Effect of Supply and Demand in Controlling GDP Using Matlab Programming

Prices and quantities have been described as the most directly observable attributes of goods produced and exchanged in a market economy. The theory of supply and demand is an organizing principle for explaining how prices coordinate the amounts produced and consumed. In microeconomics, it applies to price and output determination for a market with perfect competition, which includes the condition of no buyers or sellers large enough to have a price-setting power. In this paper we analyze, the definition of non-linearization between the partial derivative (money, taxes, and quantity) is concluded to a set-point, which is optimized of all the three major partial derivatives governing the constraint of any economy by using Matlab programming.


Introduction
According to the demand supply model, the demand curve practically follows the non-linear relationship; this is apart fro m the case we took as an ideal condition. The international market is very much dynamic and does not follow the static standardizat ion; hence it is not a linear curve.
The supply and demand model describes how prices vary as a result of a balance between product availability and demand. The graph depicts an increase [6] (that is, right-shift) in demand fro m D 1 to D 2 where (D 1 <D 2 ) along with the consequent increase in price and quantity required to reach a new equilibriu m point [6] on the supply curve (S) [7].
For a given market of a co mmodity, demand is the relation of the quantity that all buyers would be prepared to purchase at each unit price of the good. Demand theory [20] describes that,' constrained utility maximizat ion' (with inco me and wealth as the constraints on demand) [8], basically segmentation of the market.
Acco rd ing to th e law o f d emand p rice and quantity demanded in a g iven market are inversely related. That is, the higher the price of a product, the less of it people would be prepared to buy of it (other things unchanged). As the price of a co mmod ity falls, consu mers move to ward it fro m relatively mo re expensive goods (the substitution effect) [14]. In addition, purchasing power fro m the price decline increases ability to buy (the inco me effect). Other factors can change demand; for examp le an increase in inco me will shift the demand curve for a normal good outward relative to the origin [6].
It is the relation between the price of a good and the quantity available for sale at that price. It may be represented as a table or graph relat ing price and quantity supplied. Producers, for example business firms, are hypothesized to be profit-maximizes [5], mean ing that they attempt to produce and supply the amount of goods that will bring them the highest profit. Supply is typically represented as a directly-proportional [16] relat ion between price and quantity supplied (other things unchanged). The higher price makes it profitable to increase production [8]. Just as on the demand side, the position of the supply can shift; say for a change in the price of a productive input or a technical imp rovement.
Market equilibriu m occurs where quantity supplied equals quantity demanded, the intersection of the supply and demand curves in the figure above. At a price below equilibriu m, there is a shortage of quantity supplied compared to quantity demanded. This is posited to bid the price up [18]. At a price above equilibriu m, there is a surplus of quantity supplied compared to quantity demanded. This pushes the price down. The model of supply and demand predicts that for given supply and demand curves, price and quantity will stabilize at the price that makes quantity supplied equal to quantity demanded. Similarly, demand-and-supply theory [2] pred icts a new price-quantity combination of a shift in demand (as in the figure), or in supply.
For a given quantity of a consumer good, the point on the demand curve indicates the value, or marginal utility, to consumers for that unit. The corresponding point on the supply curve measures marginal cost, the increase in total cost to the supplier for the corresponding unit of the good [13]. The price in equilibriu m is determined by supply and demand. In a perfectly co mpetit ive market [ 2], supply and demand equate marginal cost and marginal utility at equilibriu m.
On the supply side of the market, some factors of production are described as (relatively ) variable in the short run. Other inputs are relatively fixed [18]. In the long run, all inputs may be adjusted by management. These distinctions translate to differences in the elasticity (responsiveness) of the supply curve in the short and long runs and corresponding differences in the price-quantity change from a shift in the supply or demand side of the market.
The consumers as attempting to reach most-preferred positions, subject to income and wealth constraints while producers attempt to maximize profits subject to their own constraints, including demand for goods produced, technology, and the price of inputs. For the consumer, that point comes where the marginal utility of a good, net of price, reaches zero, leav ing no net gain from further consumption increases [14]. Analogously, the producer compares marginal revenue (identical in price for the perfect competitor) against the marg inal cost of a good, with marginal profit [2] the difference. At the point where marginal profit reaches zero, further increases in production of the good stop. For movement to market equilib riu m and for changes in equilibriu m, price and quantity also change "at the marg in": more -or-less of something, rather than necessarily all-or-nothing.
De mand-and-supply analysis is used to explain the behavior of perfectly co mpetit ive markets, but as a standard of co mparison it can be extended to any type of market. It can also be generalized to exp lain variables across the economy; for example, total output[estimated as real GDP (Gross Domestic Product)] [9] and the general price level, as studied in macroeconomics [2].
Studying the qualitative and quantitative effects of variables that change supply and demand, whether in the short or long run is a standard exercise in applied economics. Economic theory may also specify conditions such that supply and demand through the market is an efficient mechanis m for allocating resources [1,3,10,11,12,15,19,21].
In this paper the authors suggested a comparative study on on controlling GDP in each financial year after 2006-07[Reserve Ban k of Ind ia, http://www.rbi.org.in/script s/PublicationsView.asp x?id=14525] in India and found that linear rising characteristics of each variable major contributing in GDP. Th is charaterstic curve is simulated by Matlab programming.

