Graphing Economic Theories Flashcards
What are theories built on?
Theories are built on assumptions about relationships between variables. For example, the quantity of eggs demanded is assumed to fall as the price of eggs rises, and the total amount an individual saves is assumed to rise as his or her income rises.
What is a function and a functional relation?
When one variable, X, is related to another variable, Y, in such a way that to every value of X there is only one possible value of Y, we say that Y is a function of X. When we write this relation down, we are expressing a functional relation between the two variables, and we write Y=f(X)Y=f(X) where f is the function that relates X and Y.
What are the different ways we can express a mathematical function?
In words, in a table, in a mathematical equation, or in a graph.
What is a positive relation between two variables?
When income goes up, consumption goes up. In such a relation the two variables are positively related to each other.
What is a negative relationship between two variables?
an example of variables that move in opposite directions. As the amount spent on pollution reduction goes up, the amount of remaining pollution goes down. In such a relation the two variables are negatively related to each other.
What is a linear relationship between two variables?
Both of these graphs are straight lines. In such cases the variables are linearly related to each other (either positively or negatively).
What is slope defined as?
The slope is defined as the amount of change in the variable measured on the vertical axis per unit change in the variable measured on the horizontal axis.
If we let X stand for whatever variable is measured on the horizontal axis and Y for whatever variable is measured on the vertical axis, the slope of a straight line is ΔY/ΔX.
What is marginal change?
Economists call the change in pollution when a bit more or a bit less is spent on clean-up the marginal change.
What is a Diminishing Marginal Response?
It also shows that in the type of curve illustrated, the marginal change per dollar spent is diminishing as we spend more on pollution reduction. There is always a payoff to more expenditure over the range shown in the figure, but the payoff diminishes as more is spent. This relation can be described as diminishing marginal response.
How do we get he slope of a non linear line?
The answer is that we use the slope of a straight line tangent to that curve at the point that interests us. For example, in Figure 2-8, if we want to know the slope of the curve at point Z, we draw a straight line that touches the curve only at point Z; this is a tangent line.
For non-linear functions, the slope of the curve changes as X changes. Therefore, the marginal response of Y to a change in X depends on the value of X.
What happens at a maximum or minimum of a function?
At either a minimum or a maximum of a function, the slope of the curve is zero. Therefore, at the minimum or maximum the marginal response of Y to a change in X is zero.
What is the marginal response of a variable?
The marginal response of a variable gives the amount it changes in response to a change in a second variable. When the variable is measured on the vertical axis of a diagram, its marginal response at a specific point on the curve is measured by the slope of the line at that point.
