new tax equilibrium?<br /> <br />I hope that makes sense and would appreciate some help. </blockquote>
<blockquote class="tr_bq">
Thank you so much,
</blockquote>
<br />
My response:<br />
<br />
<blockquote>
In the presence of the tax, the buyer pays more than what the seller receives. The difference is the tax. That much is fundamental. If Pb is what the buyer pays and Ps is what the seller receives, then the equation Pb = Ps + Tax or Ps = Pb - Tax (which is the same equation rewritten) is always valid. </blockquote>
<blockquote>
The rest is on how to represent this graphically, going from no tax to a tax or going from a tax to then raising the tax. What happens in these cases is called the comparative statics of competitive equilibrium with respect to the tax. You can do this as I have done in my video or via the wedge that your instructor prefers. An advantage of the wedge, as your instructor has noted, is that the underlying demand and supply curves are not changing. A disadvantage is that you may not be able to eyeball the vertical distance between demand and supply for a given quantity or, conversely, to eyeball the quantity where a given vertical distance is attained. </blockquote>
Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com7tag:blogger.com,1999:blog-6379311133959934520.post-8197683863674456462014-04-26T09:09:00.000-07:002014-04-26T09:09:10.459-07:00Externalities and Curve ShiftingDanny wrote:<br />
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<blockquote class="tr_bq">
Hi Professor Arvan,<br />
<br />
Can externalities be either on the production or consumption side? That is, for example, a negative externality, does it matter whether you shift the supply curve leftward/inward or the demand curve leftward/inward?<br />
<br />
For example, when dealing with a good such as for example, a cologne that is extremely repugnant, is the negative externality related to the consumption or production of the good? <br />
<br />
It could be argued from both perspectives, right?<br />
<br />
Hence how would you know which curve to shift in order to find the socially optimal quantity? (If you shift either, they do however end up at the same socially optimal quantity, however the prices differ (if you shift the supply curve inward, the new equilibrium would be higher, and if you shift the demand curve inward, price would be lower)<br />
<br />
I would appreciate your comments on this.<br />
<br />
Thank you.<br />
<br />
Regards,<br />
Danny</blockquote>
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<br />
My response:<br />
<br />
<blockquote class="tr_bq">
There can certainly be externalities in consumption and they can be either positive or negative. For example, sometimes there is a desire to be "part of the crowd." If many students wear bluejeans to class, other students might want to wear them for that reason. This is a positive consumption externality that is sometimes referred to as a network effect. Advertisers understand this and one economic rationale for advertisement of a certain sort is to encourage the market to congeal on that product.
<br />
<br />
I didn't quite get the example with the cologne. Presumably a person wears a scent to attract others. If the cologne were generally repugnant, that would seem to be a product without a market. But one might consider a scent that most others like yet that a few are allergic to. There would be a negative externality in that case in causing the allergic reaction. <br />
<br />
One can a little nitpicking on products that are durable by separating out purchase from use. The bluejeans mentioned about don't contribute to the network effect if they hang in the person's closet. The networks effect only arises when the person is seen wearing them. Something similar can be said for the cologne. Normally we are not so finicky in making our analysis and assume purchase and use are strongly correlated.<br />
<br />
The last point I'd make is to be careful about discussing curve shifting in the presence of the externality. In the textbook case of a factory that is polluting the air as a byproduct when operating the plant, neither the supply curve nor the demand curve shift as a consequence of the externality. Normally we analyze this case by saying the marginal social cost shifts inward (from the original supply curve) where social cost includes both the production costs and the abatement costs. In contrast, in the presence of network effects the demand curve itself actually shifts.
