L8Functions

# L8Functions - Introduction to Microeconomics Lecture 8...

This preview shows pages 1–2. Sign up to view the full content.

1 Introduction to Microeconomics Lecture 8 Maths: Functions Ian Crawford Outline z Function notation and some common functions z Linear, polynomial z Inverse functions z Composite functions z Exponential and logarithmic functions z Functions of several variables z Homogeneous Functions, and Returns to Scale Functions z y = 5 x – 8 A linear function z y depends on x. We often write y ( x ) to emphasize dependence z C(q) = 3 + 2 q 2 Total cost, C , depends on output, q z For general functions it is common to use f ( x ) in place of y : x is called the argument . z The key feature of a function is that for each value of x , the input, there is a unique value of f ( x ), the output z Ideally we should specify the domain – the set of inputs – and the range (the set of outputs). Usually in economics these are fairly obvious. z If the graph of f ( x ) is upward-sloping then f ( x ) is an increasing function (or a “ monotonic increasing function ”), e.g. many supply functions z If the graph of f ( x ) is downward-sloping the f ( x ) is a decreasing function (or a “ monotonic decreasing function ”), e.g. most demand functions z A monotonic function is either increasing or decreasing Graph of y = 5 x – 8 for x 0 30 40 50 -20 -10 0 10 20 0 2 4 6 8 10 12 x y = 5x - NB: sometimes we are interested in negative values of x and y Graph of C = 3 + 2 q 2 for q 0 150 200 250 0 50 100 0 2 4 6 8 10 12 q C Polynomials and related functions z A polynomial function takes the form f ( x ) = a n x n + a n -1 x n -1 + …+ a 0 z A linear function is a polynomial of degree 1 z A quadratic function is a polynomial of degree 2 z E.g. the cost function: C = 10 + q + 3 q 2 z A useful function is f ( x ) = x n for x > 0 z If n is an integer this is a polynomial of degree n z n can also be negative or a fraction z Q = p -2 is a demand function with n = 2 z f ( x ) = x 0.3 may represent a “production function” with x

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern