DUE 11:59

WHAT IS A SYMBOL (as it relates to Assignment 7)?

A symbol is a shorthand way of representing something else (OK -- this is not Webster's definition). I can write, "find the price of an item and square it" or I can simply write Px2 (assuming you let me get away with saying that X is the item).

Suppose I have a function with one variable, say Z, whose dependent variable is Y. If I want the first derivative of this function, I can ask you to find the first derivative, I can also ask you to find dy/dz or perhaps I get really lazy, I can ask you to find Y'.

Want the derivative of a derivative, that is, a second derivative? Find d2y/dz2 or being lazy, I could simply say, find Y'' (I claim NO originality for how these are written --- they are very standard).

NOW in Lesson 15, Interpreting Multivariate Demand (multivariate because the function has several independent variables), you get introduced to the concept of a partial derivative. Why partial?

The concept of a total derivative means that you want the incremental (marginal) influence on demand of a simultaneous incremental change in all of the independent variables. This is a mess, and does not allow you to do analysis of the influence of a change in only ONE variable.

It is useful to find the incremental (marginal) influence on demand of a change in one variable of interest to you. Suppose Q = [ a function of several variables, one of which is H]. If you are interested in the marginal influence of a change in H on dependent variable Q, how do you state what you want with a symbol ?

You cannot use dQ/dH because then H would have to be the only independent variable in the equation. Mathematicians have a very special symbol for a partial derivative. They would ask you to find ∂Q/∂H. This symbol sort of looks like a backward 6. See footnote 23 on page 59 of your text for an example of its use in a point elasticity. This symbol means find the marginal influence on the demand for Q of an incremental change in H, assuming there is no change in any of the other independent variables at the same instance. By the way, if a multiple linear regression equation is estimated of this multivariate function, the estimated coefficients of the variables ARE estimates of the partial derivatives of the respective variables.

What is a symbol.doc June 17, 2015