ECONOMICS
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Functions
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Differentiation
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Independent variable: X
Dependent variable: Y
Conclusion: a function is the relationship between X and Y
A firm’s profit function: P = f(Q) --> P = 50 + 100Q – 5Q2
Differentiation: relationship between the changes in X and changes in Y
We use the differentiation concept to determine the marginal values of a function
Marginal analysis of a Univariate Function
Þ Marginal Revenue : additional revenue from producing one more unit of output
Þ Marginal Cost the additional cost of producing one more unit of output
Þ When the MR and MC meet, the firm maximizes its profit.
Þ The slope of Y tells us the direction of function Y with respect to a change in X. Three
cases are possible:
· CASE 1: If the slope of Y = dY/dX > 0, when X increases or decreases, Y also increases or
decreases in the same direction.
· CASE 2: If the slope of Y = dY/dX < 0, when X increases or decreases, Y decreases or
increases in the opposite direction.
· CASE 3: If the slope of Y = dY/dX = 0, the function Y is at its maximum or minimum (case
of optimization).
Total value: total profit, total revenue, or total cost, the total value can be a function or
discrete data.
Marginal value: such as marginal profit or marginal value.
Average value: total value divided by the quantity of the decision