Calculus in Applied Economics



Do you know how a national income model is created and how market prices are defined in megafactories? Do you run a business and want to maximise profit, optimise the production cost and minimise excise tax? Well, mathematics has all the solutions you are looking for.

You may be wondering what economics has to do with it. Well, mathematics is the a-b-c of economists. It cannot be viewed as a discipline separate from economics but, rather, one that can be used in an integrated way to help develop economics models and economic theory. Mathematical economics is the application of mathematical methods and logic to represent theories and analyze problems in economics.


Tools Of the trade: calculus

As an advanced branch of mathematics, calculus focuses heavily on functions and derivatives.Functions examine the relationship between two or more economic variables, or entities that take on different values. If the value of Y changes as the value of X changes,then the two variables have a functional relationship.

Derivatives in calculus, or the change in one variable relative to the change in another, are identical to the economic concepts of marginalism, which examines the change in an outcome that results from a single-unit increase in another variable.

The following problem in economics underscores the application of calculus, particularly use of second order linear differential equation.

Problem statement


Given that supply and demand of a product is equal,express the dependency of price of any product on the expectancy of people regarding the fall or rise of prices.

Mathematical Analysis

Equations for supply and demand are expressed in terms of price (P), the rate of change of the price (P’), and the rate of change of the rate of change of the price (P"). The values given to the respective coefficients w, u, and v depends on the peoples expectations about how prices are changing.the concern of people about rise or fall in price is determined by w.If people think that prices are rising then the coefficient in front of the first derivative of price will be positive and if there is a belief that prices are falling then this coefficient will be negative.The magnitude and sign of the v value reflects how fast people believe that prices are rising or falling.These values can be estimated using statistics and econometric methods, but the solution is for the general case where these variable are arbitrary real numbers not equal to zero.

conclusion

Mathematical Economics help explain the interdependent relation between different variables. They try to explain what causes rise in prices or unemployment or inflation. Mathematical functions are modes through which these real life phenomena are made more understandable and logical.

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