Axiomatik

A. Three measures of productivity, or the relationship between inputs and the output, are total product, average product and marginal product This chapter introduces students to short-run production and cost. In the short-run, all production functions incur diminishing returns when variable inputs are used relative to at least one fixed input, reducing the additional amounts of the output being produced. Diminishing returns in production causes a short-run increase in the marginal cost, as ...

This chapter introduces students to the concept of elasticity of demand. A demand elasticity measures how consumer demand responds to changes in a variable in the demand function. The price elasticity of demand is the key elasticity measure discussed in this chapter. It measures the sensitivity of the consumer’s behavior to changes in the price of the product by dividing the percentage change in the quantity demanded by the percentage change in the price that induced the change in the quanti...

This chapter introduces students to the important concepts of demand and supply. The chapter uses examples to illustrate how changes in non-price factors impact demand, supply, and the resulting market equilibrium. Demand is the relationship between price and the quantity demanded of a good by consumers in a given period of time, all other factors held constant. Supply is the relationship between price and the quantity supplied of a good by producers in a given period of time, all other factors...

Recall that a nite sequence has the form fyngN n=0 and an innite sequence has the form fyng1 n=0. A dierence equation of order m has the form (1) yn+m = F(n; yn; yn+1; : : : ; yn+m

An ordinary dierential equation of order k has the form (1) F  x; y; dy dx ; d2y dx2 ; : : : ; dky dxk  = 0; where F is a function of k+2 variables. We will usually write ODE as an abreviation for ordinary dierential equation. A function y(x) is a solution of the ODE (1) in the interval a < x < b if it satises the equation (1) for all x in this interval. We will usually be interested in solving an initial value problem. For an ODE of order k, this has the form Reca...

These notes introduce the notion of derivatives for functions of several variables. It is worthwhile to rst recall the derivative of a real-valued function of a single variable. Let f : R ! R, and xed x0 2 R. The classical denition of f having a derivative f0(x0) at x0 is that the limit Notice that any linear map from R to itself is just multiplication by some constant a. This is the important conceptual leap we must make: the derivative of a function at a point is not a number, or a ve...

For every natural number n we define n-dimensional space as the set Rn of all ordered n-tuples x1 x2  xn where xi  R for i  1 2  n. One-dimensional space R1 corresponds with the set of real numbers R. For n  2 we usually denote the ordered n-tuple x1 x2     xn by x, the ordered n-tuple a1 a2     an by a, and so on. If x  x1 x2  xn, we say that xi is the i’th coor...

This unit contains a brief summary of concepts, definitions, notation, and results that you are assumed to be familiar with SETS RELATIONS AND FUNCTIONS

THESE ARE THE RULES FOR CALCULUS DIFFERENTIATION