Knizhnik–Zamolodchikov equations: Difference between revisions

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The '''Baumol–Tobin''' model is an economic model of the [[transactions demand]] for money as developed independently by [[William Baumol]] (1952) and [[James Tobin]] (1956). The theory relies on the tradeoff between the [[liquidity]] provided by holding money (the ability to carry out transactions) and the [[interest]] forgone by holding one’s assets in the form of non-interest bearing money. The key variables of the [[demand for money]] are then the [[nominal interest rate]], the level of [[GDP|real income]] which corresponds to the amount of desired transactions, and the fixed [[transaction costs]] of transferring one’s wealth between liquid money and interest-bearing assets. The model was originally developed in order to provide [[microfoundations]] for aggregate money demand functions commonly used in Keynesian and Monetarist macroeconomic models of the time. Later on, the model was extended to a [[general equilibrium]] setting by [[Boyan Jovanovic]] (1982) and [[David Romer]] (1986).


==Formal exposition of the model==


Suppose an individual receives her paycheck of <math>Y</math> dollars at the beginning of each period and subsequently spends it at an even rate over the whole period. In order to spend the income she needs to hold some portion of <math>Y</math> in the form of money balances which can be used to carry out the transactions. Alternatively, she can deposit some portion of her income in an interest bearing bank account or in short term bonds. Withdrawing money from the bank, or converting from bonds to money, incurs a fixed transaction cost equal to <math>C</math> per transfer (which is independent of the amount withdrawn). Let <math>N</math> denote the number of withdrawals made during the period and assume merely for the sake of convenience that the initial withdrawal of money also incurs this cost. Money held at the bank pays a nominal interest rate, <math>i</math>, which is received at the end of the period. For simplicity, it is also assumed that the individual spends her entire paycheck over the course of the period (there is no saving from period to period).  
Finding yourself within a legal scenario exactly where you should go to court might be frightening, however, you can reduce your pressure. You may feel good if you obtain the perfect lawyer to meet your needs. Please read on to understand more about your come across by using a lawyer.<br><br>A good tip if you're seeking to work with a legal representative is to ensure that you pick the right one. Spot can be a major aspect while looking to hire an attorney. If you're gonna becoming to judge shortly, it's totally crucial that this attorney you pick is in the area.<br><br>Do not work with a attorney without doing some track record investigation. Look their label up on the Internet and talk to buddies or family members who may possibly know the lawyer you are interested in. It will always be to your advantage to select a lawyer having an exceptional track record and very good integrity.<br><br>Assist your attorney to determine the optimum time to acquire along with them. Several legal representatives get compensated and go without consumer get in touch with for some time. Acquiring a timetable founded can help you not experience this situation.<br><br>Tend not to feel obligated to get a legal representative as you achieved a few times and got a bit of beneficial advice. You should indication an agreement only when you agree on fees and feel safe together with your legal professional. Should you be hesitating since you often hear bad reasons for this lawyer or consider the fees are extremely higher, always keep seeking.<br><br>Do your research when you are looking for organization legal professionals. They could used an excellent legal professional in past times. Illustrations would be looking at with bankers and an accountant, and even real estate professionals and insurance policy broker agents. These types of folks consult with legal professionals constantly and they also can help you for making a judgement.<br><br>It can be extremely crucial that you know precisely what your legal representative plans to do for you personally. They need to place it in writing, if at all possible, prior to signing on the dotted line. Once they enable you to get to indicator a legitimate document they may have drafted without describing it, run one other way.<br><br>Do your research in looking for a lawyer. If you want a specialist, usually do not just rely on the referrals of your general practitioner. Do background record checks, ask around those you know with personal encounters or legitimate contacts. Setting up time to use an effective legal professional normally signifies a better outcome they at some point provide you with in turn.<br><br>Sign all interaction together with the attorney. Pay attention to days, times, youtube.com/watch?v=pnh2Sdm1dbM/ - [http://www.youtube.com/watch?v=pnh2Sdm1dbM had me going] - subjects of dialogue as well as any mentions of invoicing issues. This sign can help you in handling potential problems down the road, such as big service fees you aren't familiar with.<br><br>If you have been involved in a criminal offense, will be in a car accident or believe you will need legal assist, you should employ a legal professional. How much time that you just wait around to create this selection could be a crucial element. You wish to have someone on your side that understands legal requirements as fast as possible.<br><br>When searching for an effective attorney, it could be beneficial to inquire friends and relations with regard to their tips. It appears like there is a law practice close to every part, so referrals can guide you in the direction of a great lawyer. Even when they actually do not are experts in your type of scenario, they can advise an individual similar to a colleague for your needs.<br><br>Will not go out searching for a attorney and just think about those which have very low charges. Sometimes the charges are reduced mainly because they represent the caliber of the attorney. You obtain what you purchase oftentimes, it is therefore a smart idea to enter into this being aware of you will need to spend a respectable amount of capital.<br><br>A fantastic legal professional will change your result to the far better. Don't choose someone since they're the least expensive, find someone who can perform task. Continue to keep this advice in your mind to achieve success in the court.
 
