Economics

 

What a Wonderful World

Don't know much about geography
Don't know much trigonometry
Don't know much about algebra
Don't know what a slide rule is for

And yet economists try to use calculus even though they apparently don’t know much about calculus!

Economists want to use calculus and advanced mathematics to show that they are a real science.  But unless their principles are stated correctly, then we can get mistaken economic principles. Take the macroeconomic belief that at the optimal, marginal cost must be equal to marginal revenue and that at this optimal no quantity of goods are sold. This is often expressed as MP=MR, Q=0, or that the optimal quantity of goods is when marginal price is equal to marginal revenue. Unfortunately this also requires that the volume of goods be allowed to be negative. If the statement had been correctly formatted as Revenue, Unit Price sold multiplied by the Quantity sold, and Cost = Unit Cost multiplied by the Quantity produced PLUS a constant, it can not be assumed that when marginal Revenue, the first derivative of revenue with respect to quantity, to be equal to marginal cost, the first derivative of the production cost with respect to quantity To be an optimal the quantity sold/produced must be equal to zero.  This also assumes that the quantity sold/produced can be negative and it can not.  The correct formulation, like any proper exponential distribution, which includes radioactive decay and cellular growth, follows an exponential distribution and is  Revenue = Unit Price * Quantity sold = Unit Production Cost * Quantity made PLUS a constant, where the Quantity made or sold must also be greater than or equal to 0. Instead Marginal Price = Marginal Revenue must be equal to half of the constant in the cumulative equation, and that constant does NOT become zero when the derivative is taken.  This means that the optimal quantity sold is not when MR, δR/δQ = MC, δC/δQ, when Q = 0, but instead there is no optimal quantity to be sold unless the quantity sold is allowed to also be less than or equal to zero.  If the quantity is declining, then it can approach zero but never reach zero. If the quantity is growing, revenue can approach but not exceed,  a constant related to an absolute. Expressed statistically, growth, or decay, should be regressed as log-linear, an exponential function. It is neither linear‑linear,  a trend function, or log-log, a power function.  Growth, including negative growth, also known as decay, is variable not constant.