</blockquote>
Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com2tag:blogger.com,1999:blog-6379311133959934520.post-40568456821361414662014-03-11T13:53:00.000-07:002014-03-11T13:53:04.044-07:00Estimating Demand Elasticities and Compensating Variation<div class="tr_bq">
A student posed the following question:</div>
<br />
<blockquote class="tr_bq">
Hi Respected Sir,<br />I am writing a report on Compensating Variation (CV) in case of more than two goods say 8 goods. My question is how can we estimate it in case of more than 2 goods.<br />Another Question is How can we write the equations for 8 commodities in Almost Ideal Demand System (AIDS) to calculate Own , Cross and Expenditure Elasticities of demand.<br />In which software both of the methods can be calculated?<br />I am waiting for your reply.<br />Thanks in anticipation</blockquote>
<br />
My response:<br />
<br />
<blockquote>
This question is more econometrics than it is intermediate micro. So I am only going to provide a partial response and stick to the economic theory part, though I must say I'd only teach what I discuss below at the graduate level. </blockquote>
<blockquote>
The traditional approach to consumer choice is to start with preferences, specified by a utility function, u, and combine that with a budget constraint, that depends on a price system <b>p</b> = (p1,p2,...,pn) that specifies the prices of each good or service, and the consumers income <b>y</b>. Together the price system and income determine the budget set. The consumer's choice, or demand, or optimum, call it x*(u,<b>p</b>,<b>y</b>) solves the problem of maximizing utility subject to the budget constraint. </blockquote>
<blockquote>
There is an alternative approach called the duality approach, which is useful conceptually and in laying the foundation for the econometrics. Two value functions are determined. One, measured in dollar terms, is called the Expenditure Function. It is analogous to the Cost Function developed in the theory of the firm. The expenditure function maps indifference curves (or when there are more than two goods, level sets of the utility function) and price systems into an expenditure level - the least expenditure it takes to reach that indifference curve at the given prices. The other value function, measured in utility terms, is called the Indirect Utility Function. It maps budget sets into utility levels. Alternatively, it gives the utility attained at the consumer's choice. </blockquote>
<blockquote>
One of the powerful results from duality theory is that you can recover the consumer demand's from these value functions. The compensated demands (these measure the substitution effect only) are given by the first partial derivatives of the Expenditure Function with respect to the specific price. The ordinary demands can be obtained in a similar way from the Indirect Utility Function, though the result, known as <a href="http://en.wikipedia.org/wiki/Roy's_identity">Roy's Identity</a>, is a bit more complicated. </blockquote>
<blockquote>
Let me close with the little I know about the Almost Ideal Demand System. Deaton and Mulbauer start with the Expenditure Function, express it in log form, and then linearize it locally, assuming it is some average of the expenditure at subsistence (the worst possible point) and bliss (the best possible point). This makes it suitable for estimation. </blockquote>
<blockquote>
Good luck on your paper. </blockquote>
Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-85715817524230706772013-09-05T05:32:00.001-07:002013-09-05T05:32:14.319-07:00The effect of a tax - curve shiftingVu asked:<br />
<br />
<blockquote class="tr_bq">
<span style="font-family: arial, sans, sans-serif; font-size: 13px;">Dear professor Arvan</span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">i have a question</span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">Why when a unit tax is levied directly on consumers, this make the demand curve shifts downwards? and what could be the causes of this shift ?</span><span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span><span style="font-family: arial, sans, sans-serif; font-size: 13px;">Thank you very much</span></blockquote>
<span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span>
My response:<br />
<br />
The tax is levied in some market for a good or service. Typically, buyers pay some of it and sellers pay some of it as well. The tax creates a wedge between what the buyer pays and what the seller receives, with the difference being the tax. If in the diagram the price represented is the seller's price (so the supply curve remains the same) then the demand curve shifts down by the amount of the tax. In this way if you add the tax to the seller's price, you get the price really does pay so the quantity demanded should be exactly what it was before at this higher price.Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-13366025311370324582013-07-08T12:09:00.000-07:002013-07-08T12:09:03.572-07:00Comparative Statics of Consumer ChoiceJudy asked:<br />
<br />
<blockquote class="tr_bq">
<span style="font-family: arial, sans, sans-serif; font-size: 13px;">using well labele diagrams show the total effect,income effect and substitution effect due to a price fall of good x1 assuming that the consumer baskets has only good x1 and x2. The price of good x2 remains constant.</span></blockquote>
<span style="font-family: arial, sans, sans-serif; font-size: 13px;"><br /></span>
My Response:<br />
<br />
