These resources were created by the Department of Economics at the University of Warwick, with funding from the Royal Economic Society. Hosted by the Economics Network
You should be able to
Optionally, also see if you can apply these skills to an economic application or look at the additional resources and advanced quizzes at the bottom of the page,
Differentiate both sides of an equation and rearrange to compute the derivative of a variable which is implicitly defined in terms of another.
If \(y\) is defined in terms of \(x\) via the level curve \(f(x,y)=k\), then
\( \frac{\mathrm{d}y}{\mathrm{d}x} = -\frac{f'_x}{f'_y} \)
This application introduces the concept of utility functions, indifference curves (the contour plots of utility functions), and marginal rates of substitution. In particular, it is shown that using implicit differentiation, the marginal rate of substitution exhibited by a utility function can be expressed as a ratio of marginal utilities - something that you will see often in your studies.
The following quiz allows you to test your understanding of the mathematics and economics behind the concept of marginal rate of substitution. Further, the quiz includes a common example of a utility maximization problem which can be solved by using implicit differentiation.
You can find practice quizzes on each topic in the links above the tutorial videos, or you can take the diagnostic quiz as many times as you like to If you want to test yourself further, then try the advanced quiz linked below.