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| [[Image:Cobb-Douglas.jpg|framed|right|A two-input Cobb–Douglas production function]]
| | It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.<br><br>Here are some common dental emergencies:<br>Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.<br><br>At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.<br><br>Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.<br><br>Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.<br><br>Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.<br><br>Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.<br><br>Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.<br><br>In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.<br><br>If you beloved this article so you would like to get more info concerning [http://www.youtube.com/watch?v=90z1mmiwNS8 Dentists in DC] please visit the website. |
| [[Image:Cobbdouglas.jpg|framed|Wire-grid Cobb-Douglas production surface with [[isoquant]]s]]
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| In [[economics]], the '''Cobb–Douglas production function''' is a particular functional form of the [[production function]], widely used to represent the technological relationship between the amounts of two or more inputs, particularly physical capital and labor, and the amount of output that can be produced by those inputs. The Cobb-Douglas form was developed and tested against statistical evidence by [[Charles Cobb (economist)|Charles Cobb]] and [[Paul Douglas]] during 1927–1947.
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| == Formulation ==
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| In its most standard form for production of a single good with two factors, the function is
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| <math>Y=AL^{\beta}K^{\alpha}</math> | |
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| where:
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| * ''Y'' = total production (the real value of all goods produced in a year)
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| * ''L'' = [[labour (economics)|labor]] input (the total number of person-hours worked in a year)
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| * ''K'' = [[capital (economics)|capital]] input (the real value of all machinery, equipment, and buildings)
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| * ''A'' = [[total factor productivity]]
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| * α and β are the [[Output elasticity|output elasticities]] of capital and labor, respectively. These values are constants determined by available technology.
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| Output elasticity measures the responsiveness of output to a change in levels of either labor or capital used in production, [[ceteris paribus]]. For example if α = 0.45, a 1% increase in capital usage would lead to approximately a 0.45% increase in output.
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| Further, if
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| :α + β = 1,
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| the production function has [[constant returns to scale]], meaning that doubling the usage of capital K and labor L will also double output Y. If
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| :α + β < 1,
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| returns to scale are decreasing, and if
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| :α + β > 1
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| returns to scale are increasing. Assuming [[perfect competition]] and α + β = 1, α and β can be shown to be capital's and labor's shares of output.
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| Cobb and Douglas were influenced by statistical evidence that appeared to show that labor and capital shares of total output were constant over time in developed countries; they explained this by statistical fitting [[Least squares|least-squares regression]] of their production function. There is now doubt over whether constancy over time exists.
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| == History ==
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| [[Paul Douglas]] explained that his first formulation of the Cobb–Douglas production function was developed in 1927; when seeking a functional form to relate estimates he had calculated for workers and capital, he spoke with mathematician and colleague [[Charles Cobb (economist)|Charles Cobb]], who suggested a function of the form <math>Y = AL^{\beta}K^{1- \beta}</math>, previously used by [[Knut Wicksell]]. Estimating this using [[ordinary least squares|least squares]], he obtained a result for the exponent of labour of 0.75—which was subsequently confirmed by the [[National Bureau of Economic Research]] to be 0.741. Later work in the 1940s prompted them to allow for the exponents on ''K'' and ''L'' to vary, resulting in estimates that subsequently proved to be very close to improved measure of productivity developed at that time.<ref name="doug">{{Cite journal
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| | authorlink = Paul Douglas
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| | title = The Cobb-Douglas Production Function Once Again: Its History, Its Testing, and Some New Empirical Values
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| | journal = Journal of Political Economy
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| | volume = 84
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| | number = 5
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| | pages = 903–916
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| | date = October 1976}}</ref>