As a result the total cost of money management is equal to the cost of withdrawals, <math>NC</math>, plus the interest foregone due to holdings of money balances, <math>iM</math>, where <math>M</math> is the average amount held as money during the period. Efficient money management requires that the individual minimizes this cost, given her level of desired transactions, the nominal interest rate and the cost of transferring from interest accounts back to money.
 
The average holdings of money during the period depend on the number of withdrawals made. Suppose that all income is withdrawn at the beginning (N=1) and spent over the entire period. In that case the individual starts with money holdings equal to Y and ends the period with money holdings of zero. Normalizing the length of the period to 1, average money holdings are equal to Y/2. If an individual initially withdraws half her income, <math>Y/2</math>, spends it, then in the middle of the period goes back to the bank and withdraws the rest she has made two withdrawals (N=2) and her average money holdings are equal to <math>Y/4</math>. In general, the person’s average money holdings will equal <math>Y/2N</math>.
 
This means that the total cost of money management is equal to:
 
<math>NC+\frac {Yi} {2N}</math>  
 
The minimum number of withdrawals can be found by taking the derivative of this expression with respect to <math>N</math> and setting it equal to zero (note that the second derivative is positive, which ensures that this is a minimum, not a maximum).
 
The condition for minimum is then given by:
 
<math>C-\frac {Yi} {2{N^2}}=0</math>
 
Solving this for N we get the optimal number of withdrawals:
 
<math>N^{*}= \left ( \frac {Yi} {2C} \right ) ^{\frac {1} {2}}</math>
 
Using the fact that average money holdings are equal to Y/2N we obtain a demand for money function:
 
<math>M= \left ( \frac {CY} {2i} \right )^{\frac {1} {2}}</math>
 
The model can be easily modified to incorporate an average price level which turns the money demand function into a demand for liquidity function:
 
<math>L(Y,i)=\frac {M} {P}= \left (\frac {CY} {2i} \right )^{\frac {1} {2}}</math>
 
==See also==
*[[Money demand]]
*[[Transactions demand]]
*[[Speculative demand]]
*[[Money supply]]
 
==References==
;Original papers
* Baumol, William J., (1952), “The Transactions Demand for Cash: An Inventory Theoretic Approach”, ''Quarterly Journal of Economics'', November, vol. 66, pp.&nbsp;545–556.
* Tobin, James, (1956), “The Interest Elasticity of the Transactions Demand for Cash”, ''Review of Economics and Statistics'', August, vol. 38, no. 3, pp.&nbsp;241–247.
* Baumol, William J. and Tobin, James (1989), "The Optimal Cash Balance Proposition: Maurice Allais' Priority", ''Journal of Economic Literature'', September, Vol. 27, No. 3, pp.&nbsp;1160–1162. http://www.jstor.org/stable/2726778
 
;Extensions to general equilibrium
* Jovanovic, Boyan, (1982), “Inflation and Welfare in the Steady State”, ''Journal of Political Economy'', vol. 90, no. 3, pp.&nbsp;561–577.
* Romer, David, (1986), “A Simple General Equilibrium Version of the Baumol-Tobin Model”, ''Quarterly Journal of Economics'', November, vol. 101, no. 4, pp.&nbsp;663–686.
 
