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BSEN 401 (10)

William Huddleston (10)

Lecture

School

University of CalgaryDepartment

Business and EnvironmentCourse Code

BSEN 401Professor

William HuddlestonThis

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LINEAR PRODUCTION POSSIBILITIES CURVES

We can express a Production Possibilities Curve with constant Opportunity Cost as a linear

equation.

e.g. Suppose that the equation for production of Y and X is Y = 150 – 2X where Y is the

quantity of Y and X is the quantity of X.

We will graph this with Y on the vertical axis and X on the horizontal axis (as usual).

i) What is the maximum output of Y if no X is produced, i.e., X = 0?

X = 0, => Y = 150 – 2(0) = 150

This gives the ‘vertical intercept’ of the diagram, i.e., the amount of Y when X = 0.

ii) What is the maximum output of X if no Y is produced (Y = 0)?

Y = 0, => 0 = 150 – 2X => X = 150/2 = 75

This gives the ‘horizontal intercept’ of the diagram, i.e., the amount of X when Y = 0

These two pieces of information are sufficient to draw the Production Possibilities Curve

because the function is linear, i.e., a straight line between two points.

150

75

Quantity of Y

Quantity of X

iii) What is the slope of the Production Possibilities Curve?

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The slope of this line = rise/run = ∆Y/∆X = -150/75 = -2. The coefficient of X in the linear

equation gives us the slope directly as –2 since an increase in X of 1 causes a decrease in Y of 2.

iv) What is the Opportunity Cost of an increase of one unit of X given full employment?

The opportunity cost of a one unit increase in X is 2 units of Y.

Opportunity Cost = - ∆X/∆Y = -(-2) = 2

The Opportunity Cost is constant so the function is linear.

v) What is the Opportunity Cost of an increase of one unit of Y given full employment?

One unit of Y costs 75/150 = ½ unit of X.

We could also find this by expressing our equation in terms of X to get X = 75 – Y/2. This

would also show that opportunity cost of Y is X/2.

The simplest way to find the Opportunity Cost of X is to realize that ∆Y/∆X = 1/(∆X/∆Y).

The opportunity cost of one unit of X is 1/-(∆X/∆Y) = ½.

vi) Suppose that the economy presently produces 40 units of X and 50 units of Y. What is the

opportunity cost of increasing X to 50 units? Of increasing X to 60 units?

The combination 40X and 100Y are below the production possibilities curve because

production of 50Y would allow production of 50X at full employment. An increase in the

production of X to 50 units would have 0 opportunity cost therefore.

Production of 60 units of X would allow production of a maximum of 30 units of Y. The

opportunity cost of moving from (50, 50) to (60, 30) is 20 units of Y.

Sources of Growth:

Growth of the output possibilities of an economy implies increased productive capacity.

This can occur in two ways.

1. An increase in resources

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