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| A major criticism at the time was that estimates of the production function, although seemingly accurate, were based on such sparse data that it was hard to give them much credibility. Douglas remarked "I must admit I was discouraged by this criticism and thought of giving up the effort, but there was something which told me I should hold on."<ref name="doug"/> The breakthrough came in using [[US census]] data, which was [[cross-sectional data|cross-sectional]] and provided a large number of observations. Douglas presented the results of these findings, along with those for other countries, at his 1947 address as president of the [[American Economic Association]]. Shortly afterwards, Douglas went into politics and was stricken by ill health—resulting in little further development on his side. However, two decades later, his production function was widely used, being adopted by economists such as [[Paul Samuelson]] and [[Robert Solow]].<ref name="doug"/> The Cobb–Douglas production function is especially notable for being the first time an aggregate or economy-wide production function had been developed, estimated, and then presented to the profession for analysis; it marked a landmark change in how economists approached [[macroeconomics]].<ref>{{Cite journal
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| | author = Jesus Filipe and Gerard Adams
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| | title = The Estimation of the Cobb Douglas Function
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| | journal = Eastern Economic Journal
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| | volume = 31
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| | number = 3
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| | pages = 427–445
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| | year = 2005}}</ref>
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| == Difficulties and criticisms ==
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| === Dimensional analysis ===
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| The Cobb–Douglas model is criticized by some [[Austrian school|Austrian]] economists on the basis of [[dimensional analysis]]. They argue it does not have meaningful or economically reasonable [[units of measurement]] unless <math>\alpha = \beta = 1</math> (implying unreasonably highly increasing return to scale).<ref>{{Harv | Barnett | 2007 | loc=p. 96}}</ref> However, other economists in reply to Barnett have argued that the units used are not fundamentally more unnatural than other units commonly used in physics such as [[logarithm|log]] temperature or distance squared.<ref>{{Harv | Barnett | 2007 | loc=p. 102}}</ref>
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| === Lack of microfoundations ===
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| The Cobb–Douglas production function was not developed on the basis of any knowledge of engineering, technology, or management of the production process. It was instead developed because it had attractive mathematical characteristics, such as [[Diminishing returns|diminishing marginal returns]] to either factor of production and the property that expenditure on any given input is a constant fraction of total cost. Crucially, there are no [[microfoundations]] for it. In the modern era, economists try to build models up from individual agents acting, rather than imposing a functional form on an entire economy. However, many modern authors have developed models which give Cobb–Douglas production function from the micro level; many [[New Keynesian]] models, for example.<ref>{{Cite book | |
| | last = Walsh
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| | first = Carl
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| | title = Monetary Theory and Policy
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| | publisher = [[MIT Press]]
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| | edition = 2nd
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| | location = Cambridge
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| | year = 2003}}</ref> It is nevertheless a mathematical mistake to assume that just because the Cobb–Douglas function applies at the micro-level, it also always applies at the macro-level. Similarly, it is not necessarily the case that a macro Cobb–Douglas applies at the disaggregated level. An early microfoundation of the aggregate Cobb–Douglas technology based on linear activities is derived in Houthakker (1955).<ref>{{Citation
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| | last = Houthakker
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| | first = H.S.
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| | title = The Pareto Distribution and the Cobb–Douglas Production Function in Activity Analysis
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| | journal = The Review of Economic Studies
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| | volume = 23
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| | number = 1
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| | pages = 27–31
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| | year = 1955}}</ref>
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| == Some applications ==
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| Nonetheless, the Cobb–Douglas function has been applied to many other contexts besides production. It can be applied to [[utility]]<ref>{{Cite book
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| | last = Brenes
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| | first = Adrián
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| | title = Cobb-Douglas Utility Function
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| | url = http://www.wiziq.com/tutorial/160571-Cobb-Douglas-Utility-Function
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| | year = 2011}}</ref> as follows:
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| U(x<sub>1</sub>,x<sub>2</sub>)=x<sub>1</sub><sup>α</sup>x<sub>2</sub><sup>β</sup>;
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| where x<sub>1</sub> and x<sub>2</sub> are the quantities consumed of good #1 and good #2.