{{DEFAULTSORT:Baumol-Tobin model}}
[[Category:Keynesian economics]]
[[Category:Demand]]
[[Category:Demand for money|*]]

Latest revision as of 19:05, 20 August 2014


Finding yourself within a legal scenario exactly where you should go to court might be frightening, however, you can reduce your pressure. You may feel good if you obtain the perfect lawyer to meet your needs. Please read on to understand more about your come across by using a lawyer.

A good tip if you're seeking to work with a legal representative is to ensure that you pick the right one. Spot can be a major aspect while looking to hire an attorney. If you're gonna becoming to judge shortly, it's totally crucial that this attorney you pick is in the area.

Do not work with a attorney without doing some track record investigation. Look their label up on the Internet and talk to buddies or family members who may possibly know the lawyer you are interested in. It will always be to your advantage to select a lawyer having an exceptional track record and very good integrity.

Assist your attorney to determine the optimum time to acquire along with them. Several legal representatives get compensated and go without consumer get in touch with for some time. Acquiring a timetable founded can help you not experience this situation.

Tend not to feel obligated to get a legal representative as you achieved a few times and got a bit of beneficial advice. You should indication an agreement only when you agree on fees and feel safe together with your legal professional. Should you be hesitating since you often hear bad reasons for this lawyer or consider the fees are extremely higher, always keep seeking.

Do your research when you are looking for organization legal professionals. They could used an excellent legal professional in past times. Illustrations would be looking at with bankers and an accountant, and even real estate professionals and insurance policy broker agents. These types of folks consult with legal professionals constantly and they also can help you for making a judgement.

It can be extremely crucial that you know precisely what your legal representative plans to do for you personally. They need to place it in writing, if at all possible, prior to signing on the dotted line. Once they enable you to get to indicator a legitimate document they may have drafted without describing it, run one other way.

Do your research in looking for a lawyer. If you want a specialist, usually do not just rely on the referrals of your general practitioner. Do background record checks, ask around those you know with personal encounters or legitimate contacts. Setting up time to use an effective legal professional normally signifies a better outcome they at some point provide you with in turn.

Sign all interaction together with the attorney. Pay attention to days, times, youtube.com/watch?v=pnh2Sdm1dbM/ - had me going - subjects of dialogue as well as any mentions of invoicing issues. This sign can help you in handling potential problems down the road, such as big service fees you aren't familiar with.

If you have been involved in a criminal offense, will be in a car accident or believe you will need legal assist, you should employ a legal professional. How much time that you just wait around to create this selection could be a crucial element. You wish to have someone on your side that understands legal requirements as fast as possible.

When searching for an effective attorney, it could be beneficial to inquire friends and relations with regard to their tips. It appears like there is a law practice close to every part, so referrals can guide you in the direction of a great lawyer. Even when they actually do not are experts in your type of scenario, they can advise an individual similar to a colleague for your needs.

Will not go out searching for a attorney and just think about those which have very low charges. Sometimes the charges are reduced mainly because they represent the caliber of the attorney. You obtain what you purchase oftentimes, it is therefore a smart idea to enter into this being aware of you will need to spend a respectable amount of capital.

A fantastic legal professional will change your result to the far better. Don't choose someone since they're the least expensive, find someone who can perform task. Continue to keep this advice in your mind to achieve success in the court.

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