# Utility functions are discussed in detail in appendix

This preview shows pages 9–10. Sign up to view the full content.

(Utility functions are discussed in detail in Appendix 3 of your text.) Economists also use the concept of a production function , which relates combined quantities of inputs to the quantity of output each combination produces. If there are just two types of input, labour-days ( L ) and machine-days ( K , for “capital”), then we can treat the output Q (in tonnes, say) as a function of the inputs of L and K : Q = f ( L, K ) (M.1.10) Equation M.1.10 is a general form of the production function; Appendix 9 in the text dis- cusses a number of speciFc production functions. (See also Module 8.) Even demand and supply functions, in their general form, are functions of several variables. We normally assume, for instance, that an individual’s demand for a good X ( X D ) is determined by (among other factors) its own price P X , the price of other goods P Y , and the individual’s income ( M ); that is, X D = f ( P X , P Y , M ). (M.1.11) It is only when we assign speciFc values to all of the other determinants of the quanti- ty demanded of a good except its own price and make the ceteris paribus (“other deter- minants remain unchanged”) assumption that we can draw the conventional demand curve, with its quantity demanded as a function of its own price alone. We shall see how this works in the Exercises for this Module. 2. Exercises 1. ±or the following equations, state whether y is or is not a function of x ; whether the equation is linear or nonlinear; whether the equation is strictly increasing, strictly decreasing, constant, or non-monotonic; and whether an inverse function exists. (a) xy = 20 (b) xy = – 20 (c) x = 4 – 2 y (d) y = 4 – 2 x (e) y = 3 x 2 + 4 x – 4 (f) y = 2 x (g) x= 2 y (h) x = 3( y 2 – 6) (i) 6 x + 12 y = 9 (j) x = 7 (k) y = 14 2. Plot the following on the same graph, and label the vertical and horizontal intercepts and the slope in each case:

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

View Full Document
3. Plot the following 6 functions on the same graph: 4. Plug in values for x , calculate the corresponding values for y , and graph the follow- ing two functions: (a) y = x 3 and (b) y = x 1/3 . Which of these two functions has an inverse function? 5. You are given the following demand function for good X , where X is measured in kilograms, P X is in \$/kg, the price of good Y ( P Y ) is in \$/unit, and income M is in thousands of dollars (so that if income is \$10,000, M = 10): X D = 20 – P X + 0.5 P Y + 5 M.
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