I encourage you to watch <a href="http://www.youtube.com/watch?v=GgzS04HCVbw">my video on income and substitution effects</a>. There the goods are labeled x and y (instead of x1 and x2) and it is for a price increase rather than a price decrease. I suspect you covered something similar in your class and now your instructor wants you to think through what happens when the price change is in the opposite direction. <br />
<br />
From my video in the description there is a link to the spreadsheet. Go to the tab labeled Income and Substitution Effects. There is a button called Raise Price of Good X. Push on that and look at the cell next to the button. It has positive values. If you type into that cell a negative value, say -15, you will get the graph for a price reduction of Good X. Note that because this was designed for a price increase, the new budget line doesn't extent all the way to X axis. It should.<br />
<br />
Also, your instructor may feel I'm doing your homework for you and not be happy about it. So if you pose another question of this sort to Ask The Prof, please also include what you've tried to do in response. This way I can help you without giving away the answer to the question.Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-37416889660985753222013-04-30T09:59:00.001-07:002013-04-30T09:59:07.897-07:00Produce or Not in the Short Run?Joe R. asks:<div>
<br /></div>
<blockquote class="tr_bq">
Working on a question with a full chart to reference but am lost where to get the date for the answer. The question ask about the product price of $56, will this firm produce in the short run.?</blockquote>
<div>
<br /></div>
<div>
My response:</div>
<div>
<br /></div>
<div>
There is a fairly complete analysis of the general issues in the video <a href="http://working%20on%20%20aquestion%20with%20a%20full%20chart%20to%20reference%20but%20am%20lost%20where%20to%20get%20the%20date%20for%20the%20answer.%20the%20question%20ask%20about%20the%20product%20price%20of%20%2456%2C%20will%20this%20firm%20produce%20in%20the%20short%20run./?">Short Run Cost</a>. The question is asking, in effect, whether there is any output level were Average Variable Cost is below $56. If the answer is yes, then producing at that output level nets some producer surplus (the difference between revenue and variable cost), so it makes sense to produce. If not, then it is best not to produce.</div>
<div>
<br /></div>
<div>
Note that the fix cost is not relevant for this calculation. It is sunk in the short run and therefore must be paid regardless of whether production occurs. </div>
<div>
<br /></div>
<div>
Your chart that you refer to may not have Average Variable Cost broken out, in which case you must compute it by dividing Total Variable Cost by Output. If it is broken out, then it is simply a matter of eyeballing it to see if it ever is below $56.</div>
Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-49706789544832103712013-04-18T03:41:00.001-07:002013-04-18T08:07:06.724-07:00On the Weak and General Axiom of Revealed PreferenceJohn asked the following:<br />
<br />
<br />
<blockquote>
"I have two related questions on Choice. </blockquote>
<blockquote>
I know that we can satisfy WARP but have nevertheless a violation of GARP. My question is if we can have a situation where WARP is violated, but GARP is satisfied? </blockquote>
<blockquote>
Secondly, from the definition of GARP it is always spoken of a bundle being revealed preferred to another bundle through a chain or ""sequence"" of revealed preferences. My question is, if this defined ""sequence"" can consist of only two observations, so that we have actually a direct revealed preference after all? In other words, does ""revealed preferred"" include the case of ""direct revealed preferred""?"</blockquote>
<br />
My response:<br />
<br />
The quick answers are, to the first question, no, and to the second question, yes. In other words, GARP implies WARP and the chain can have only two elements, which is WARP directly. <br />
<br />
A longer response would include making a comparison between revealed preference and the usual assumptions made about preference. These are about a preference relation, <b>R</b>. x<b>R</b>y is then read as, x is preferred to or indifferent to y. So from <b>R</b> one can also define<b> P</b> and <b>I</b> by:<br />
<br />
<ul>
<li>x<b>P</b>y if x<b>R</b>y and not y<b>R</b>x.</li>
<li>x<b>I</b>y if x<b>R</b>y and y<b>R</b>x.</li>
</ul>
<br />
<br />
There are three "logical" assumption about preference orderings.<br />
<br />
<b>R</b> is complete. For every x and y in the Consumption set (the set of possible consumption bundles) either x<b>R</b>y or y<b>R</b>x. This means comparisons can be made between any two consumption bundles. Note that neither <b>P</b> nor <b>I</b> are complete. <br />
<br />
<b>R</b> is reflexive. For every x in the Consumption set x<b>R</b>x. <br />
<br />
<b>R</b> is transitive. For every x, y, and z in the Consumption set, if x<b>R</b>y and y<b>R</b>z then x<b>R</b>z. <br />
<br />
These properties allow one to define a choice, provided the choice set is closed. In this case if the choice set is C then x in C is a choice (a maximal element under <b>R</b>) if x<b>R</b>y for all y in C. Note that there is no greatest number less than 100. If you posit it is 99, then 99.9 is greater and you can always add an additional 9 to the right. So for a choice to exist, the choice set must be closed. 100 is the greatest number less than or equal to 100. The choice set being closed means it includes its boundary.<br />
<br />
