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Basic Mathematics for Economists - Rosser - Chapter 4

4 Graphs and functions Interpret the meaning of functions and inverse functions. Draw graphs that correspond to linear, non-linear and composite functions. Find the slopes of linear functions and tangents to non-linear function by graphical analysis. Use the slope of a linear demand function to calculate point elasticity. | 4 Graphs and functions Learning objectives After completing this chapter students should be able to Interpret the meaning of functions and inverse functions. Draw graphs that correspond to linear non-linear and composite functions. Find the slopes of linear functions and tangents to non-linear function by graphical analysis. Use the slope of a linear demand function to calculate point elasticity. Show what happens to budget constraints when parameters change. Interpret the meaning of functions with two independent variables. Deduce the degree of returns to scale from the parameters of a Cobb-Douglas production function. Construct an Excel spreadsheet to plot the values of different functional formats. Sum marginal revenue and marginal cost functions horizontally to help find solutions to price discrimination and multi-plant monopoly problems. 4.1 Functions Suppose that average weekly household expenditure on food C depends on average net household weekly income Y according to the relationship C 12 0.3Y For any given value of Y one can evaluate what C will be. For example if Y 90 then C 12 27 39 Whatever value of Y is chosen there will be one unique corresponding value of C. This is an example of a function. A relationship between the values of two or more variables can be defined as a function when a unique value of one of the variables is determined by the value of the other variable or variables. If the precise mathematical form of the relationship is not actually known then a function may be written in what is called a general form. For example a general form demand 1993 2003 Mike Rosser function is Qd f P This particular general form just tells us that quantity demanded of a good Qd depends on its price P . The f is not an algebraic symbol in the usual sense and so f P means is a function of P and not f multiplied by P . In this case P is what is known as the independent variable because its value is given and is not dependent on the value of Qd i.e. it is .