Qualitative Economics
It refers to the representation and analysis of informat ion about the direction of change (+, -o r 0) in some economic variable(s) as related to change of some other economic variable(s). For the non-zero case, what makes the change qualitative is that its direction but not its magnitude is specified.
Typical exercises of qualitative economics include comparative-static changes studied in microeconomics or macroeconomics and comparative equilibriu m-growth states in a macroeconomic gro wth model. A simp le examp le illustrating qualitative change is fro m macroeconomics.
Let: GDP = no minal gross domestic product, a measure of national inco me.
M =money supply. T = total taxes. Monetary theory gives a positive relat ionship between GDP the dependent variable and M the independent variable. Equivalent ways to represent such a qualitative relationship between them are as a signed functional relationship and as a signed derivative [9]: + GDP= f (M) or df(M)/dM >0 Where the '+' indexes a positive relationship of GDP to M, that is, as M increases, GDP increases, and vice versa.
Another model o f GDP hypothesizes that GDP has a negative relationship to T. This can be represented similarly to the above, with a theoretically appropriate sign change as indicated [20]: ̶ GDP =f(T) or df(T)/dT <0 That is, as T increases, GDP decreases, and vice versa. A combined model uses both M and T as independent variables. The hypothesized relationships can be equivalently represented as signed functional relat ionships and signed partial derivatives (suitable for mo re than one independent variable): + ̶ GDP=f(M,T) or df(M,T)/dM>0 , df(M,T)/dT<0 Qualitative hypotheses occur in the early history of formal economics but only as to formal economic models fro m the late 1930s with Hicks's model [4] of general equilibriu m in a competitive economy . A classic exposition of qualitative economics is Samuelson, 1947. There Samuelson [4] identifies qualitative restrict ions and the hypotheses of maximization and stability of equilib riu m as the three fundamental sources of meaningful theorems-hypotheses about empirical data that could conceivably be refuted by emp irical data.

The New Model as a Set-Point
The following model suggested that the new approach, in which there are three variables M, T, Q. Where Q is the quantity.
+ ̶ GDP= f(M ,T,Q) The model indicates a quantity that sold or purchased in following country which is independent variable with reference to GDP. Thus with the help of simu lation plotting the quantity.

Money Suppl y
It shows the linear relationship [17] as the curve tends to linear characteristics. As it plotted against time, the money we spend on the production of goods is regularly increasing in magnitude, other terms of partial d ifferential remain constant. This is shown up by the red line in Fig. 2. (Fig. 1).

Taxes Imposed
It shows the parabolic output ,as taxes imposed tends to parabolic increasing characteristics [17], positive raising characteristics taxes imposed and negative decaying characteristics [6] shows that taxes decline as good does not exist. This is shown up by violet line in Fig. 2.

Quantity Supplied as Per Demand
Shows the exact parabolic raising characteristics if demand is positive and time is also positive the curve shows the rising positive pattern and increase in supply [6], If demand is positive and time is negative it is helpful in demand forecasting and helpful in setting production aim. This is shown up by the blue line in Fig. 4.     programming software as shown below, the 2 positive set points. In Fig. 3 and Fig. 4, there are two different possible set-points after substituting the parameters M, T, Q.

Conclusions
This is advisable that to fix certain set-points in an outflow & inflo w of goods as it controls the GDP. This analysis of Matlab programming is suitable for v iable control a GDP and input many key impo rtant goods (as 16 products are major contributed in a control of GDP), as the variable v ia simu lation process and a suitable part of cash inflo w and outflow, to take the organizational goal setting the set point keep the track of optimal usage of different parameters and its deviation fro m the desired output.