To these logical assumptions, one usually adds an economic assumption - monotonicity or more is preferred to less. This assumption rules about satiation points as well as "thick indifference curves," The upshot of this assumption is that when the choice problem is given by a budget set, the choice will always be on the budget line, never inside the line. <br />
<br />
A further assumption that is frequently made is that preferences are Convex, which gives indifference curves their usual shape. This is done do when the Budget environment changes in a small way, the choice also changes at most in a small way. Or, if you prefer, the demands are continuous function of the budget environment. <br />
<br />
Now, with all this machinery, what does WARP get you? In this way of thinking, WARP is equivalent to completeness, reflexivity, and monotonicity. You need GARP to bring in transitivity. There is also something called SARP, the strong axiom. It is WARP plus the assumption that preferences are strictly convex, so the choice is always unique. <br />
<br />
I hope that helps.<br />
<br />
<br />Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com2tag:blogger.com,1999:blog-6379311133959934520.post-78635953839778605232012-12-16T05:41:00.000-08:002012-12-16T05:41:11.777-08:00Follow Up On Measuring UtilityJonathan came back with this:<br />
<br />
<br />
<blockquote class="tr_bq">
<span style="color: #990000;">Hi, thanks for that Professor. IMO Utility does describe the feeling, or at least the “something” that kicks-in mentally, particularly with ""money"" based decisions - when you know (or don’t) you are detaching yourself from the wholly rational course of action (expected return) to take the money on the table offered, or a sum offered with certainty that is just enough of a push - for you to cash in your chips.<br />Where I’m stuck – is that there is a load of books and research about the abstract pro’s and cons – but I can’t find anything anywhere on the net that explains just how to go about discovering how to assess yourself (e.g. a clear example from the grass up).<br />Any ideas?<br />Thanks again,<br />Jon </span></blockquote>
<br />
My response:<br />
<br />
If you took the standard expected utility theory at face value, then you would approximate the utility function locally with a quadratic. The benefit of doing that is you get that for small gambles around the mean, the theory says the risk premium should be the Arrow-Pratt measure of absolute risk aversion at the mean, r, times the variance of the gamble. <br />
<br />
For example suppose you face the gamble of $1,001 with probability .5 and $999 with probability .5, so the mean is $1,000 and the variance of this gamble is $1, which is small relative to the mean. You then try to elicit what amount of money for certain would make the person indifferent between having that or having the gamble. Suppose you find the certainty equivalent determined experimentally is $999.60. So in this case the risk premium is $.40 and hence the inferred Arrow-Pratt measure of absolute risk aversion is .4. <br />
<br />
Now if you do this seriously, you would like to see whether the theory is really confirmed. So you might try other small gambles with mean $1000. For example you might consider the gamble (a) of $1001 with probability .8 and $996 with probability .2 as well as the gamble (b) of $1004 with probability .2 and $999 with probability .8. Each of these gambles has the same variance, $4. So ahead of time you might guess based on what you discovered before that the measured risk premium would be $1.60, which must be the case if the formula in the first paragraph held exactly and you measured the risk premium perfectly in the previous experiment. You might get something close to that for the gamble (a) but you definitely won't for gamble (b) because that says the certainty equivalent is $998.40, which is lower than the $999, what is attained in the lower income state.<br />
<br />
There are two possible source of error here: (1) measurement of the risk premium in the first experiment and (2) the formula that relates risk premium to the Arrow-Pratt measure and the variance of the gamble. The second error becomes less as the variance gets smaller but the first error gets bigger that way. So even if you take the theory as fully correct, you will have issues in measuring the utility function. <br />
<br />
Let me make one more point on this. The psychologist Daniel Kahneman, winner of the Nobel Prize in Economics, has shown that the standard expected utility theory is wrong and that something else called Prospect Theory is closer to how we actually behave. In that a reference point matters for evaluating gambles and then whether the outcome is a win with respect to the reference point (where the individual is then risk averse) or a loss with respect to the reference point (where the individual is then risk seeking). Put another way, the utility function for Prospect Theory is convex-concave, with an inflection point at the reference point. If you find this interesting you might read Kahneman's recent book, <a href="http://www.amazon.com/Thinking-Fast-Slow-Daniel-Kahneman/dp/0374275637/ref=sr_1_1?s=books&ie=UTF8&qid=1355664674&sr=1-1&keywords=thinking+fast+and+slow">Thinking Fast and Slow</a>. <br />
<br />
<br />
Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com1tag:blogger.com,1999:blog-6379311133959934520.post-40163457628484425612012-12-12T05:54:00.002-08:002012-12-12T05:54:53.747-08:00Can (Expected) Utility Functions Be Measured Empirically?Jonathan asked:<br />
<br />
<br />
<blockquote class="tr_bq">