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| In its generalized form, where x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>L</sub> are the quantities consumed of good #1, good #2, ..., good #L, a utility function representing the Cobb–Douglas preferences may be written as:
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| :<math>\tilde{u}(x)=\prod_{i=1}^L x_i^{\lambda_{i}}</math>
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| with x = (x<sub>1</sub>, x<sub>2</sub>, ..., x<sub>L</sub>). Setting <math>\lambda=\lambda_1+\lambda_2+...+\lambda_L</math> and because the function <math>x \mapsto x^\frac1\lambda</math> | |
| is strictly monotone for x > 0, it follows that <math>u(x)=\tilde{u}(x)^{\frac1\lambda}</math> represents the same preferences. Setting <math>\alpha_i ={\lambda_i}/\lambda</math> it can be shown that <math>u(x)=\prod_{i=1}^L x_i^{\alpha_{i}}, \quad \sum_{i=1}^L\alpha_{i}=1</math>
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| The utility may be maximized by looking at the logarithm of the utility <math>\ln u(x)=\sum_{i=1}^L {\alpha_{i}}\ln x_i</math>
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| which makes the consumer's optimization problem:
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| :<math> \max_x \sum_{i=1}^L {\alpha_{i}}\ln x_i \text{ s.t. } \sum_{i=1}^L p_i x_i= w </math>
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| This has the solution that:
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| :<math> x_j^\star=\frac{w \alpha_j}{p_j},\quad \forall j</math>
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| which has the interpretation that the per-unit fraction of the consumers incomes used in purchasing good ''j'' is exactly the marginal term <math>\alpha_j</math>
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| == Various representations of the production function ==
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| The Cobb–Douglas function form can be estimated as a linear relationship using the following expression:
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| :<math> \log_e(Y) = a_0 + \sum_i{a_i \log_e(I_i)} </math>
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| Where:
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| * <math>Y = \text{Output}</math>
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| * <math> I_i = \text{Inputs}</math>
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| * <math> a_i = \text{Model coefficients}</math>
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| The model can also be written as
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| :<math> Y = (I_1)^{a_1} * (I_2)^{a_2} \cdots </math>
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| As noted, the common Cobb–Douglas function used in macroeconomic modeling is
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| :<math> Y = K^\alpha L^{\beta} </math>
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| where K is capital and L is labor. When the model exponents sum to one, the production function is first-order [[homogeneous function|homogeneous]], which implies constant returns to scale—that is, if all inputs are scaled by a common factor greater than zero, output will be scaled by the same factor.
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| === Translog (transcendental logarithmic) production function ===
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| The translog production function is a generalization of the Cobb–Douglas production function. The name translog stands for 'transcendental logarithmic'.
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| The three factor translog production function is:
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| :<math>
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| \begin{align}
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| \ln(Y) & = \ln(A) + a_L\ln(L) + a_K\ln(K) + a_M\ln(M) + b_{LL}\ln(L)\ln(L) \\
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| & {} \qquad {} +b_{KK}\ln(K)\ln(K) + b_{MM}\ln(M)\ln(M) + b_{LK}\ln(L)\ln(K) \\
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| & {} \qquad {} + b_{LM}\ln(L)\ln(M) + b_{KM}\ln(K)\ln(M) \\
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| & = f(L,K,M).
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| \end{align}
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| </math>
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| where ''A'' = total factor productivity, ''L'' = labor, ''K'' = capital, ''M'' = materials and supplies, and ''Y'' = output.
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| == Derived from a CES function ==
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| The [[constant elasticity of substitution]] (CES) function is | |
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| :<math> Y = A[\alpha K^\gamma + (1-\alpha) L^\gamma]^{\frac{1}{\gamma}}, </math>
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| in which the limiting case <math>\gamma = 0</math> corresponds to a Cobb–Douglas function, <math>Y=AK^\alpha L^{1-\alpha},</math> with constant returns to scale.
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| To see this, the log of the CES function,
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| : <math> \ln(Y) = \ln(A) + \frac{\ln[\alpha K^\gamma + (1-\alpha) L^\gamma]}{\gamma}</math>
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| can be taken to the limit by applying [[l'Hôpital's rule]]:
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| :<math> \lim_{\gamma\rightarrow 0} \ln(Y) = \ln(A) + \alpha \ln(K) + (1-\alpha) \ln(L).</math> | |
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| Therefore, <math>Y=AK^\alpha L^{1-\alpha}</math>.
