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Economics 2301. Lecture 17 Differential. Average and marginal functions. The average function rises as long as the marginal function lies above it. The average function declines as long as the marginal function lies below it. Average and marginal functions. Basic Question.

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economics 2301

Economics 2301

Lecture 17

Differential

average and marginal functions
Average and marginal functions
  • The average function rises as long as the marginal function lies above it.
  • The average function declines as long as the marginal function lies below it.
basic question
Basic Question
  • How does a dependent variable change when the independent variable changes given that we have started at some initial value of the independent variable?
  • We will discover that an easy solution to this question comes from the use of the differential.
quality of approximation
Quality of Approximation
  • The extent to which the differential serves as a good approximation to the actual change of the value of a function for discrete changes in its argument depends upon the size of the change of the argument.
  • Table on next slide illustrates for our tax revenue function.
quality of differential
Quality of Differential

Actual and Approximate Changes with Varying Nonlinearity (x0=10 dx=1)