<span style="color: #990000;">Hi Professor Arvan,<br />I just watched your ExpUty video on Youtube -<br />In reality, how would you go about capturing personal utility functions and preferences? Is there a defacto approach / way or template for doing this for Money, or other goods? I referring to the question construction, interpretation / ranking of the answers and then the maths behind plotting the curve? Or do you know of a spreadsheet / program solution? I take it ""Utils"" can only ever be ordinal, in reality? I would appreciate any further advice on the subject - Thanks, Jon</span></blockquote>
<br />
My response:<br />
<br />
There are lots of issues that question. So it is a good one in bringing those to the surface. Let's get to some of these:<br />
<br />
(1) <b>Is the person rational a la the expected utility hypothesis or do "animal spirits" better serve as a guide to behavior?</b> And here instead of animal spirits think of Darwin and the decision to fight or flee. Moderate financial risk is qualitatively different, in my view, than the threat of somebody doing physical violence on your person, or the chance you may catch some serious disease. For the latter two, I doubt expected utility theory is useful at all. For the first, at least there is some hope it might be. <br />
<br />
(2) <b> How does the person assess the probability distribution in practice? </b> We understand how to do this in coin flipping, or casino games, but for real-world uncertainty do probability assessments at all conform with what the actuaries tell us we should believe? There is psychological research on this and it confirms that people are bad at making probability assessments on their own and typically over estimate the chance that a threat will materialize. The expression is "better safe than sorry" and the research supports that conclusion. But it also means the individual is not being rational in the expected utility sense. On the flip slide of this people of modest income are known to buy lottery tickets, even when the odds are quite bad for them. They are fascinated with the prospect of a high payoff, irrespective of the odds.<br />
<br />
(3) <b>When there is more than just one good, money, but rather several commodities does it make sense to monetize them all and speak of a single dimension of risk preference or is it harder than that? </b>As far as I know there is no good theory of risk preference in a multi-dimensional commodity setting. Since consumption bundles are themselves random - for example, if you buy a knock off computer instead of a name brand to save a few bucks how well does it function - the issues certainly appear there but whether there can be a coherent risk preference theoretically, I doubt it. I do think that psychologically we tend to convert these sorts of risk into unto time units - as a measure of the possible inconvenience - and if necessary then try to monetize those, but we do it only in a very rough way.<br />
<br />
(4) <b>Are a person's risk preferences stable over time or do they vary?</b> Let me give just one example here. People may drink alcohol because it "loosens them up," which you might interpret as becoming less risk averse. If the choice to drink alcohol in the first place is rational, and some might question that, then it is as if the risk aversion is a constraint that the person wants to shed. (And this is why there is so much discussion about peer pressure and drinking, because it may be others who want the person to shed the risk aversion, not the person himself or herself.) There are certain circumstances where a normally mild person (one who will take flight most of the time) becomes extremely aggressive (opts to fight and then does so with a fiery intensity) so it's almost a Dr. Jekyll and Mr. Hyde thing. <br />
<br />
<b>Conclusion.</b> Given these various caveats, each which bring realism to the story, you might ask whether expected utility is at all useful as an approach. I would say, yes it is useful especially if you restrict the domains where you apply it. The first is that it provides a nice explanation of the demand for insurance. The second is that in trading risks across individuals, it offers the reasonable intuition that with increasing wealth risk aversion should decline simply because there are better opportunities for diversifying the portfolio as one gets wealthier and hence suggests where there may be gains from trade from better sharing risks.<br />
<br />
Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-83317921424420601312012-11-14T14:02:00.000-08:002012-11-14T14:02:08.273-08:00Perfect Complements AgainNorman asked:<br />
<blockquote class="tr_bq">
<br />
We have a Leontief utility function like U(x1,x2)= min (x1,x2).What i want to do is to solve x1 and x2. I have read a lot about the theory but i couldn't find any solved example for Leontief utility maximization. I really will be very pleased if you can give clues for that problem. Thank you for your treasure time.</blockquote>
<br />
My response:<br />
<br />
Take a look at <a href="http://asktheprof.blogspot.com/2012/10/perfect-complements.html">this post</a> and see if that does it for you. If there are further questions post them as comments here.Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-88341477955312699262012-11-13T15:47:00.001-08:002012-11-13T15:47:40.959-08:00Consumer SurplusSerdar asked:<br />
<br />
<blockquote class="tr_bq">
