The purpose of this exercise is to acquaint you with some simple mathematical relationships and how they translate into graphs. Economic models can come under the form of equations such as Y=F(L), where Y is sometimes called the "dependent variable" and L is the "independent variable." F, called "function," tells us what the precise relationship between Y and L is. Theoretical relationships (models) are those that can be described by an equation like this. When equations are sufficiently simple, they can be put under the form of a curve in a graph. Consider the equation Y=2×L, where Y is the number of apple pies that Jonathan can cook in L hours. This equation describes the process of producing apple pies.
a. How many pies does Jonathan cook in 2, 3, 4, and 5 hours?
b. Draw a vertical axis and label it Y; draw a horizontal axis and label it L. Show on this graph the four pairs (L, Y) you determined in parta.
c. Draw a line connecting your four points and extend it to the left until it reaches the vertical axis.
d. Identify a few assumptions that underlie your apple pie production model.
e. Are your assumptions realistic?
f. Can you identify a few limitations of your model?
g. What could you use this model for?

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The Answer of The purpose of this exercise is to acquaint you with some simple mathematical relationships and how they translate into graphs. Economic models can come under the form of equations such as Y=F(L), where Y is sometimes called the "dependent variable" and L is the "independent variable." F, called "function," tells us what the precise relationship between Y and L is. Theoretical relationships (models) are those that can be described by an equation like this. When equations are sufficiently simple, they can be put under the form of a curve in a graph. Consider the equation Y=2×L, where Y is the number of apple pies that Jonathan can cook in L hours. This equation describes the process of producing apple pies.
a. How many pies does Jonathan cook in 2, 3, 4, and 5 hours?
b. Draw a vertical axis and label it Y; draw a horizontal axis and label it L. Show on this graph the four pairs (L, Y) you determined in parta.
c. Draw a line connecting your four points and extend it to the left until it reaches the vertical axis.
d. Identify a few assumptions that underlie your apple pie production model.
e. Are your assumptions realistic?
f. Can you identify a few limitations of your model?
g. What could you use this model for?

The Purpose of This Exercise Is to Acquaint You with Some