Embedded Files
Primer on Using Math in Economics - Calculus is use in economics to examine the rate of change between two things. The term "marginal" is used in economics to describe the way the change in one thing affect a change in something else. In mathematics, the slope shows this relationship.
Finding the slope for a straight line is simple because it is constant across the whole length of the line. The ratio of the rise in height to the run of the distance describes the slope. In economics, linear (straight line) relationships are shown in supply and demand curve.
Finding the slope for a nonlinear (curved line) relationship is more difficult because it changes. Calculus can be used to determine the slope of a curve at any point along the curve. There are many situations in economics where calculus can be used to analyze the changing relationship between to variables, such as with utility, production and cost functions.
The power rule in calculus is a simple rule for finding slope of some types of nonlinear equations. This is the formula for using the power rule:
Problem - The equation below shows a total utility function. Use the power rule to find the marginal utility equation and then use this information to find the quantity that will produce the maximum total utility.
Production - Sprocket’s Rockets makes mechanical rockets. They want your help in determining the optimal number of workers to hire. This is Sprocket’s Rockets production function:
A. Is this a short-run or long-run production function? Explain how you know this?
B. How many workers will Sprocket’s Rockets employ if it wants to maximize its production?
C. At what worker does production shift from increasing returns to diminishing returns? (i.e. what is the point of diminishing marginal returns?)
D. Why does the marginal product (productivity) of each worker go down after the point of diminishing marginal returns?
Problem # 2 - Big Belly Chair Company - The manager at the the Big Belly Chair Company would like your help in determining if the company can be profitable in the chair market. The manager shows you the total cost curve for the Big Belly Chair Company in the hope that you can use this one piece of information to help the company:
A. What is the equation for the marginal cost curve? What does the marginal cost curve show?
B. What is the equation for the average cost curve? Why is it important to know information about average cost?
C. If you were running this company, what would be the minimum price that you could sell chairs at (assuming you could live without a profit)?
D. Are there any fixed costs for the Big Belly Chair Company? What might this mean about the ability of Big Belly Chairs to adjust to changes in the chair market?
E. Assume that the production function (and costs) for Big Belly Chair Company is similar to other chair companies. Based on this, do you think it would be easy for new chair companies to enter the market?
F. What effect do you think this will have on the ability of Big Belly Chair Company to make a profit in the long run?
Page updated
Report abuse