For the arguement of "Compansated variation is always bigger than consumer surplus under all price changes", could you please discuss whether it is true or not by drawing the necessary graphs? And i would be pleased if you can give a numerical example to support the arguement (utility function is a Cobb-Douglas utility function). thank you in advance.</blockquote>
<br />
My response:<br />
<br />
This is discussed in the video, <a href="https://www.youtube.com/watch?v=cFgV0PlmllA&feature=plcp">CV EV and Change in CS</a>. The graph below is from the <a href="https://docs.google.com/file/d/0Bz9kxuxY68EJZDg5MTQ4NTYtNTRiMC00OTkwLTgyMDMtZjFjNWJhZGYzMmFh/edit">spreadsheet</a> used to make that video. Let's review the definitions of CV and CS and then consider the determinants of which is bigger.<br />
<br />
CV - this is the area to the left of the compensated (Hicksian) demand curve for the original optimum between the original price and the new price. <br />
<br />
Decrease in CS - this is area to the left of the ordinary demand curve between the original price and the new price.<br />
<br />
<div class="separator" style="clear: both; text-align: center;">
<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQuW6KtcBnwU6Zm6Oh108XiFVY2yyaHx_IJdBuzwyftWEmiqUpsiRNZaAe9jXuY1fwguxcOAafw-B6JNhh0-7rPL8sIv7Tx2fWC9gswwmxEV9P8-K7TcXYUacVD-xgJMe9aO-tElJICHE/s1600/CV_EV_and_CS.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" height="238" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgQuW6KtcBnwU6Zm6Oh108XiFVY2yyaHx_IJdBuzwyftWEmiqUpsiRNZaAe9jXuY1fwguxcOAafw-B6JNhh0-7rPL8sIv7Tx2fWC9gswwmxEV9P8-K7TcXYUacVD-xgJMe9aO-tElJICHE/s400/CV_EV_and_CS.png" width="400" /></a></div>
<div class="separator" style="clear: both; text-align: center;">
<br /></div>
<div class="separator" style="clear: both; text-align: left;">
Remember that the compensated demand measures the substitution effect only, but that the ordinary demand measures the substitution effect and the income effect in combination. For a good where there is no income effect, CV = Decrease in CS.</div>
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<br /></div>
<div class="separator" style="clear: both; text-align: left;">
More generally, what matters are:</div>
<div class="separator" style="clear: both; text-align: left;">
(1) the direction of the price change, and</div>
<div class="separator" style="clear: both; text-align: left;">
(2) whether the good is normal or inferior.</div>
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<br /></div>
<div class="separator" style="clear: both; text-align: left;">
In the graph above the original price is given by the height of the dashed horizontal line. Then the price rises and the new price is indicated by the height of the dotted horizontal line. The blue curve is the ordinary demand curve. The red curve is the compensated demand curve for the original optimum. In this diagram, the blue curve is more elastic at the original price than the red curve. That will be the case for a normal good. The area to the left of the red curve between the two prices is greater than the area to the left of the blue curve between the two prices. Thus in this case CV > Decrease in CS. </div>
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<br /></div>
<div class="separator" style="clear: both; text-align: left;">
I leave it to you to consider the case of a price decrease and/or the case where the good is inferior. By the way, if the utility function is Cobb-Douglas, then the good is normal.</div>
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Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-14536978134521986272012-10-20T06:51:00.001-07:002012-10-20T19:06:03.478-07:00Isoquant and IsocostA student posted the following question:<br />
<br />
<br />
<blockquote>
"The owner of a small car-rental service is trying to decide on the appropriate numbers of vehicles and mechanics to use in the business for the current level of operations. He recognizes that his choice represents a trade-off between the two resources. His past experience indicates that this trade-off is as follows:<br />
Vehicles: 100 70 50 40 35 32<br />
Mechanics: 2.5 5 10 15 25 35<br />
a] Assume that annual (leasing) cost per vehicle is $6,000 and the annual salary per mechanic is $25,000. What combination of vehicles and mechanics should he employ? - Already got the answer to which is 70 vehicles and 5 mechanics<br />
b] Illustrate this problem with the use of an isoquant/isocost diagram. Indicate graphically the optimal combination of resources.<br />
<br />
Thank you for your help and time"</blockquote>
<br />
My response: <br />
<br />
Your goal here should be not just to answer the question but more importantly to gain some understanding for why the answer is correct. To do that you should solve this both numerically and graphically.<br />
<br />
<u>Numerically</u> - The various combinations of points given lie on the same isoquant. There is economics in computing the slope of the segment between consecutive points. The absolute value of that slope is called the rate of technical substitution. (Sometimes the word marginal precedes that so the entire expression is marginal rate of technical substitution.) You should compute the full schedule of RTS.<br />
<br />
Then you should compute the ratio of the input prices. Students doing this for the first time are unsure whether that ratio should be (price vehicles)/(price mechanics) or (price mechanics)/(price vehicles). The graphical approach should help there. Which input is on the x axis? the y axis? Knowing that you can plot a line of constant expenditure on input bundles. The input price ratio you want is the absolute value of the slope of the line.<br />
