Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

A utility function in economics is a mathematical representation that assigns a numerical value to different combinations of goods and services, allowing us to rank them based on the level of utility (i.e. satisfaction) a consumer derives from them.

Graph functions, plot points, visualize algebraic equations, add sliders, animate graphs, and more.

Feb 5, 2025 · Our first step is to explain what a function of more than one variable is, starting with functions of two independent variables. This step includes identifying the domain and range of such functions and learning how to graph them.

Functions containing two potentially independent variables. If one variable is influencing another variable, then you will have bivariate data that has an independent and dependent variable. Useful for understanding how utility increases with the increased consumption of both [latex]A[/latex] and [latex]B[/latex], i.e., the graph of [latex]U=A ...

Here’s the utility function \hat u (x_1,x_2) = 2\sqrt {x_1x_2} u(x1,x2) = 2 x1x2 plotted, along with its indifference map. We can see that it produces a lot more “utils” from the left-hand graph than the figure above, but the indifference curve through any given point is exacty the same:

How do we graph indi⁄erence curves? 1. Choose a utility level: U (x;y) = U (a number) 2. Choose one of the variables (we™ll choose x) and vary it. 3. Solve for the other variable (in this case y) for each x given U . 4. Go back to (1:) and choose another utility level Ub Three examples: 1. U (x;y) = x + y x + y = 10 x y x + y = 10 0 10 x ...

In this section we generalize that result, and see how it can be useful when modeling utility. If two utility functions generate the same indifference curves, they also have the same expression for the MRS at any given point.

One way to study the graph z = f(x, y) of a function of two variables is to study the graphs of the functions of one variable that are obtained by holding x or y constant. To understand this process, we need to look at the geometric significance of setting x or y equal to a constant.

Aug 2, 2022 · The graph of a function of two variables is a surface in three-dimensional space. Let's start by looking at the 3-dimensional rectangular coordinate system, how to locate points in three dimensions, and distance between points in three dimensions.