Math Modeling For Economics

Modeling is crucial in economics because it is used in place of the real experiments that could be expensive, time consuming, and dangerous. Mathematical models describe situations with a few words using tools and theorems for making general statements. Here, the focus is on how to explicitly state assumptions with a clear and precise ease of making multi dimensionality descriptions.Advertising We will write a custom essay sample on Math Modeling For Economics specifically for you for only $16.05 $11/page Learn More In economics different mathematical models have been developed to address certain market trends and behaviors such as demand and supply with time. One such is the models related to competitive markets. The product demand and supply and price changes are dynamic aspects of the system and can be modeled through a differential equation with a constant solution referred to as the equilibrium of the equation. Here, x(t) = f (x) (equilibrium equati on)- definition Based on the above definition, the linear differential equation can be expressed as: x + u (t) = w (t) In this case, w (t) and u (t) are functions of t in the above expression. The homogeneous case here is u (t) =a and w (t) =0 giving the solution for the differential expression: x + ax =0 as x (t) =Ae-at. In this case A is taken as an arbitrary constant. The case for a non-homogeneous situation is x + ax = b where b≠ 0 and a =0,as solution is x (t) =bt +A providing a solution with known initial state x(0) as given by:Advertising Looking for essay on business economics? Let's see if we can help you! Get your first paper with 15% OFF Learn More x (t) = {x(0)-b/a} e-at +b/a A typical example is the demand and supply mentioned in the above scenario. The dynamics of a price of a single commodity is considered. The demand and supply function is stated as below: Qd=a1-b1P, Qs=a2-b2P, both satisfy the condition aj, bj0. In the above expressions, Qd and Q s are respective values for the demand and supply for the given price P within the parameters aj and bj. If the price changes are taken with the changes in time t, excess demand proportional to the time t is Qd– Qs expressed as P (t) =m (((Qd (t) – Qs (t))), where m0 When substituted: P (t) + m (b1+b2) P = m (a1+a2) giving the solution shown here:Advertising We will write a custom essay sample on Math Modeling For Economics specifically for you for only $16.05 $11/page Learn More In this case Satisfying the general case: In this case, the problem related to the above model is demand and supply of a product and its effect on price with time illustrated as x (t) = f (x). This essay on Math Modeling For Economics was written and submitted by user Ellen Sharpe to help you with your own studies. You are free to use it for research and reference purposes in order to write your own paper; however, you must cite it accordingly. You can donate your paper here.