<br />
The economics is in understanding when the RTS does not equal the relative price: movement in which direction along the isoquant will result in lower cost?<br />
<br />
<u>Graphically</u> - You should plot the isoquant. In the same diagram you should plot several isocost lines including one that lies entirely below the isoquant and another that crosses the isoquant through a non-optimal input bundle. If at that crossing point the isoquant is steeper, which direction along the isoquant leads to lower cost. Your goal here is to tie the graphical approach to the numerical approach. They are different representations of the same idea.<br />
<br />
Only after doing the above should you plot the isocost through the cost minimizing bundle. The conditions that characterize the optimum are best understood as being when the conditions for a non-optimal bundle don't hold.<br />
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<br />Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-78211484484168033352012-10-03T04:33:00.001-07:002012-11-14T13:07:36.315-08:00Perfect ComplementsJoseph wrote:<br />
<br />
<br />
<blockquote class="tr_bq">
"LUCAS has fixed money income, I which spent two goods X and Y. The prices of X and Y are fixed. Lucas,s Utility is based on following utility function. U(x,y)= min(4X,16Y). His income share for X is SX where Sx = PxX/I<br />
and his income share for Y is Sy, where Sy = PyY/I<br />
a: derive his demand function for X and Y.<br />
b; using your answers from a, derive the own-price elasticity of demand, cross-price elasticity of demand and the income elasticity of demand for X and Y.<br />
Thanks your help is appreciated."</blockquote>
<br />
My response:<br />
<br />
This looks like a problem from a textbook. My preference is to not provide answers to those but only some general guidelines to help you think it through. Here I will content myself with part a of the question question. Part b asks you to do some grinding based your answer to part a.<br />
<br />
The question is asking about choice for a particular class of preferences called "perfect complements" or fixed proportion preferences or Leontief preferences, after the economist Wassily Leontief. It turns out that the demands generated by these preferences have no substitution effect. The have only an income effect.<br />
<br />
This first graph gives an idea of what the indifference curves look like when the proportions are 1:1.<br />
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7nq6wBWNRbXpaBgnCzoX1Q20BNTSYNzoBqjTVvoHY5iUsmjtR0XxDFuAmbUnQq6NgikOBVIqqY-o-SKv-C630lB16dVmZhIiCdKLohq0gg5Dic1rXu4uZEKFY3pMUJdce4jauXe9NGys/s1600/perfect+complements+1.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi7nq6wBWNRbXpaBgnCzoX1Q20BNTSYNzoBqjTVvoHY5iUsmjtR0XxDFuAmbUnQq6NgikOBVIqqY-o-SKv-C630lB16dVmZhIiCdKLohq0gg5Dic1rXu4uZEKFY3pMUJdce4jauXe9NGys/s1600/perfect+complements+1.png" /></a></div>
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The indifference curve has a right angle at the 45 degree line. Above and to the left of the 45 degree line Good 2 is redundant and Good 1 is scarce. Then utility is determined by the amount of Good 1. Below and to the right of the line Good 1 is redundant and Good 2 is scarce. Then utility is determined by the amount of Good 2. In the problem posed the proportions are not. 1:1. It looks like they are either 4:1 or 1:4. Figuring out which is something you'll need to determine.</div>
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The second graph should give you and idea about how to solve for the demands. </div>
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<a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXquxjuCV6_0PybLlIQyCXKEOh9vsUHScAXLXPCurD5QngCM1OwzWJWnqxSdFEebFJ5PFNKOVT7oh0nMW60pCBPs-63ERcrzRt_GPuHXKExU1QgKbDswFtS7fmXTLtlLEwXLWP710RySo/s1600/perfect+complements+2.png" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiXquxjuCV6_0PybLlIQyCXKEOh9vsUHScAXLXPCurD5QngCM1OwzWJWnqxSdFEebFJ5PFNKOVT7oh0nMW60pCBPs-63ERcrzRt_GPuHXKExU1QgKbDswFtS7fmXTLtlLEwXLWP710RySo/s1600/perfect+complements+2.png" /></a></div>
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Since it is always optimal to consume the goods such that neither is redundant, the choice will always end up on the dashed line, ergo the fixed proportions. The choice will also be on the budget line. That gives two linear equations that must be solved to get the demands.</div>
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Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-6686748482894680152012-10-02T07:14:00.001-07:002012-10-02T07:18:19.333-07:00The effect of a price of X changeElly asked:<br />
<br />
<blockquote class="tr_bq">
Hi Prof, can i ask you some questions regarding the budget line and indifference curve? When price of X falls, and X is normal, does it mean that normal good will always be on the right side of the budget line that has been separated by a point C? If that is the case, when price of X rises, and X is inferior, does the inferior good always falls on the right of budget line? Because from what i've known, when price of X rises, the budget line will rotate to the left from the original budget line, which means income decreases, so people will buy more inferior good, so inferior good will be on the right. Is that always true? I have also seen a few cases where the inferior good is on the left side even though Price of X rises and i cannot understand. Thank you for taking time to read my enquiries.</blockquote>