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| == See also ==
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| * [[Leontief production function]]
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| * [[Microeconomics]]
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| * [[Outline of industrial organization]]
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| * [[Production-possibility frontier]]
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| * [[Production theory]]
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| == References ==
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| {{reflist|30em}}
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| {{refbegin}}
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| *{{Cite journal
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| | title = Dimensions and Economics: Some Problems
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| | author = William Barnett II
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| | year = 2007
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| | volume = 7
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| | issue = 1
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| | journal = [[Quarterly Journal of Austrian Economics]]
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| | url = http://mises.org/journals/qjae/pdf/qjae7_1_10.pdf
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| | ref = harv
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| }}
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| * {{cite journal |last=Cobb |first=C. W. |authorlink= |coauthors=Douglas, P. H. |year=1928 |month= |title=A Theory of Production |journal=[[American Economic Review]] |volume=18 |issue=Supplement |pages=139–165 |url= |accessdate=|quote= |ref=harv }}
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| {{refend}}
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| == External links ==
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| * [http://www2.hawaii.edu/~fuleky/anatomy/anatomy.html Anatomy of Cobb-Douglas Type Production Functions in 3D]
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| * [http://www.wiziq.com/tutorial/160571-Cobb-Douglas-Utility-Function Analysis of the Cobb-Douglas as a utility function]
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| {{economics}}
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| {{DEFAULTSORT:Cobb-Douglas production function}}
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| [[Category:Utility]]
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| [[Category:Microeconomics]]
| |
It is very common to have a dental emergency -- a fractured tooth, an abscess, or severe pain when chewing. Over-the-counter pain medication is just masking the problem. Seeing an emergency dentist is critical to getting the source of the problem diagnosed and corrected as soon as possible.
Here are some common dental emergencies:
Toothache: The most common dental emergency. This generally means a badly decayed tooth. As the pain affects the tooth's nerve, treatment involves gently removing any debris lodged in the cavity being careful not to poke deep as this will cause severe pain if the nerve is touched. Next rinse vigorously with warm water. Then soak a small piece of cotton in oil of cloves and insert it in the cavity. This will give temporary relief until a dentist can be reached.
At times the pain may have a more obscure location such as decay under an old filling. As this can be only corrected by a dentist there are two things you can do to help the pain. Administer a pain pill (aspirin or some other analgesic) internally or dissolve a tablet in a half glass (4 oz) of warm water holding it in the mouth for several minutes before spitting it out. DO NOT PLACE A WHOLE TABLET OR ANY PART OF IT IN THE TOOTH OR AGAINST THE SOFT GUM TISSUE AS IT WILL RESULT IN A NASTY BURN.
Swollen Jaw: This may be caused by several conditions the most probable being an abscessed tooth. In any case the treatment should be to reduce pain and swelling. An ice pack held on the outside of the jaw, (ten minutes on and ten minutes off) will take care of both. If this does not control the pain, an analgesic tablet can be given every four hours.
Other Oral Injuries: Broken teeth, cut lips, bitten tongue or lips if severe means a trip to a dentist as soon as possible. In the mean time rinse the mouth with warm water and place cold compression the face opposite the injury. If there is a lot of bleeding, apply direct pressure to the bleeding area. If bleeding does not stop get patient to the emergency room of a hospital as stitches may be necessary.
Prolonged Bleeding Following Extraction: Place a gauze pad or better still a moistened tea bag over the socket and have the patient bite down gently on it for 30 to 45 minutes. The tannic acid in the tea seeps into the tissues and often helps stop the bleeding. If bleeding continues after two hours, call the dentist or take patient to the emergency room of the nearest hospital.
Broken Jaw: If you suspect the patient's jaw is broken, bring the upper and lower teeth together. Put a necktie, handkerchief or towel under the chin, tying it over the head to immobilize the jaw until you can get the patient to a dentist or the emergency room of a hospital.
Painful Erupting Tooth: In young children teething pain can come from a loose baby tooth or from an erupting permanent tooth. Some relief can be given by crushing a little ice and wrapping it in gauze or a clean piece of cloth and putting it directly on the tooth or gum tissue where it hurts. The numbing effect of the cold, along with an appropriate dose of aspirin, usually provides temporary relief.
In young adults, an erupting 3rd molar (Wisdom tooth), especially if it is impacted, can cause the jaw to swell and be quite painful. Often the gum around the tooth will show signs of infection. Temporary relief can be had by giving aspirin or some other painkiller and by dissolving an aspirin in half a glass of warm water and holding this solution in the mouth over the sore gum. AGAIN DO NOT PLACE A TABLET DIRECTLY OVER THE GUM OR CHEEK OR USE THE ASPIRIN SOLUTION ANY STRONGER THAN RECOMMENDED TO PREVENT BURNING THE TISSUE. The swelling of the jaw can be reduced by using an ice pack on the outside of the face at intervals of ten minutes on and ten minutes off.
If you beloved this article so you would like to get more info concerning Dentists in DC please visit the website.