<br />
My response:<br />
<br />
First, let's stick to the case where the price of X rises. Afterward, the case where the price of X<br />
falls can be worked through by doing the same analysis but in reverse. Next, note that there are two effects to consider from a price change - a substitution effect and an income effect. Let's consider those effects separately and then put them together.<br />
<br />
<u>Substitution effect</u><br />
<br />
An increase in the price of X causes an increase in the relative price of X, because the price of Y has remained constant. When a good's relative price has risen the substitution effect says less of the good (move to the left in the way Elly expresses it above).<br />
<br />
<u>Income effect</u><br />
<br />
An increase in the price of X rotates the budget line inward around the Y intercept. As long as some X was being consumed before the price change, that bundle is no longer affordable so this change means <i>a reduction of real income</i>. The consequence of that income change on the amount of X consumed depends on whether X is normal or inferior. When X is normal the reduction of income leads to reduced consumption of X (again, that is a move to the left). When X is inferior, the reduction of income leads to an increase in the consumption of X.<br />
<br />
<u>Overall</u><br />
<br />
The substitution and income effects support each other when X is normal. In this case the overall is to have less X consumed. When X is inferior, however, the income effect offsets the substitution effect. As an empirical matter we think that mainly the overall is determined by the substitution effect, so there still will be less X. But it is logically possible for the income effect to win out, in which case the good is called a Giffen Good, named after the Scottish economist Sir Robert Giffen. <br />
<br />Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-49396631078776603362012-09-06T18:44:00.000-07:002012-09-07T05:51:40.054-07:00Question from TraceyTracey asked:<br />
<br />
<blockquote class="tr_bq">
<span style="background-color: #f2f2f2; font-family: arial, sans, sans-serif; font-size: 12.727272033691406px;">Hi Professor Arvan,</span><br />
<span style="background-color: #f2f2f2; font-family: arial, sans, sans-serif; font-size: 12.727272033691406px;">I have viewed some of your video's on YouTube, and was wondering if you provide people with the Excel spreedsheet's? I am particularly interested in having a closer look at the one you used for the Expected Utility Hypothesis video.</span></blockquote>
All the spreadsheets can be found here. Each of the workbooks there must be downloaded and used in Excel. There are multiple spreadsheets per workbook. The name of the spreadsheet should coincide with the name of the video.<br />
<br />
<a href="https://docs.google.com/#folders/0Bz9kxuxY68EJOTczMWM3ZmMtNmExYS00NDFjLTg4NTQtYTRlMjE3MWE5MjIx">https://docs.google.com/#folders/0Bz9kxuxY68EJOTczMWM3ZmMtNmExYS00NDFjLTg4NTQtYTRlMjE3MWE5MjIx</a>
Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com0tag:blogger.com,1999:blog-6379311133959934520.post-54449403454541995232012-09-06T18:16:00.000-07:002012-09-07T05:51:20.992-07:00Question from Mark<div class="tr_bq">
Mark asked:</div>
<br />
<blockquote>
<span style="background-color: #fac984; font-family: arial, sans, sans-serif; font-size: 12.727272033691406px;">First off, thanks for your videos. They help.</span><span style="background-color: #fac984; font-family: arial, sans, sans-serif; font-size: 12.727272033691406px;">My question:</span><span style="background-color: #fac984; font-family: arial, sans, sans-serif; font-size: 12.727272033691406px;">Assuming I have 0 means lottery X, (-6 with 1/2 probability and 6 with 1/2 probability) and utility function u(w)=w for w<=10 and u(w)=1/2w+5 for w>=10</span><br />
<span style="background-color: #fac984; font-family: arial, sans, sans-serif; font-size: 12.727272033691406px;">Can I apply the Arrow-Pratt approximation of pi(w;X)=1/2 (sigma)^2A(w)?</span><br />
<span style="background-color: #fac984; font-family: arial, sans, sans-serif; font-size: 12.727272033691406px;">My hunch is no since A(w)=0 in either case of u(w)...i think?? My question is what does A(w)=0 mean? and why does Arrow-Pratt not work here?</span></blockquote>
<br />
My response - The Arrow-Pratt Measure applies to utility functions that are twice differentiable. In the example above the utility function is piece-wise linear, with a kink at 10. It is not differentiable at the kink, so it is outside the class of functions for which the measure is intended. Alternatively, if you prefer, when w is not 10, the individual is risk neutral (for small gambles). When w is 10, the individual is infinitely risk averse. Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com2tag:blogger.com,1999:blog-6379311133959934520.post-47312808925641594832012-05-18T04:47:00.003-07:002012-05-18T04:47:43.868-07:00How this should workStudents post their questions via the Web form on the third tab. They also provide links to any ancillary information they believe is relevant. The Prof takes that information and uses it as the start of a blog post. Then The Prof provides a response that might be plain text, perhaps include a diagram or other support visuals, and might also be a short video. <br />
<br />
All students, the student posing the question initially and any other student as well, can ask follow up questions using the comments area in the blog post.Professor Arvanhttp://www.blogger.com/profile/15256000730474030475noreply@blogger.com1